Jsarmi - New pages [en]

Ideas/abalorios/ejemplos

Jsarmi — Tue, 12 Jan 2010 21:02:36 GMT

Jsarmi: Created page with '::4 pepas de cristal :: 1 cuerda de guitarra :: Soneto de Cortazar ::un sauce de cristal :: un chopo de agua :: un alto surtidor que el viento arquea'

::4 pepas de cristal :: 1 cuerda de guitarra :: Soneto de Cortazar
::un sauce de cristal :: un chopo de agua :: un alto surtidor que el viento arquea

Ideas/abalorios

Jsarmi — Tue, 12 Jan 2010 20:04:31 GMT

Jsarmi:

"Narrative" Design como en la obra de Stuart [ ]
the suggestive power of objects, evocative, misterious
iconicidad pictórica, posible en el lenguaje poético
La autoreferencialidad libera los sistemas intertextuales de significado.
de acuerdo con Henri Bergson descubrimos el fluir de nuestra personalidad a través del tiempo

Juego de los Abalorios
Playing the game well requires years of hard study of music, mathematics, and cultural history. Essentially the game is an abstract synthesis of all arts and scholarship. It proceeds by players making deep connections between seemingly unrelated topics.
http://en.wikipedia.org/wiki/Glass_bead_game

Moritz Waldemeyer

No es una tarjeta es una cajita/grid con objetos
Los objetos son para que el que las recibe los pondere, sus caracterIsticas significado, su combinaciOn (rotaciOn), su sequencia, su procedencia

Los dos componentes a explorar son los diferentes grids y los objetos

El grid mas pequeNo tiene 1 objeto pero no tiene narrativa? [x]

Luego viene el grid de 2 que es la dualidad pero se puede orientar de muchas maneras:
[ [x] [x] ]

[X]
[X]

[X]
?
[X]

ESPIRAL? (a lo vigotsky... cada "vuelta" es lo mismo pero diferente! expandido, enriquecido)

En tres dimensiones uno enfrente del otro

El grid de tres tiene otras posibilidades una de las mAs comunes siendo el triAngulo que aunque tenga porciones iguales tiene una en el Apice. El rectAngulo puede ser un grid de 3

El grid de cuatro es el tipico rectAngulo pero no tiene que ser solo esto.

Grid/cajita Fen-Shuei tiene X divisiones y puede contenter muchos objetos

You could pitch this to hallmark but then you will loose it. You will have to construct a system to create many combinations and then see if that is a lot to own it. You could do it with poems, with phrases, with stories, with so many things ann emptiness counts.

You could make a grid that is growable so as people get more pieces they grow their grid or they grow it themselves. They could pass them around a group of friends or family every member adding one. Could we do this only... es esta una versiOn del juego de los abalorios?

[ Un verso de Vallejo ]
al lado o debajo, o sin conectarse pero esperando que alguien la conecte
[Sofa by Frank Zappa tocado por Michael Hedges]

Made out of wire so that you could hang them

Mom could help me find so many old things in Colombia

LOS OBJETOS

los objetos pueden evocar pero pueden tambien sugerir ciertas direcciones. Por ejemplo, los objetos pueden tener caracteristicas o posibilidades. Un galgo con un pata rota, un reloj detenido en una hora, un objeto que se puede rotar pero solo en una direcciOn. Un objeto que cabe dentro de otro, etc. etc.

WHAT TO DO?
Take 3-position-grids (which are the minimally interesting), 4 position grids, and 9 position grids and experiment with them. First creae a platform so that it would be extremely easy to create many (e.g. an html table where pics can be aeasily asigned)

Fill 20 of each and document them. Try some "anonimous" objects (white, not discrete) and empty positions (or missing positions) o siluetas o "archetipos' de objetos pero con caracterIsticas definidas (alto, ancho, roto/degradado). Estas figuras, a propOsito, se podrIan usar estos objetos para enseNar a los ninos la operaciOn cognitiva de "identificar" caracterIsticas de objetos.

EXPLORE THE PROBLEM SPACE

Makit it a "meaning-making" game for kids not a competition game

[x] [?] [?]

Make it so that people can write different "interpretations" online and have the interpretations play within their own grids :)

Is this like TAROT or ORACLE CARDS: "when X comes after Y then..." kind of but the language is much more varied and the interpretation more open, It has numerology because if you have n number of one object in one cell then you need to think about that

ABOUT NUMEROLOGY... what is the meaning of each one of the grid sizes: 1, 3, 4, 9?

Literature
Tarot was used as early as the 16th century to compose poems, called "tarocchi appropriati", describing ladies of the court or famous personages. In modern literature, two exceptional examples of novels centered on the Tarot are The Greater Trumps (1932) by Charles Williams and Il Castello dei destini incrociati (1969) (English translation: The Castle of Crossed Destinies [1979]) by Italo Calvino. In the former, the Tarot is used by the main characters to move through space and time, create matter, and raise powerful natural storms. In the latter, Mediaeval travellers meeting at a castle are inexplicably unable to speak, and use a Tarot deck to describe their stories, which are reconstructed by the narrator, calling forth implications of the nature of communication, fate, and the presence of the transcendent in daily life. Tarots also appear in T.S. Eliot's modernist poem The Waste Land (1922), in connection with the figure of Madame Sosostris, one of the characters which appear in the first part, "The Burial of the Dead". Some of the cards mentioned in the poem really exist in the tarot deck (the Hanged Man, the Wheel), some have been invented by Eliot. The 2007 novel Sepulchre by British author Kate Mosse features a fictional Tarot deck.

A GRID THAT HAS 10 "lines" for ten key words of a "dEcima"
Piedra de sol estA escrito en 584 endecasIlabos! (11 sIlabas)

[edit] Psychological
Carl Jung was the first psychologist to attach importance to tarot symbolism.[21] He may have regarded the tarot cards as representing archetypes: fundamental types of persons or situations embedded in the subconscious of all human beings. The theory of archetypes gives rise to several psychological uses. Since the cards represent these different archetypes within each individual, ideas of the subject's self-perception can be gained by asking them to select a card that they 'identify with'. Equally, the subject can try and clarify the situation by imagining it in terms of the archetypal ideas associated with each card. For instance, someone rushing in heedlessly like the Knight of Swords, or blindly keeping the world at bay like the Rider-Waite-Smith Two of Swords.

More recently Timothy Leary has suggested that the Tarot Trump cards are a pictorial representation of human development from infant to adult, with the Fool symbolizing the newborn infant, the Magician symbolizing the stage at which an infant begins to play with artifacts, etc. In Leary's view the Tarot Trumps may be viewed as a blueprint for the human race as it matures.

Immaterial Culture
folklore, beliefs, values, ideologies, philosophies, customs, traditions, legends, idioms, humour, methodologies, music, science, the sublime & the ridiculous.
http://typhon.autonomous.org/

Piedra de Sol tiene 584 lineas, como dias tiene el periodo synoidea de Venus.
Pregunta... ese periodo es un perido medido en dias de la tierra o en dias de Venus. Los dias en Venus duran 24 horas de la tierra? Lo dudo... pero por lo menos la definiciOn de "dia" es la misma" salida y puesta del sol?

Como era otra vez esos shatzkys en el peru? los nuditos aquellos usados para grabar y reconstruir memorias? QuE eran las filas y las columnas?

Que lindo que serIa hacer una piedra solar con "celdas" en las que en cada una se pone un elemento de cada una de las lIneas del poema de Octavio Paz... no toda la frase pero un objeto que evoque la frase... sauce chopo surtidor viento o

un sauce de cristal, un chopo de agua,
un alto surtidor que el viento arquea, U NAL TO SUR TI DOR QUE EL VIEN TO AR
un árbol bien plantado mas danzante, U NAR BOL BIEN PLAN TA DO MAS DAN ZAN TE
un caminar de río que se curva,
avanza, retrocede, da un rodeo A VAN ZA RE TRO CE DE DA UN RO DEO
y llega siempre: Y LLE GA SIEM PRE = 5

un caminar tranquilo UN CA MI NAR TRAN QUI LO = 7
de estrella o primavera sin premura,
agua que con los párpados cerrados
mana toda la noche profecías,
unánime presencia en oleaje,
ola tras ola hasta cubrirlo todo,
verde soberanía sin ocaso
como el deslumbramiento de las alas
cuando se abren en mitad del cielo,

un caminar entre las espesuras
de los días futuros y el aciago
fulgor de la desdicha como un ave
petrificando el bosque con su canto
y las felicidades inminentes
entre las ramas que se desvanecen,
horas de luz que pican ya los pájaros,
presagios que se escapan de la mano,

una presencia como un canto súbito,
como el viento cantando en el incendio,
una mirada que sostiene en vilo
al mundo con sus mares y sus montes,
cuerpo de luz filtrado por un ágata,
piernas de luz, vientre de luz, bahías,
roca solar, cuerpo color de nube,
color de día rápido que salta,
la hora centellea y tiene cuerpo,
el mundo ya es visible por tu cuerpo,
es transparente por tu transparencia,

Writing/list

Jsarmi — Thu, 07 Jan 2010 21:38:44 GMT

Jsarmi: Created page with ':From Mental Models to Experienced Situations ::Introduce Situated Cognition to the UX world ::Include Phenomenology & Pragmatism. Dewey's --> Experience'

:From Mental Models to Experienced Situations
::Introduce Situated Cognition to the UX world
::Include Phenomenology & Pragmatism. Dewey's --> Experience

Dharma/ideas

Jsarmi — Thu, 07 Jan 2010 21:13:28 GMT

Jsarmi:

Una iniciativa cercana a mi pasiOn en la que pueda participar mi mamA desde Colombia y que sea una fuente de ingresos (adicional o principal) y que sea una fuente de realizaciOn y alegria. Vamos a coleccionar ideas y a madurarlas.

:CafeLectura para PapAs e Hijos
::Vienes dejas tu nino en 2 o 3 pods de lectura compartida (e interacciOn) te tomas un cafE, hablas con una amigo/a y compras libros. Entras con un carnet anual que te da descuentos. El sitio solo vende 10 libros nuevos al mes pero son buenIsimos y los miembros pueden sugerir. El sitio es mAs un respiro para errands o para un pequeNo time off pero no es una guarderIa. Te dan un dispositivo para que te puedan ubicar en caso de llanto, problemas, etc. El diseNo del sitio le permite al padre tener una visual directa con el sitio donde estA el niNo. Los cuentos son cortos y rotan relativamente rApido.

References/

Jsarmi — Thu, 07 Jan 2010 20:55:26 GMT

Jsarmi: Created page with ':Label Placement in Forms By Matteo Penzo (2006) ::http://www.uxmatters.com/mt/archives/2006/07/label-placement-in-forms.php ::Left Aligned Labels = x secs ::Right Aligned Labels…'

:Label Placement in Forms By Matteo Penzo (2006)
::http://www.uxmatters.com/mt/archives/2006/07/label-placement-in-forms.php
::Left Aligned Labels = x secs
::Right Aligned Labels = x/2 secs
::Top aligned labels = 10-15 % faster than Right Aligned Labels (0.425x secs.)

M/toread.html

Jsarmi — Thu, 07 Jan 2010 19:57:01 GMT

Jsarmi:

:The Greenwood encyclopedia of folktales and fairy tales / edited by Donald Haase
:Location: Van Pelt Library Reference Stacks
:Call Number: GR74 .G73 2008
:Notes: This is an updated/enhanced version of Thompson's collection

Oratura

Admin — Wed, 05 Aug 2009 20:49:43 GMT

Admin:

Oratura
un bar para leer

Secuencias de memorizaciOn en los Vedas
http://in.answers.yahoo.com/question/index?qid=20090306075642AAdtVE7

Epiclesis

Admin — Tue, 28 Jul 2009 15:13:08 GMT

Admin:

The epiclesis (greek επίκλησις - invocation), (also sometimes spelled epiklesis, being a transliterated Greek word) is that part of the anaphora, or Eucharistic prayer, by which the priest invokes the Holy Spirit (or the power of His blessing), in some Christian churches. [1] Some Eastern Orthodox theologians hold that the epiclesis is essential to the Eucharist, since the entire mystery is based on the action of the Holy Spirit. The term epiclesis can also be used for the prayer over water to be used to perform a baptism.

epikaleîn call upon, f. EPI- + kaleîn call

Ulysses and the Irish god By Frederick K. Lang
This book is a lucid, detailed, and provocative study of how Joyce radically transvalues and transmutes key elements of Scripture, theology, and liturgy in Ulysses.

Projects

Admin — Fri, 26 Jun 2009 17:43:43 GMT

Admin:

=Sections to develop=

:Prints
:: [http://www.printcenter.org Philadelphia Print Center]
:Graphic Novel: Frames and Sequences
:Heidegger's bridge
:Serra's Tilted Arch
:Sequences in Deliberate Practice

Social Networks

Admin — Tue, 28 Oct 2008 13:13:06 GMT

Admin:

*'''Web-based Social Networks''' (Goldbeck, 2005)

# Tickle http://tickle.com 18,000,000
# Friendster http://friendster.com 17,000,000
# Adult Friend Finder http://adultfriendfinder.com 15,700,000
# Black Planet http://blackplanet.com 14,000,000
# Hi5 http://hi5.com 6,100,000
# Asia Friend Finder http://asiafriendfinder.com 6,000,000
# My Space http://myspace.com 6,000,000
# LiveJournal http://livejournal.com 5,700,000
# Friend Finder http://friendfinder.com 3,600,000
# Amigos http://amigos.com 3,500,000
# Orkut http://orkut.com 3,000,000
# gradFinder http://www.gradfinder.com/ 3,000,000
# Alt.com http://alt.com 2,600,000
# LinkedIn http://linkedin.com 1,500,000
# Zero Degrees http://www.zerodegrees.com/ 1,300,000
# Out Personals http://outpersonals.com 1,050,000
# The Face Book http://thefacebook.com 1,000,000
# Fotolog http://fotolog.net 1,000,000

*'''Relationship Metrics''' (Goldbeck, 2005)

# Website URL Relationship Characteristic Rating Scale
# Orkut http://orkut.com Trust [0-3], Sexy [0-3], Cool [0-3]
# Overstock http://auctions.overstock.com Business Rating [-2 - +2] Personal Rating [0-5]
# RepCheck http://repcheck.com Social Trust [0-5], Business Trust [0-5]
# Trust Project http://trust.mindswap.org Trust [1-10]

*'''Other:'''
**More data from: [http://www.comscore.com Comscore]
**A long but non-comprehensive list of [http://en.wikipedia.org/wiki/List_of_social_networking_websites Social Networking sites] from Wikipedia

Dataset2/TeamD

Jsarmi — Tue, 30 Sep 2008 02:24:40 GMT

Jsarmi:

==Session I==

Aza2 joins the room 5/26/06 8:05:25 AM EDT
Roohiya2 joins the room 5/26/06 8:06:13 AM EDT
Aza2 5/26/06 8:12:20 AM EDT: r we supposed to wait for the other two?
rtoledosj joins the room 5/26/06 8:12:23 AM EDT
Aza2 5/26/06 8:12:40 AM EDT: does sophia have NCC?
rtoledosj 5/26/06 8:13:27 AM EDT: To see the problem that youwill work with, click the View Topic tab.
rtoledosj 5/26/06 8:13:27 AM EDT: You can begin.
Aza2 5/26/06 8:13:52 AM EDT: ok
M
Aza2 5/26/06 8:15:32 AM EDT: roohiya are u there?
M
dchia joins the room 5/26/06 8:15:52 AM EDT
M
dchia leaves the room 5/26/06 8:15:56 AM EDT
Roohiya2 5/26/06 8:16:33 AM EDT: this can be done by the fomula-initiator+diff. multiplt by n
M M M M M M M M M M M M
Aza2 5/26/06 8:18:20 AM EDT: hmm
Aza2 5/26/06 8:18:41 AM EDT: im trying to draw diagram 4
Aza2 5/26/06 8:18:48 AM EDT: but it turned out distorted
Roohiya2 5/26/06 8:19:14 AM EDT: does not matter
Aza2 5/26/06 8:19:15 AM EDT: 28 matchsticks right
Aza2 5/26/06 8:19:23 AM EDT: so...
Roohiya2 5/26/06 8:19:34 AM EDT: bur that's is the right one i guess
Roohiya2 5/26/06 8:19:44 AM EDT: yeah it is
Aza2 5/26/06 8:19:56 AM EDT: 4: 28 sticks, 10 squares
Aza2 5/26/06 8:20:21 AM EDT: btw, where's xinliang
Xinliang2 joins the room 5/26/06 8:20:28 AM EDT
Roohiya2 5/26/06 8:20:29 AM EDT: just place the squares on top of the previos ones
Aza2 5/26/06 8:20:42 AM EDT: shes trying to get in
Roohiya2 5/26/06 8:20:43 AM EDT: hey xinliang
Aza2 5/26/06 8:20:50 AM EDT: oh there she is
Aza2 5/26/06 8:21:00 AM EDT: the ques is in view topic
Roohiya2 5/26/06 8:21:11 AM EDT: lets get back to the question
Aza2 5/26/06 8:21:37 AM EDT: so the no. of squares is just (1+2.....+N), where N is the pattern number
M
Aza2 5/26/06 8:21:49 AM EDT: is it?
M M M M M M M M M
rtoledosj 5/26/06 8:22:41 AM EDT: Hi Xinliang, to see what the rest have been doing before click on the double twistes arrow icon at the top of the chat box.
M M M M M
Aza2 5/26/06 8:23:03 AM EDT: ur drawing pattern 5 right?
M M
Roohiya2 5/26/06 8:23:12 AM EDT: yeah
M M M M M M M
Xinliang2 5/26/06 8:23:45 AM EDT: where's the qn?
M M
Roohiya2 5/26/06 8:23:56 AM EDT: click on view topic
Aza2 5/26/06 8:24:13 AM EDT: lets wait for her to finish seeing the ques
Roohiya2 5/26/06 8:24:22 AM EDT: my fig. is quite distorted
Aza2 5/26/06 8:24:36 AM EDT: maybe mine isnt tt bad
Roohiya2 5/26/06 8:24:44 AM EDT: there's no eraser i guess
Xinliang2 5/26/06 8:24:54 AM EDT: wad question are u doingtight now?
Xinliang2 5/26/06 8:25:00 AM EDT: *right
Aza2 5/26/06 8:25:07 AM EDT: the view topic ques
Aza2 5/26/06 8:25:35 AM EDT: the matchstick etc
rtoledosj 5/26/06 8:25:36 AM EDT: You can select what you want to erase by using the arrow icon and then pressing delete.
M
Xinliang2 5/26/06 8:25:52 AM EDT: is it 1,2 or 3?
M M M M M M M M
Aza2 5/26/06 8:26:17 AM EDT: huh?
M
Xinliang2 5/26/06 8:26:34 AM EDT: there r 3 questions there
Aza2 5/26/06 8:26:34 AM EDT: we have to fill in the blanks
M
Xinliang2 5/26/06 8:26:43 AM EDT: where r all of u now?
M
Aza2 5/26/06 8:26:45 AM EDT: so we were finding a pattern
M
rtoledosj 5/26/06 8:26:53 AM EDT: This is a shared whiteboard, so what you erase gets erased for everybody.
M M M
Xinliang2 5/26/06 8:27:05 AM EDT: alright
Xinliang2 5/26/06 8:27:08 AM EDT: i get it
M M M M M
Aza2 5/26/06 8:27:47 AM EDT: this was where we reached till
M M M M M M M M M
Aza2 5/26/06 8:28:12 AM EDT: Roohiya, its ok
M M M M M
rtoledosj 5/26/06 8:29:05 AM EDT: You can create a text box by using the 9th icon from the left. This wayyou will not have to draw letters.
Roohiya2 5/26/06 8:29:07 AM EDT: so lets see how it grows
Xinliang2 5/26/06 8:29:20 AM EDT: where r u supposed to write the ans?
Aza2 5/26/06 8:29:31 AM EDT: so basically.. the no. of squares is (1+2+....+N), where N is the figure or pattern no
Roohiya2 5/26/06 8:29:42 AM EDT: oh thanks i didnt see that
Aza2 5/26/06 8:29:57 AM EDT: grows? u mean goes, right?
Roohiya2 5/26/06 8:30:10 AM EDT: i do not understand wat u maen aza
Aza2 5/26/06 8:30:29 AM EDT: (lets see how it grows) was wat u said
Roohiya2 5/26/06 8:30:30 AM EDT: i mean grows
Aza2 5/26/06 8:30:32 AM EDT: wat grows?
Roohiya2 5/26/06 8:30:37 AM EDT: look at the qn
Xinliang2 5/26/06 8:30:40 AM EDT: for the number of squares right
Roohiya2 5/26/06 8:30:50 AM EDT: 'the growth'
Roohiya2 5/26/06 8:30:57 AM EDT: ya
Aza2 5/26/06 8:30:58 AM EDT: ok
Aza2 5/26/06 8:31:03 AM EDT: yah xinliang
Aza2 5/26/06 8:31:08 AM EDT: ???
Roohiya2 5/26/06 8:31:29 AM EDT: basically it just grows like 1 then 2 then 3 then so on
Roohiya2 5/26/06 8:31:40 AM EDT: sq. i mean
Xinliang2 5/26/06 8:31:41 AM EDT: yes
Xinliang2 5/26/06 8:31:44 AM EDT: tht's wad i meant
Xinliang2 5/26/06 8:31:52 AM EDT: it's in the whiteboard now
M
Aza2 5/26/06 8:32:00 AM EDT: it is
M
Aza2 5/26/06 8:32:04 AM EDT: ??
Aza2 5/26/06 8:32:06 AM EDT: oh
Roohiya2 5/26/06 8:32:09 AM EDT: so didnt we find the ans already
M
Aza2 5/26/06 8:32:09 AM EDT: i c it
M
Aza2 5/26/06 8:32:31 AM EDT: u need to find the no. of matchsticks used
Xinliang2 5/26/06 8:32:39 AM EDT: okay
Xinliang2 5/26/06 8:33:03 AM EDT: do we need to draw all the figures?
Roohiya2 5/26/06 8:33:14 AM EDT: like for fig. 1 there is 1 sq, fig. 2, 2 sq
Aza2 5/26/06 8:33:18 AM EDT: i dont think so
Aza2 5/26/06 8:33:29 AM EDT: just count the no of matchsticks in these figures
Xinliang2 5/26/06 8:33:37 AM EDT: okay!!
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
Roohiya2 5/26/06 8:34:28 AM EDT: for fig5 34
Xinliang2 5/26/06 8:34:37 AM EDT: i know how to count the no of matchsticks
Roohiya2 5/26/06 8:34:59 AM EDT: ooops sorry
M
Roohiya2 5/26/06 8:35:21 AM EDT: sorry 35
M
Xinliang2 5/26/06 8:35:29 AM EDT: how do u write on the whiteboard?
M M M
Roohiya2 5/26/06 8:35:36 AM EDT: sorry 38
M
rtoledosj 5/26/06 8:35:57 AM EDT: You can create a text box.
Roohiya2 5/26/06 8:36:03 AM EDT: use the text box
Aza2 5/26/06 8:36:10 AM EDT: wanna double check both figures?
Xinliang2 5/26/06 8:36:14 AM EDT: but i need to write on it?
M
Roohiya2 5/26/06 8:36:16 AM EDT: ok
rtoledosj 5/26/06 8:36:25 AM EDT: like this.
Xinliang2 5/26/06 8:36:40 AM EDT: but how do u write on it?
Aza2 5/26/06 8:36:41 AM EDT: i counted wrongly too
Aza2 5/26/06 8:36:47 AM EDT: sorry!
rtoledosj 5/26/06 8:37:01 AM EDT: Click inside the text boxand you can write in it.
Xinliang2 5/26/06 8:37:04 AM EDT: i need to write desperately
Roohiya2 5/26/06 8:37:05 AM EDT: i again counted wrongly agian
Roohiya2 5/26/06 8:37:19 AM EDT: u noe wat lets not di ot this way
Xinliang2 5/26/06 8:37:29 AM EDT: i still cant write
rtoledosj 5/26/06 8:37:55 AM EDT: choose the pointer icon and then click on the text box.
M M
Roohiya2 5/26/06 8:38:36 AM EDT: count the no. of sticks for fiq. 2 and 3 its simpler
Xinliang2 5/26/06 8:38:44 AM EDT: yes
Xinliang2 5/26/06 8:38:56 AM EDT: for fig 2 right,
Xinliang2 5/26/06 8:39:09 AM EDT: it's 4 + 2(3)
Aza2 5/26/06 8:39:20 AM EDT: i get it
Xinliang2 5/26/06 8:39:21 AM EDT: u use add 4 everytime
Roohiya2 5/26/06 8:39:22 AM EDT: they have given 10
Xinliang2 5/26/06 8:39:24 AM EDT: for fig 3 right
Roohiya2 5/26/06 8:40:01 AM EDT: the diff increases by 2
Aza2 5/26/06 8:40:02 AM EDT: in this case
Xinliang2 5/26/06 8:40:05 AM EDT: it's 4 + 3(2+3)
Aza2 5/26/06 8:40:08 AM EDT: iniator is 0, right?
Xinliang2 5/26/06 8:40:12 AM EDT: then for fig 4
Roohiya2 5/26/06 8:40:20 AM EDT: count it
Roohiya2 5/26/06 8:40:24 AM EDT: count it
Aza2 5/26/06 8:40:39 AM EDT: fig 4:28 and fig 5:40
Xinliang2 5/26/06 8:40:39 AM EDT: it's 4+ 3(2+2+4)
Roohiya2 5/26/06 8:40:41 AM EDT: initiator is not 0
Aza2 5/26/06 8:40:50 AM EDT: 4-4=0
Xinliang2 5/26/06 8:40:54 AM EDT: *it's 4+ 3(2+3+4)
Aza2 5/26/06 8:40:59 AM EDT: 6-2=4
Xinliang2 5/26/06 8:41:04 AM EDT: do u get it/
Aza2 5/26/06 8:41:12 AM EDT: hang on
M M
Roohiya2 5/26/06 8:41:29 AM EDT: but the diff should be the same if u use the fomula
Aza2 5/26/06 8:41:40 AM EDT: isnt it like the first time
Xinliang2 5/26/06 8:41:45 AM EDT: SO THE FORMula is
Roohiya2 5/26/06 8:42:15 AM EDT: initiator + diff. multiply by (n)
Aza2 5/26/06 8:42:18 AM EDT: 0+4=4 then, 4+(4+2)=10, then, 10+(4+2+2)=18
Aza2 5/26/06 8:42:22 AM EDT: etc
sophia joins the room 5/26/06 8:42:24 AM EDT
Aza2 5/26/06 8:42:29 AM EDT: hi
Roohiya2 5/26/06 8:42:32 AM EDT: hey sophia
Aza2 5/26/06 8:42:35 AM EDT: finally
Roohiya2 5/26/06 8:42:36 AM EDT: atlast
Xinliang2 5/26/06 8:43:10 AM EDT: 4 + 3(n+(n-1)+(n-2))
Xinliang2 5/26/06 8:43:19 AM EDT: sth like that
Xinliang2 5/26/06 8:43:20 AM EDT: is it?
Roohiya2 5/26/06 8:43:20 AM EDT: so can we do this quickly we r takin a lot if time
Aza2 5/26/06 8:43:23 AM EDT: w8
Aza2 5/26/06 8:43:36 AM EDT: 2nd pattern right
rtoledosj 5/26/06 8:45:05 AM EDT: Hi Sophia!
sophia joins the room 5/26/06 8:45:29 AM EDT
sophia joins the room 5/26/06 8:45:31 AM EDT
Xinliang2 5/26/06 8:45:44 AM EDT: we got to hurry up
Xinliang2 5/26/06 8:45:56 AM EDT: we are stil stuck at this question
Roohiya2 5/26/06 8:46:01 AM EDT: the no. of sticks in fig. 4 i s 28
Aza2 5/26/06 8:46:41 AM EDT: is 10 which is (4*2)+(1*2) and 3rd is 18= (4*3)+(3*2) and 4th is 28= (4*4)+(3*4)
Aza2 5/26/06 8:46:45 AM EDT: u noe wat
Roohiya2 5/26/06 8:46:52 AM EDT: i got it
Aza2 5/26/06 8:46:54 AM EDT: xinliang's explanation sounds sensible
Aza2 5/26/06 8:46:57 AM EDT: mine doesnt
Roohiya2 5/26/06 8:47:09 AM EDT: fig. 1 * 4
Aza2 5/26/06 8:47:39 AM EDT: U GOT IT?
Aza2 5/26/06 8:47:46 AM EDT: i didnt get it myself
Xinliang2 5/26/06 8:47:51 AM EDT: aza's explanation sounds very reasonable
Aza2 5/26/06 8:47:52 AM EDT: i mean wat i juz said
Xinliang2 5/26/06 8:47:56 AM EDT: we haf to test it out
Aza2 5/26/06 8:47:58 AM EDT: it does
Roohiya2 5/26/06 8:48:14 AM EDT: times the no. sq by 3
Roohiya2 5/26/06 8:48:26 AM EDT: for each fig
Roohiya2 5/26/06 8:48:55 AM EDT: sorry tt's wrong
Aza2 5/26/06 8:49:06 AM EDT: i got it
Xinliang2 5/26/06 8:49:08 AM EDT: why (4*2)?
Aza2 5/26/06 8:49:33 AM EDT: fig 2= (3*2)+(2*2)= 10
Aza2 5/26/06 8:49:45 AM EDT: the (4*2) was an error
Roohiya2 5/26/06 8:49:48 AM EDT: then
Xinliang2 5/26/06 8:49:50 AM EDT: why is it like that?
Xinliang2 5/26/06 8:49:58 AM EDT: how do u get it?
Roohiya2 5/26/06 8:50:12 AM EDT: its just a pattern
Aza2 5/26/06 8:50:15 AM EDT: but then its still wrong
Roohiya2 5/26/06 8:50:23 AM EDT: really
Aza2 5/26/06 8:50:36 AM EDT: coz fig 3 doesnt match
Roohiya2 5/26/06 8:50:45 AM EDT: oh mt god we r never going to get to the bottom of this
Xinliang2 5/26/06 8:51:14 AM EDT: let's get a rough paper and work it out first
Xinliang2 5/26/06 8:51:22 AM EDT: is it alright
Aza2 5/26/06 8:51:27 AM EDT: u noe wat
Xinliang2 5/26/06 8:51:35 AM EDT: otherwise it will be so messy here.
Aza2 5/26/06 8:51:40 AM EDT: we're supposed to draw fig for N 6 too
Roohiya2 5/26/06 8:51:51 AM EDT: i''l do tt
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Roohiya2 5/26/06 8:52:06 AM EDT: u use ur rough paper
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Xinliang2 5/26/06 8:52:20 AM EDT: then i try to do the solving of the no of sticks
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Aza2 5/26/06 8:52:58 AM EDT: ok
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
Roohiya2 5/26/06 8:54:42 AM EDT: done
Roohiya2 5/26/06 8:55:06 AM EDT: xin liang hv u found out
Aza2 5/26/06 8:55:19 AM EDT: 53 is the no. of matchsticks
M
Roohiya2 5/26/06 8:55:41 AM EDT: ok then
Roohiya2 5/26/06 8:56:00 AM EDT: we r supposed to see the growth
Aza2 5/26/06 8:56:10 AM EDT: isit
Roohiya2 5/26/06 8:56:26 AM EDT: 4, 10, 18, 28,
Roohiya2 5/26/06 8:56:41 AM EDT: how many r there in fig. 5
Aza2 5/26/06 8:56:54 AM EDT: 54
Aza2 5/26/06 8:57:00 AM EDT: miscalculation
Roohiya2 5/26/06 8:57:18 AM EDT: ok so
Aza2 5/26/06 8:57:20 AM EDT: fig 1=4
Xinliang2 5/26/06 8:57:25 AM EDT: so there's 54 matchsticks in fig 5 is it?
Aza2 5/26/06 8:57:36 AM EDT: fig2=4+(4+2)
Roohiya2 5/26/06 8:57:37 AM EDT: 4, 10, 18, 28, 54,
Roohiya2 5/26/06 8:57:43 AM EDT: in fig. 6?
sophia joins the room 5/26/06 8:57:45 AM EDT
Aza2 5/26/06 8:57:51 AM EDT: fig 3=fig2+(4+2+2)
Aza2 5/26/06 8:58:04 AM EDT: fig 4=fig3+(4+2+2+2)
Aza2 5/26/06 8:58:27 AM EDT: 5=fig4+(4+4(2))
Roohiya2 5/26/06 8:58:34 AM EDT: i dont clearly see the pattern of growth for the sticks
Aza2 5/26/06 8:58:42 AM EDT: wait
Roohiya2 5/26/06 8:59:00 AM EDT: sorry growth of pattern
Aza2 5/26/06 8:59:19 AM EDT: 3={4+(4+2)}+{4+2(2)}
Aza2 5/26/06 8:59:27 AM EDT: 3 refers to fig 3
Roohiya2 5/26/06 8:59:33 AM EDT: aza wat r u doing
Aza2 5/26/06 8:59:47 AM EDT: wait the pattern is tt
Aza2 5/26/06 8:59:53 AM EDT: evertime
Aza2 5/26/06 9:00:00 AM EDT: everytime
Aza2 5/26/06 9:00:08 AM EDT: for fig N=
Roohiya2 5/26/06 9:00:34 AM EDT: yeah go on
Aza2 5/26/06 9:00:35 AM EDT: fig(N-1)+(diff bet. fig (N-1) and (N-2) +2
Aza2 5/26/06 9:00:45 AM EDT: i think im juz confusing u more
Roohiya2 5/26/06 9:00:48 AM EDT: uh?
Roohiya2 5/26/06 9:00:53 AM EDT: ya u r
Aza2 5/26/06 9:00:57 AM EDT: for eg
Aza2 5/26/06 9:01:05 AM EDT: fig 4 has 28 ms
Aza2 5/26/06 9:01:17 AM EDT: ms is matchstick
Roohiya2 5/26/06 9:01:23 AM EDT: xin liang and sophia HELP US!!!
Xinliang2 5/26/06 9:01:35 AM EDT: i brainstorming!!!
Aza2 5/26/06 9:01:38 AM EDT: fig 3 has 18 ms
Aza2 5/26/06 9:01:53 AM EDT: so the diff bet fig 3 and 4 is 10
Roohiya2 5/26/06 9:01:54 AM EDT: WAT IS MS???
Aza2 5/26/06 9:02:01 AM EDT: and fig 4 has 28 ms
Aza2 5/26/06 9:02:04 AM EDT: matchstick
Aza2 5/26/06 9:02:08 AM EDT: wait
Roohiya2 5/26/06 9:02:12 AM EDT: OK
Aza2 5/26/06 9:02:17 AM EDT: remember these two things
Aza2 5/26/06 9:02:32 AM EDT: the diff in no. of ms bet fig 3 and 4 is 10
Aza2 5/26/06 9:02:44 AM EDT: and the no. of ms in fig 4 is 28
Roohiya2 5/26/06 9:02:46 AM EDT: ok
Aza2 5/26/06 9:02:49 AM EDT: ok?
Xinliang2 5/26/06 9:02:55 AM EDT: yupp
Roohiya2 5/26/06 9:02:58 AM EDT: ya
Aza2 5/26/06 9:03:04 AM EDT: so to find the no. of ms in fig 5
Aza2 5/26/06 9:03:22 AM EDT: u have to add (28) + (10+2) = 40
sophia joins the room 5/26/06 9:03:30 AM EDT
Aza2 5/26/06 9:03:31 AM EDT: ok?
Roohiya2 5/26/06 9:03:40 AM EDT: ok
Aza2 5/26/06 9:03:47 AM EDT: 28 is the no. of ms in the prev. fig
sophia joins the room 5/26/06 9:03:59 AM EDT
Roohiya2 5/26/06 9:04:01 AM EDT: ok
sophia joins the room 5/26/06 9:04:02 AM EDT
sophia joins the room 5/26/06 9:04:06 AM EDT
Aza2 5/26/06 9:04:10 AM EDT: so now using tt
Aza2 5/26/06 9:04:18 AM EDT: we must form a formula
Aza2 5/26/06 9:04:19 AM EDT: ok
sophia joins the room 5/26/06 9:04:23 AM EDT
sophia joins the room 5/26/06 9:04:23 AM EDT
Roohiya2 5/26/06 9:04:24 AM EDT: ok
nan joins the room 5/26/06 9:04:37 AM EDT
Roohiya2 5/26/06 9:04:56 AM EDT: aza do it fast
Xinliang2 5/26/06 9:05:09 AM EDT: i got the formula!!!!
Aza2 5/26/06 9:05:18 AM EDT: u did
Roohiya2 5/26/06 9:05:18 AM EDT: wat??????/
Xinliang2 5/26/06 9:05:19 AM EDT: let me write it out
Aza2 5/26/06 9:05:24 AM EDT: ok
Roohiya2 5/26/06 9:05:29 AM EDT: ok
Xinliang2 5/26/06 9:05:32 AM EDT: im going to write in order of the layer
Xinliang2 5/26/06 9:05:39 AM EDT: starting from the bottom
Xinliang2 5/26/06 9:05:40 AM EDT: ok?
Roohiya2 5/26/06 9:05:40 AM EDT: ok
Aza2 5/26/06 9:05:42 AM EDT: n no1 interrupt
Xinliang2 5/26/06 9:05:57 AM EDT: for fig 3
Xinliang2 5/26/06 9:06:18 AM EDT: the bottommost layer is 4 + 3(2)
Xinliang2 5/26/06 9:06:24 AM EDT: do u get this?
Roohiya2 5/26/06 9:06:30 AM EDT: ya
Aza2 5/26/06 9:06:32 AM EDT: yup
Xinliang2 5/26/06 9:06:37 AM EDT: ok
Xinliang2 5/26/06 9:06:56 AM EDT: the 2nd layer will be 3 + 2(1)
nan 5/26/06 9:07:00 AM EDT: hi sophia
Roohiya2 5/26/06 9:07:15 AM EDT: ok
nan 5/26/06 9:07:19 AM EDT: hi everybody, i'm one of the facilitators today
Aza2 5/26/06 9:07:23 AM EDT: hi
Xinliang2 5/26/06 9:07:27 AM EDT: oh hi
nan 5/26/06 9:07:29 AM EDT: sophia just joined our room
Roohiya2 5/26/06 9:07:31 AM EDT: hello
Xinliang2 5/26/06 9:07:39 AM EDT: kae...let's get back to the question
nan 5/26/06 9:07:40 AM EDT: can anyone of you catch her up?
Aza2 5/26/06 9:07:42 AM EDT: i think im getting wat u r trying to sa
Roohiya2 5/26/06 9:07:42 AM EDT: hi sophia
Xinliang2 5/26/06 9:08:03 AM EDT: do u get wad im saying about the 2nd layer
Roohiya2 5/26/06 9:08:11 AM EDT: xinliang dont beat abt the bush
Roohiya2 5/26/06 9:08:20 AM EDT: juz tell the formula
Xinliang2 5/26/06 9:08:22 AM EDT: ok
Roohiya2 5/26/06 9:08:37 AM EDT: we r stuck on this for too long
Aza2 5/26/06 9:08:43 AM EDT: i noe
Xinliang2 5/26/06 9:08:49 AM EDT: then the 3rd layer for fig 3 is plus 3
Xinliang2 5/26/06 9:08:53 AM EDT: ok
Roohiya2 5/26/06 9:09:01 AM EDT: ok
Aza2 5/26/06 9:09:28 AM EDT: now i get it
nan 5/26/06 9:09:48 AM EDT: i'm not sure sophia can see the room for some reason (i was talking to her in the lobby room too)
Roohiya2 5/26/06 9:09:48 AM EDT: wat
nan 5/26/06 9:09:58 AM EDT: go ahead and continue your work
Xinliang2 5/26/06 9:10:01 AM EDT: so the formula is 4 + 3(n-1) + 3+2(n-2)+ 3+ 2(n-3)+ 3+2(n-4) and it goes on
Roohiya2 5/26/06 9:10:05 AM EDT: ok
Xinliang2 5/26/06 9:10:21 AM EDT: does anyone of u do not understand my formula?
Aza2 5/26/06 9:10:22 AM EDT: ok
Roohiya2 5/26/06 9:10:29 AM EDT: ya
nan 5/26/06 9:10:31 AM EDT: thanks guys
Roohiya2 5/26/06 9:10:45 AM EDT: anythimg else
Xinliang2 5/26/06 9:10:57 AM EDT: nope
Aza2 5/26/06 9:10:59 AM EDT: thanks?
Xinliang2 5/26/06 9:11:04 AM EDT: so tht's the formula
Roohiya2 5/26/06 9:11:09 AM EDT: ok
Roohiya2 5/26/06 9:11:25 AM EDT: ppl i m in a hurry
Aza2 5/26/06 9:11:30 AM EDT: so lets FINALLY fill in the blanks and submit it
Xinliang2 5/26/06 9:11:36 AM EDT: okay
Xinliang2 5/26/06 9:11:40 AM EDT: who's doing it?
Roohiya2 5/26/06 9:12:26 AM EDT: the fig are done juz the explanations
sophia joins the room 5/26/06 9:12:37 AM EDT
Aza2 5/26/06 9:12:38 AM EDT: i still dont get how to post the ans
sophia joins the room 5/26/06 9:12:43 AM EDT
sophia joins the room 5/26/06 9:12:44 AM EDT
Aza2 5/26/06 9:12:46 AM EDT: hi sophia
sophia joins the room 5/26/06 9:12:47 AM EDT
sophia joins the room 5/26/06 9:12:49 AM EDT
sophia joins the room 5/26/06 9:12:49 AM EDT
sophia joins the room 5/26/06 9:12:51 AM EDT
Xinliang2 5/26/06 9:13:02 AM EDT: ask nan
Aza2 5/26/06 9:14:31 AM EDT: should i clear the whiteboard
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Aza2 5/26/06 9:14:50 AM EDT: to write the answer
nan 5/26/06 9:14:51 AM EDT: hi
rtoledosj 5/26/06 9:15:01 AM EDT: You can scroll the whiteboard to see more of it.
Xinliang2 5/26/06 9:15:11 AM EDT: don't erase
Xinliang2 5/26/06 9:15:19 AM EDT: the fig for 5 and 6 are there
sophia leaves the room 5/26/06 9:15:20 AM EDT
Xinliang2 5/26/06 9:15:25 AM EDT: it's precious
nan 5/26/06 9:15:26 AM EDT: right, make sure you scroll the bar of whiteboard (on the left) all the way to the bottom
Aza2 5/26/06 9:15:38 AM EDT: hi sophia
Aza2 5/26/06 9:15:46 AM EDT: yah
nan 5/26/06 9:15:52 AM EDT: i think she's having technical probelm
Aza2 5/26/06 9:15:58 AM EDT: oh
nan 5/26/06 9:16:02 AM EDT: and she's trying to sign in again
Aza2 5/26/06 9:16:27 AM EDT: who's writing the answer?
nan 5/26/06 9:16:31 AM EDT: to write the answer, you can create a text box and write down what you found
Xinliang2 5/26/06 9:16:39 AM EDT: ok
Xinliang2 5/26/06 9:16:41 AM EDT: i'll write
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
Aza2 5/26/06 9:20:24 AM EDT: xinliang the table is at the bottom
Aza2 5/26/06 9:20:31 AM EDT: its a bit weird but anw
Xinliang2 5/26/06 9:20:34 AM EDT: ok
Wang joins the room 5/26/06 9:20:43 AM EDT
Xinliang2 5/26/06 9:20:46 AM EDT: help me with the no of squares and the pattern
Xinliang2 5/26/06 9:21:02 AM EDT: i'll write the sticks part
Xinliang2 5/26/06 9:21:04 AM EDT: alright?
Aza2 5/26/06 9:21:07 AM EDT: ok
M M M M M M M M M M
Wang leaves the room 5/26/06 9:22:34 AM EDT
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rtoledosj 5/26/06 9:25:07 AM EDT: Ok, it's about 9:30, we should think of concluding this session.
Xinliang2 5/26/06 9:25:20 AM EDT: yup
Xinliang2 5/26/06 9:25:22 AM EDT: im finishing
Xinliang2 5/26/06 9:25:24 AM EDT: hold on
rtoledosj 5/26/06 9:25:38 AM EDT: This room will be in your 'My Rooms' tab.
Aza2 5/26/06 9:26:04 AM EDT: ok
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rtoledosj 5/26/06 9:26:16 AM EDT: Your teacher knows when the next session will be.
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rtoledosj 5/26/06 9:27:01 AM EDT: Since this room will be in your 'My Rooms' tab, you can go back to it and look at what you have done.
Aza2 5/26/06 9:27:01 AM EDT: but xinliang
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Xinliang2 5/26/06 9:27:12 AM EDT: yes?
Aza2 5/26/06 9:27:36 AM EDT: the no. of sticks formula might be wrong becoz it does not apply to the 1st pattern
rtoledosj 5/26/06 9:27:37 AM EDT: You will get feedback for your work.
Aza2 5/26/06 9:27:43 AM EDT: ok
Aza2 5/26/06 9:27:58 AM EDT: its supposed to apply to all the patterns
Xinliang2 5/26/06 9:28:07 AM EDT: tht's why im not sure about the 1st pattern
Xinliang2 5/26/06 9:28:14 AM EDT: but it works for the other patterns
Aza2 5/26/06 9:28:56 AM EDT: doesnt it seem too complicated and i think it should apply for all patterns
rtoledosj 5/26/06 9:29:08 AM EDT: You might want to write a summary of what you have found out during this session.
Xinliang2 5/26/06 9:29:21 AM EDT: im sure there's an easier method
Xinliang2 5/26/06 9:29:28 AM EDT: ok
Xinliang2 5/26/06 9:29:33 AM EDT: so we sum up first
Xinliang2 5/26/06 9:29:44 AM EDT: and we will discuss the next session?
Aza2 5/26/06 9:29:49 AM EDT: ok
Aza2 5/26/06 9:30:19 AM EDT: next discussion we'll start with the 1st pattern and find the possible combos like 2(2)=4 etc
Xinliang2 5/26/06 9:30:32 AM EDT: yup
Aza2 5/26/06 9:30:35 AM EDT: and hopefully sophia will be able to solve the prob
Aza2 5/26/06 9:30:39 AM EDT: anw
Aza2 5/26/06 9:30:47 AM EDT: we need to complete the last square
Xinliang2 5/26/06 9:30:54 AM EDT: erm..rtoledosj...how do u sum up?
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sophia joins the room 5/26/06 9:31:04 AM EDT
Aza2 5/26/06 9:31:08 AM EDT: oh
rtoledosj 5/26/06 9:31:20 AM EDT: Hi Sophia!
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Aza2 5/26/06 9:32:15 AM EDT: sophia is ur comp prob solved?
rtoledosj 5/26/06 9:32:42 AM EDT: You might describe the main findings that you have. For example, describe how the sticks increase with every new pattern, how the squares increase with every new pattern.
Xinliang2 5/26/06 9:33:11 AM EDT: do we discuss it on the whiteboard?
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Aza2 leaves the room 5/26/06 9:35:30 AM EDT
Xinliang2 5/26/06 9:36:14 AM EDT: roohiya..are we going to sum up?
rtoledosj 5/26/06 9:38:21 AM EDT: After you have summed up, you can click on 'Send Mail' to inform the mentors that you have made a summary.
Xinliang2 5/26/06 9:39:40 AM EDT: is the table considered a sum up?
Aza2 joins the room 5/26/06 9:40:02 AM EDT
Aza2 5/26/06 9:40:10 AM EDT: im so sorry!
rtoledosj 5/26/06 9:40:11 AM EDT: Just add a little explanation.
Aza2 5/26/06 9:40:22 AM EDT: i closed the main window by accident
rtoledosj 5/26/06 9:41:14 AM EDT: You have done great work. I look forward to being with you in future sessions.
Aza2 5/26/06 9:41:44 AM EDT: is it done?
Xinliang2 5/26/06 9:41:47 AM EDT: hey...girls...wad do we write for the sum-up
Xinliang2 5/26/06 9:41:49 AM EDT: help!!
Aza2 5/26/06 9:41:57 AM EDT: ummm
Xinliang2 5/26/06 9:42:07 AM EDT: we r left with the summing up
rtoledosj 5/26/06 9:42:11 AM EDT: Feel free to enter this system and explore it, especially through the Sandbox and the help areas.
Xinliang2 5/26/06 9:42:14 AM EDT: roohiya help!!!
Xinliang2 5/26/06 9:42:24 AM EDT: sophia help!!!
nan 5/26/06 9:43:06 AM EDT: i don't think sophia is actually here, i talked to her in the lobby and she can't see the room window
Aza2 5/26/06 9:43:28 AM EDT: okay so for the squares the increase in the no. of squares from the prev pattern is just the pattern no. (pat2=pat1+2(which is pat no.)
Aza2 5/26/06 9:43:43 AM EDT: is tt considered an explanation?
Aza2 5/26/06 9:44:44 AM EDT: xinliang, r u there?
Xinliang2 5/26/06 9:44:50 AM EDT: yepp
Xinliang2 5/26/06 9:45:23 AM EDT: we can write it down first
Xinliang2 5/26/06 9:45:35 AM EDT: it's al least considered an explanation
Aza2 5/26/06 9:45:42 AM EDT: ok
Aza2 5/26/06 9:45:44 AM EDT: ill do tt
Aza2 5/26/06 9:45:54 AM EDT: and try to make it more easy to understand :)
Xinliang2 5/26/06 9:47:59 AM EDT: can u say that: to find the no. of squares, u keep adding the consecutive numbers starting from 2
Xinliang2 5/26/06 9:48:03 AM EDT: *1
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Xinliang2 5/26/06 9:53:44 AM EDT: is that alright?
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Aza2 5/26/06 9:54:02 AM EDT: yup
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Aza2 5/26/06 9:54:45 AM EDT: wait should i change it back
Xinliang2 5/26/06 9:54:54 AM EDT: it's alright
Xinliang2 5/26/06 9:54:59 AM EDT: it's contributions
Xinliang2 5/26/06 9:55:12 AM EDT: roohiya, contribute to the summing up
Aza2 5/26/06 9:55:45 AM EDT: i think her father is using the comp
Aza2 5/26/06 9:55:50 AM EDT: so she doesnt noe wats going on
Xinliang2 5/26/06 9:56:01 AM EDT: okay
Aza2 5/26/06 9:56:12 AM EDT: poor sophia
Aza2 5/26/06 9:56:22 AM EDT: shes been trying to get in for 2 hrs
Xinliang2 5/26/06 9:56:30 AM EDT: yes...she keeps having problems with her com
Aza2 5/26/06 9:56:34 AM EDT: next time we have to be much more organised
nan 5/26/06 9:56:37 AM EDT: yes, she's been very patient
Xinliang2 5/26/06 9:56:40 AM EDT: yes
Aza2 5/26/06 9:56:52 AM EDT: do we have to explain the number of matchsticks
nan 5/26/06 9:56:52 AM EDT: feel very sorry for her
rtoledosj 5/26/06 9:57:22 AM EDT: It's getting late.
rtoledosj 5/26/06 9:57:22 AM EDT: We should be looking at finishing up.
Xinliang2 5/26/06 9:57:34 AM EDT: but we still need to find a better and more undrstandable method first before we sum that part up
Aza2 5/26/06 9:57:44 AM EDT: sry
Xinliang2 5/26/06 9:57:59 AM EDT: so i think we are almost done for this session
Aza2 5/26/06 9:58:08 AM EDT: i guess we have no choice just finish it up quickly
Aza2 5/26/06 9:58:21 AM EDT: at least one part seems reasonable
Xinliang2 5/26/06 9:58:38 AM EDT: yeah
Aza2 5/26/06 9:58:38 AM EDT: actually both are reasonable
Aza2 5/26/06 9:58:44 AM EDT: one is juz complicated
Xinliang2 5/26/06 9:58:46 AM EDT: so we send it to the mentor?
Aza2 5/26/06 9:58:54 AM EDT: i guess so
rtoledosj 5/26/06 9:58:59 AM EDT: Yes.
Aza2 5/26/06 9:59:07 AM EDT: we cant do anything more than this
Aza2 5/26/06 9:59:24 AM EDT: ur sending it right, xinliang
Xinliang2 5/26/06 9:59:56 AM EDT: im sending (:
Aza2 5/26/06 10:00:06 AM EDT: tell me when ur done
Xinliang2 5/26/06 10:01:06 AM EDT: Xinliang2 sent an email to mentors.
Subject: please check our work. give us your feedback
Message:
we wrote the summary on the whiteboard, please go and take a look. thanks !!
Xinliang2 5/26/06 10:01:07 AM EDT: send!!!
nan 5/26/06 10:01:37 AM EDT: great work, everyone
Aza2 5/26/06 10:01:45 AM EDT: ok then
Aza2 5/26/06 10:01:51 AM EDT: omg
nan 5/26/06 10:02:04 AM EDT: please make sure you keep updated by your teacher about the time for next session
Aza2 5/26/06 10:02:09 AM EDT: we so made u stay back unecessarily
nan 5/26/06 10:02:28 AM EDT: no problem at all.
nan 5/26/06 10:02:36 AM EDT: i'm sorry i was late for the session
nan 5/26/06 10:02:46 AM EDT: i'll make sure this won't happen again
nan 5/26/06 10:03:00 AM EDT: (it was 8am for me and i forgot to set my alarm)
Aza2 5/26/06 10:03:02 AM EDT: n we'll make sure we won't end tt late
Xinliang2 5/26/06 10:03:06 AM EDT: thanks!!
Xinliang2 5/26/06 10:03:19 AM EDT: nan, which part of the world are u in?
nan 5/26/06 10:03:20 AM EDT: thank you all for participating
nan 5/26/06 10:03:32 AM EDT: US, east coast
Aza2 5/26/06 10:03:46 AM EDT: so its morning there?
nan 5/26/06 10:03:55 AM EDT: yeah:-)
Xinliang2 5/26/06 10:04:10 AM EDT: gd morning!!
Aza2 5/26/06 10:04:12 AM EDT: oh
nan 5/26/06 10:04:15 AM EDT: it will be harder for me to sleep in on evening;)
Xinliang2 5/26/06 10:04:22 AM EDT: it's 10 plus at night
Aza2 5/26/06 10:04:30 AM EDT: yup
nan 5/26/06 10:04:31 AM EDT: right
Xinliang2 5/26/06 10:04:31 AM EDT: in Singapore
nan 5/26/06 10:04:35 AM EDT: 12 hours difference
nan 5/26/06 10:04:51 AM EDT: i hope you all enjoyed working together today
nan 5/26/06 10:05:13 AM EDT: i'll see you very soon for next session!
Xinliang2 5/26/06 10:05:14 AM EDT: yes...we did!!
nan 5/26/06 10:05:21 AM EDT: great
Aza2 5/26/06 10:05:22 AM EDT: yup
Xinliang2 5/26/06 10:05:26 AM EDT: alright
Aza2 5/26/06 10:05:31 AM EDT: i gtg
nan 5/26/06 10:05:36 AM EDT: ok, everybody have a good night and great weekend
Xinliang2 5/26/06 10:05:42 AM EDT: thanks rtoledosj too!!
rtoledosj 5/26/06 10:05:44 AM EDT: Ok, people, you have earned your right to sleep. ;-)
Aza2 5/26/06 10:05:47 AM EDT: thanks
Xinliang2 5/26/06 10:05:47 AM EDT: yup
Xinliang2 5/26/06 10:05:51 AM EDT: i gotta sleep
nan 5/26/06 10:05:55 AM EDT: haha
Aza2 5/26/06 10:06:00 AM EDT: bye
Xinliang2 5/26/06 10:06:01 AM EDT: haha
nan 5/26/06 10:06:02 AM EDT: thank you all
rtoledosj 5/26/06 10:06:02 AM EDT: Sweet dreams!
Xinliang2 5/26/06 10:06:04 AM EDT: byebye!1
nan 5/26/06 10:06:05 AM EDT: bye
Aza2 leaves the room 5/26/06 10:06:07 AM EDT
rtoledosj 5/26/06 10:08:11 AM EDT: To log out, just close this window.
nan 5/26/06 10:08:26 AM EDT: good call
nan leaves the room 5/26/06 10:10:01 AM EDT
sophia leaves the room 5/26/06 10:10:24 AM EDT
Roohiya2 5/26/06 10:10:24 AM EDT: bye
Roohiya2 leaves the room 5/26/06 10:10:31 AM EDT
rtoledosj leaves the room 5/26/06 10:19:36 AM EDT

==Session II==
jsarmi joins the room 5/30/06 9:22:31 AM EDT
jsarmi 5/30/06 9:22:53 AM EDT: Xinliang2?
jsarmi leaves the room 5/30/06 9:29:19 AM EDT
jsarmi joins the room 5/30/06 9:42:16 AM EDT
jsarmi leaves the room 5/30/06 4:41:07 PM EDT
tutor joins the room 5/31/06 4:26:31 PM EDT
tutor leaves the room 5/31/06 4:43:47 PM EDT
Quicksilver joins the room 6/3/06 9:21:45 PM EDT
Quicksilver leaves the room 6/3/06 9:22:29 PM EDT
tutor joins the room 6/4/06 6:03:06 PM EDT
TBryant joins the room 6/4/06 6:36:39 PM EDT
TBryant 6/4/06 6:39:37 PM EDT: Tutor are you working?
TBryant leaves the room 6/4/06 6:42:46 PM EDT
TBryant joins the room 6/4/06 7:34:25 PM EDT
tutor 6/4/06 7:36:55 PM EDT: Yes, I am looking at this log to prepare the feedback for the group.
TBryant 6/4/06 7:37:55 PM EDT: When does this project end and a community chat begin?
tutor 6/4/06 7:38:40 PM EDT: This group just started and they will have a few more sessions.
TBryant 6/4/06 7:38:53 PM EDT: Also, how do new school groups get into this program?
tutor 6/4/06 7:40:03 PM EDT: We invite teachers to invite their students to these sessions. We then facilitate them.
TBryant 6/4/06 7:40:46 PM EDT: So they can join a session already in progress.
tutor 6/4/06 7:41:45 PM EDT: Right now, it is really students of a particular teacher who should join a session.
tutor 6/4/06 7:43:02 PM EDT: What we would want in the future to have is situation where students create their own problem-solving sessions which they ay, if they wish, open to oters.
tutor 6/4/06 7:43:18 PM EDT: ay = may, others = others.
TBryant 6/4/06 7:43:36 PM EDT: Sounds great!
TBryant 6/4/06 7:44:19 PM EDT: Okay I will let you get back to work thanks for the info. Bye
tutor 6/4/06 7:44:20 PM EDT: We are trying to learn from these sessions how to make them more appealing to students.
tutor 6/4/06 7:44:47 PM EDT: Glad to be of assistance. See you in other sessions.
TBryant 6/4/06 7:45:25 PM EDT: So the real sessions have not started as for your ultimate goal of random problem solving.
tutor 6/4/06 7:48:14 PM EDT: These are real sessions. However, in this environment, we have not yet run sessions which are participated in by a truly international group, e.g. participants from Asia, Europe, North America, South America in a problem-solving session.
TBryant 6/4/06 7:50:03 PM EDT: I meant a session where someone comes with a problem and a group takes the problem and helps them solve it. I will not keep you. Thanks
tutor 6/4/06 7:51:58 PM EDT: This is our dream scenario.
TBryant 6/4/06 7:52:27 PM EDT: That would be awesome!!
TBryant leaves the room 6/4/06 7:55:08 PM EDT
M M M M M M M M M M M M M M M
tutor 6/4/06 9:35:24 PM EDT: Feedback from a tutor.
tutor 6/4/06 9:36:16 PM EDT: tutor sent an email to room members.
Subject: Feedback Message:Feedback for your group has been posted.
tutor leaves the room 6/4/06 9:36:18 PM EDT
Quicksilver joins the room 6/4/06 9:49:31 PM EDT
Quicksilver leaves the room 6/4/06 9:50:13 PM EDT
tutor joins the room 6/4/06 10:07:36 PM EDT
tutor leaves the room 6/4/06 10:08:23 PM EDT
TBryant joins the room 6/5/06 11:44:54 AM EDT
TBryant leaves the room 6/5/06 11:47:51 AM EDT
tutor joins the room 6/6/06 2:01:41 AM EDT
tutor leaves the room 6/6/06 2:08:05 AM EDT
jsarmi joins the room 6/6/06 9:54:10 AM EDT
M M M M
jsarmi leaves the room 6/6/06 9:57:10 AM EDT
sophia joins the room 6/7/06 4:15:03 AM EDT
sophia leaves the room 6/7/06 4:17:31 AM EDT
EChua joins the room 6/7/06 4:58:05 AM EDT
EChua leaves the room 6/7/06 4:58:10 AM EDT
EChua joins the room 6/7/06 5:17:28 AM EDT
M M M
EChua leaves the room 6/7/06 5:35:13 AM EDT
rtoledosj joins the room 6/7/06 7:50:04 AM EDT
Aza2 joins the room 6/7/06 7:57:17 AM EDT
rtoledosj 6/7/06 7:59:02 AM EDT: Hi Aza2
Aza2 6/7/06 7:59:26 AM EDT: hi
rtoledosj 6/7/06 7:59:37 AM EDT: While waiting for the others, you can look at the feedback.
Aza2 6/7/06 7:59:45 AM EDT: ok
sophia joins the room 6/7/06 8:00:20 AM EDT
rtoledosj 6/7/06 8:00:28 AM EDT: Hi Sophia!
Aza2 6/7/06 8:00:41 AM EDT: hi
sophia 6/7/06 8:01:22 AM EDT: hi
Aza2 6/7/06 8:01:33 AM EDT: how did ur camp go?
sophia 6/7/06 8:01:42 AM EDT: very fun
sophia 6/7/06 8:01:55 AM EDT: it's some promotion camp
Aza2 6/7/06 8:02:08 AM EDT: roohiya is coming. is xinliang coming?
sophia 6/7/06 8:02:16 AM EDT: and i'm one of the few awardees
Aza2 6/7/06 8:02:20 AM EDT: oh she juz came
Aza2 6/7/06 8:02:22 AM EDT: cool
sophia 6/7/06 8:02:28 AM EDT: yep, xinliang's coming
Aza2 6/7/06 8:02:46 AM EDT: roohiya is coming. she's juz late i think
sophia 6/7/06 8:03:20 AM EDT: yep
M
rtoledosj 6/7/06 8:04:15 AM EDT: Since there are already two of you here, you can begin.
Aza2 6/7/06 8:04:35 AM EDT: do we continue with the same ques as the last session
sophia 6/7/06 8:05:12 AM EDT: eh, i think we continue with the qn
rtoledosj 6/7/06 8:05:26 AM EDT: You can click 'View Topic', and scroll it up to see your task for Session 2.
sophia 6/7/06 8:05:32 AM EDT: ok
Aza2 6/7/06 8:05:35 AM EDT: ok
Xinliang2 joins the room 6/7/06 8:08:12 AM EDT
Aza2 6/7/06 8:08:18 AM EDT: hi xinliang
rtoledosj 6/7/06 8:08:37 AM EDT: Hi Xinliang
Xinliang2 6/7/06 8:09:01 AM EDT: hi!!
sophia 6/7/06 8:09:22 AM EDT: hihihi
Aza2 6/7/06 8:09:32 AM EDT: gd roohiya is here too
Roohiya2 joins the room 6/7/06 8:09:38 AM EDT
Aza2 6/7/06 8:09:48 AM EDT: hi roo
rtoledosj 6/7/06 8:10:18 AM EDT: To see what has happened before, you can click on the 'double arrow' icon at the upper right corner of the chat box.
rtoledosj 6/7/06 8:10:27 AM EDT: Hi Roohiya2
Roohiya2 6/7/06 8:10:36 AM EDT: hello
Xinliang2 6/7/06 8:11:09 AM EDT: do we have a new topic?
Aza2 6/7/06 8:11:17 AM EDT: the feedback is tt we should have a formula applicable to all values of N is it?
Aza2 6/7/06 8:11:44 AM EDT: scroll down
sophia 6/7/06 8:11:50 AM EDT: er,i think so
Aza2 6/7/06 8:11:51 AM EDT: in the view topic
Aza2 6/7/06 8:12:07 AM EDT: the instructions for session 2 and 3 are there
Roohiya2 6/7/06 8:12:16 AM EDT: do we start a new topic
Aza2 6/7/06 8:12:22 AM EDT: no
Aza2 6/7/06 8:12:29 AM EDT: actually.... im not sure
Roohiya2 6/7/06 8:12:37 AM EDT: then we continue on the same one
Aza2 6/7/06 8:12:37 AM EDT: coz i dont understand wat they mean
Aza2 6/7/06 8:12:55 AM EDT: the dunno wat new patterns etc
sophia 6/7/06 8:13:10 AM EDT: we are to consider other polygons to do patterns
Aza2 6/7/06 8:13:19 AM EDT: ok
Xinliang2 6/7/06 8:13:26 AM EDT: i think we have to group similar numbers together
Aza2 6/7/06 8:13:30 AM EDT: but we have to discuss feedback first right
sophia 6/7/06 8:13:37 AM EDT: i understand-- to form patterns with other types of polygons
Xinliang2 6/7/06 8:13:38 AM EDT: so tht it won't look so complicated
Aza2 6/7/06 8:13:56 AM EDT: omg
sophia 6/7/06 8:14:02 AM EDT: then, to get fomula for the patterns
Roohiya2 6/7/06 8:14:11 AM EDT: ppl i dun understand wat's going on
Aza2 6/7/06 8:14:13 AM EDT: the no. of sticks is so simple
Aza2 6/7/06 8:14:34 AM EDT: its juz N(N+3)
sophia 6/7/06 8:14:49 AM EDT: really?
Xinliang2 6/7/06 8:14:55 AM EDT: really?
Xinliang2 6/7/06 8:15:00 AM EDT: how do u do it?
Aza2 6/7/06 8:15:18 AM EDT: see when n is 1
sophia 6/7/06 8:15:18 AM EDT: yep, how do you do it?
Aza2 6/7/06 8:15:30 AM EDT: its 1 times (1+3) which is 4
Xinliang2 6/7/06 8:15:43 AM EDT: yes.go on
sophia 6/7/06 8:15:53 AM EDT: yep...
Roohiya2 6/7/06 8:16:06 AM EDT: that's ok but how did u go abt finding the formula
Aza2 6/7/06 8:16:07 AM EDT: and for N=2
Aza2 6/7/06 8:16:14 AM EDT: 2 times (2+3)
Aza2 6/7/06 8:16:17 AM EDT: which is 10
sophia 6/7/06 8:16:31 AM EDT: N os the munber of squares isit?
Aza2 6/7/06 8:16:44 AM EDT: no the pattern no
Xinliang2 6/7/06 8:16:47 AM EDT: N is the pattern no.
Aza2 6/7/06 8:16:53 AM EDT: i got the formula by guessing
Roohiya2 6/7/06 8:17:00 AM EDT: ooooooooh
sophia 6/7/06 8:17:02 AM EDT: oh..
Aza2 6/7/06 8:17:14 AM EDT: i did like 4=2 times 2
Aza2 6/7/06 8:17:18 AM EDT: or 2+2
Roohiya2 6/7/06 8:17:20 AM EDT: so is tt how we go abt doing in exams
Aza2 6/7/06 8:17:27 AM EDT: or 1times 4
Aza2 6/7/06 8:17:34 AM EDT: and 1 times 4
Aza2 6/7/06 8:17:39 AM EDT: is actually
Aza2 6/7/06 8:17:44 AM EDT: 1 times 1+3
sophia 6/7/06 8:17:45 AM EDT: er...
Aza2 6/7/06 8:17:48 AM EDT: so yah
Aza2 6/7/06 8:18:07 AM EDT: i feel so...
Aza2 6/7/06 8:18:11 AM EDT: nvm
Aza2 6/7/06 8:18:20 AM EDT: so my point is
Roohiya2 6/7/06 8:18:25 AM EDT: anw wat do we do next
Aza2 6/7/06 8:18:30 AM EDT: there has got to be a simpler way for no. of squares
Aza2 6/7/06 8:19:10 AM EDT: i have a really weird formula for no. of squares
Roohiya2 6/7/06 8:19:32 AM EDT: i thought we already found the formula
Aza2 6/7/06 8:19:43 AM EDT: its N times (N-1)(0.5)
Aza2 6/7/06 8:19:51 AM EDT: they think its too complicated
sophia 6/7/06 8:20:17 AM EDT: wait your that one cannot work for 1 square
Aza2 6/7/06 8:20:17 AM EDT: they want a COMMON formula for ALL values of N
Xinliang2 6/7/06 8:20:28 AM EDT: ur formula iirds kinda we
Xinliang2 6/7/06 8:20:38 AM EDT: but let's try it out!!
Aza2 6/7/06 8:20:38 AM EDT: i noe...
Aza2 6/7/06 8:20:49 AM EDT: but i THINK it works
Aza2 6/7/06 8:20:53 AM EDT: nvm
Aza2 6/7/06 8:21:11 AM EDT: actually
Xinliang2 6/7/06 8:21:15 AM EDT: c'mmon don'y give up
Aza2 6/7/06 8:21:16 AM EDT: i made an error
Xinliang2 6/7/06 8:21:29 AM EDT: let's continue to try!!!
Aza2 6/7/06 8:21:47 AM EDT: ok wait
sophia 6/7/06 8:21:52 AM EDT: the last number to add is the pattern no.
Aza2 6/7/06 8:21:53 AM EDT: ill tell u the pattern
Aza2 6/7/06 8:22:12 AM EDT: for N=2, the no. of sticks is N times 1.5
Aza2 6/7/06 8:22:21 AM EDT: for N=3, its N times 2
M
Aza2 6/7/06 8:22:33 AM EDT: for N=4, its N times 2.5
Aza2 6/7/06 8:22:35 AM EDT: etc etc
M
Xinliang2 6/7/06 8:23:56 AM EDT: so do u mean for every pattern, we have to add 0.5 to the previous no.?
Aza2 6/7/06 8:24:25 AM EDT: yup
sophia 6/7/06 8:24:39 AM EDT: but fot N pattern, you wont know when the adding of 0.5 will end
Aza2 6/7/06 8:24:40 AM EDT: but tt still doesnt gv a COMMON formula
Aza2 6/7/06 8:24:51 AM EDT: exactly
Roohiya2 6/7/06 8:24:56 AM EDT: the number of squres increases by 1 every time
Aza2 6/7/06 8:25:17 AM EDT: so we can TRY to get a formula from this....... i guess
sophia 6/7/06 8:25:31 AM EDT: wat is the formula for the no. of sticks?
Aza2 6/7/06 8:25:44 AM EDT: tts wat im trying to figure out
sophia 6/7/06 8:25:48 AM EDT: isit N(N+3)?
Roohiya2 6/7/06 8:25:49 AM EDT: the one we got is too long
Aza2 6/7/06 8:25:59 AM EDT: oh for sticks yah
Aza2 6/7/06 8:26:10 AM EDT: why its tt way, dont ask me
Roohiya2 6/7/06 8:26:11 AM EDT: tt's the no. of sticks
Aza2 6/7/06 8:26:15 AM EDT: coz i really dont noe
Xinliang2 6/7/06 8:26:29 AM EDT: so the formula 4 sticks is N(N+3)?
Roohiya2 6/7/06 8:26:37 AM EDT: yes
sophia 6/7/06 8:26:37 AM EDT: yep
Xinliang2 6/7/06 8:26:45 AM EDT: ok
Roohiya2 6/7/06 8:27:02 AM EDT: now we have find the formula for the sq.
Aza2 6/7/06 8:27:13 AM EDT: its frustrating right? we tried so much and we figure it out now...
Xinliang2 6/7/06 8:27:15 AM EDT: ok
Xinliang2 6/7/06 8:27:21 AM EDT: yah...
Xinliang2 6/7/06 8:27:26 AM EDT: but dun give up
Xinliang2 6/7/06 8:27:31 AM EDT: we can do it!!
sophia 6/7/06 8:28:18 AM EDT: yep
sophia 6/7/06 8:28:19 AM EDT:
sophia 6/7/06 8:28:22 AM EDT: haha
Roohiya2 6/7/06 8:28:36 AM EDT: yes ppl can we go on
sophia 6/7/06 8:28:46 AM EDT: i agree man!
Roohiya2 6/7/06 8:29:39 AM EDT: is it (n+1)
Aza2 6/7/06 8:29:43 AM EDT: is the formula right?
Xinliang2 6/7/06 8:29:54 AM EDT: can the formula on the whiteboard work?
Roohiya2 6/7/06 8:30:05 AM EDT: sorry is it n
Roohiya2 6/7/06 8:30:19 AM EDT: sorry tt's wrong too
sophia 6/7/06 8:30:25 AM EDT: nope, i think the formula shld be 'longer'
Aza2 6/7/06 8:30:30 AM EDT: i so wish i could write, its so much easier
Xinliang2 6/7/06 8:30:39 AM EDT: mine is adding the consecutive no together
Aza2 6/7/06 8:30:42 AM EDT: is the formula in the square right
Aza2 6/7/06 8:30:46 AM EDT: the one i juz added
Xinliang2 6/7/06 8:30:46 AM EDT: yeah
M M
Aza2 6/7/06 8:31:19 AM EDT: wats sophia doing
sophia 6/7/06 8:31:36 AM EDT: er, some error
Aza2 6/7/06 8:32:07 AM EDT: the whiteboard is so messy
Roohiya2 6/7/06 8:32:10 AM EDT: i dun see anything
Xinliang2 6/7/06 8:32:14 AM EDT: u know the formula we got the previous time?
Xinliang2 6/7/06 8:32:19 AM EDT: it works
Aza2 6/7/06 8:32:19 AM EDT: yah
Aza2 6/7/06 8:32:29 AM EDT: they said u need a common formula
Aza2 6/7/06 8:32:49 AM EDT: as in
Aza2 6/7/06 8:33:08 AM EDT: the formula shouldn't be like dependant on N
Aza2 6/7/06 8:33:20 AM EDT: as in u noe wat is in between
Aza2 6/7/06 8:33:26 AM EDT: do u get wat i mean?
Roohiya2 6/7/06 8:33:37 AM EDT: no
Roohiya2 6/7/06 8:33:37 AM EDT:
Aza2 6/7/06 8:33:38 AM EDT: u should noe all the values u r using
sophia 6/7/06 8:33:39 AM EDT: i think couldit be (N+1)(N/2)
Roohiya2 6/7/06 8:33:53 AM EDT: why
Aza2 6/7/06 8:33:59 AM EDT: lets try
sophia 6/7/06 8:34:10 AM EDT: er, i got that thing from pattern 3
Roohiya2 6/7/06 8:35:04 AM EDT: ya but 4 pattern 1 u get a dec.
Aza2 6/7/06 8:35:07 AM EDT: i think it works
Aza2 6/7/06 8:35:16 AM EDT: yay!
Aza2 6/7/06 8:35:20 AM EDT: it works
Aza2 6/7/06 8:35:23 AM EDT: gd job sophia
Xinliang2 6/7/06 8:35:32 AM EDT: it works!!!
Xinliang2 6/7/06 8:35:43 AM EDT: how do u get tht sophia?
sophia 6/7/06 8:35:46 AM EDT: really?
Roohiya2 6/7/06 8:35:48 AM EDT: how
sophia 6/7/06 8:36:36 AM EDT: coz in pattern 3 rite, there is a odd number, which is 2, which is half of 1+3, so i got it
Roohiya2 6/7/06 8:36:45 AM EDT: ppl can it work for pattern 1
Aza2 6/7/06 8:36:57 AM EDT: yah its 2 times half
Roohiya2 6/7/06 8:37:11 AM EDT: oh yes
Roohiya2 6/7/06 8:37:35 AM EDT: WE GOT IT!!!!!!!!!!!!!!!!!!!!!!!!!
Roohiya2 6/7/06 8:37:41 AM EDT: YAY!!!!!!!!!!!!!!!!!!!!!
Xinliang2 6/7/06 8:37:46 AM EDT: yay!!
sophia 6/7/06 8:37:48 AM EDT: it works for the pther pattern too!
Xinliang2 6/7/06 8:37:49 AM EDT: thnks sophia
sophia 6/7/06 8:37:56 AM EDT: bwahahaha
Roohiya2 6/7/06 8:38:15 AM EDT: so are we done?
Aza2 6/7/06 8:38:16 AM EDT: y couldnt u get in for the last session
Xinliang2 6/7/06 8:38:17 AM EDT: so now we haf to make changes in the whiteboard
Aza2 6/7/06 8:38:17 AM EDT: sigh
Aza2 6/7/06 8:38:20 AM EDT: yup
Aza2 6/7/06 8:38:29 AM EDT: its done
Aza2 6/7/06 8:38:39 AM EDT: ill erase the old one
Aza2 6/7/06 8:39:04 AM EDT: (sigh) xinliang all our hard work
sophia 6/7/06 8:39:23 AM EDT: how to'write on the board?
sophia 6/7/06 8:39:25 AM EDT: wait
Aza2 6/7/06 8:39:33 AM EDT: the textbox
sophia 6/7/06 8:39:36 AM EDT: dont erase the tavle
Xinliang2 6/7/06 8:39:37 AM EDT: haha
Aza2 6/7/06 8:39:41 AM EDT: ok
Roohiya2 6/7/06 8:39:44 AM EDT: ppl i forgot how to erase
Xinliang2 6/7/06 8:39:50 AM EDT: at least we improved it
Aza2 6/7/06 8:39:58 AM EDT: yup
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sophia 6/7/06 8:40:18 AM EDT: just add a new colum to write thenew fomulas for the sticks and the squares
Xinliang2 6/7/06 8:40:19 AM EDT: u cant erhinkase anything i t
Xinliang2 6/7/06 8:40:30 AM EDT: *u can erase anything
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Xinliang2 6/7/06 8:41:29 AM EDT: there's no eraser
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Roohiya2 6/7/06 8:41:45 AM EDT: how do u erase
Aza2 6/7/06 8:42:01 AM EDT: u dont need to erase
Roohiya2 6/7/06 8:42:04 AM EDT: the previous time we ersed it
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Aza2 6/7/06 8:42:43 AM EDT: juz click on the box to edit the text
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Xinliang2 6/7/06 8:43:55 AM EDT: oooh
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sophia 6/7/06 8:44:24 AM EDT: i see
Aza2 6/7/06 8:44:25 AM EDT: im juz copying and pasting for the no. of squares
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Roohiya2 6/7/06 8:45:28 AM EDT: so aren't we done with this question
Aza2 6/7/06 8:45:46 AM EDT: yes but we have to make the changes
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Roohiya2 6/7/06 8:46:06 AM EDT: where
Aza2 6/7/06 8:46:19 AM EDT: done
Aza2 6/7/06 8:46:24 AM EDT: the table has been edited
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Roohiya2 6/7/06 8:46:38 AM EDT: yah
Aza2 6/7/06 8:46:48 AM EDT: so less complicated
Roohiya2 6/7/06 8:46:58 AM EDT: i noe
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Aza2 6/7/06 8:47:19 AM EDT: who's mrt?
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rtoledosj 6/7/06 8:47:41 AM EDT: mrt is another facilitator.
Aza2 6/7/06 8:47:52 AM EDT: oh
sophia 6/7/06 8:47:56 AM EDT: wat do we do next?
Aza2 6/7/06 8:48:08 AM EDT: discuss probs related to matchsticks?
rtoledosj 6/7/06 8:48:26 AM EDT: At ths point, you can begin to think in terms of other patterns that you might want to explore.
Xinliang2 6/7/06 8:48:38 AM EDT: we haf to work on qn 2 of section 2
Roohiya2 6/7/06 8:48:46 AM EDT: is this the only question we are going to do?
Aza2 6/7/06 8:49:23 AM EDT: u mean like pyramids etc made from matchsticks?
Xinliang2 6/7/06 8:50:04 AM EDT: and polygons
Aza2 6/7/06 8:50:16 AM EDT: so like pyramids using triangles
sophia 6/7/06 8:50:36 AM EDT: wat do we do? isit think of the other pattern for other polygons?
Aza2 6/7/06 8:50:55 AM EDT: maybe we should juz look through our primary sch problem sums
Aza2 6/7/06 8:51:05 AM EDT: they ALWAYS used to give patterns
sophia 6/7/06 8:51:24 AM EDT: haha
Aza2 6/7/06 8:51:33 AM EDT: and the legs one was another favourite
Roohiya2 6/7/06 8:51:56 AM EDT: ppl do not digress
Aza2 6/7/06 8:52:06 AM EDT: ok ok
sophia 6/7/06 8:52:14 AM EDT: arh, the cow and the chicken legs...
Xinliang2 6/7/06 8:52:21 AM EDT: yah
Xinliang2 6/7/06 8:52:26 AM EDT: i know this qn
sophia 6/7/06 8:52:26 AM EDT: ops sory
Xinliang2 6/7/06 8:52:38 AM EDT: do we wrap up this session
Xinliang2 6/7/06 8:52:49 AM EDT: it's about time already.
Aza2 6/7/06 8:52:55 AM EDT: no we're supposed to discuss other patterns
Aza2 6/7/06 8:52:59 AM EDT: i think
Roohiya2 6/7/06 8:53:26 AM EDT: maybe a rectangle would be good
sophia 6/7/06 8:53:41 AM EDT: hey, cool
Roohiya2 6/7/06 8:53:44 AM EDT: u noe it is the same as a square
sophia 6/7/06 8:53:46 AM EDT: lets try on that
Roohiya2 6/7/06 8:53:55 AM EDT: ok
Roohiya2 6/7/06 8:53:57 AM EDT: ok
sophia 6/7/06 8:54:19 AM EDT: a rectangle made up of 6 sticks
Roohiya2 6/7/06 8:54:23 AM EDT: or a parrellologram
sophia 6/7/06 8:54:52 AM EDT: yep, but both of them has similar concepts
Aza2 6/7/06 8:54:54 AM EDT: ppl.... did u see the VMT Wiki link
Aza2 6/7/06 8:54:57 AM EDT: its freaky
Aza2 6/7/06 8:55:13 AM EDT: the explanations they have there are so... complicated
sophia 6/7/06 8:55:21 AM EDT: as in the number of sticks and no. of shapes
sophia 6/7/06 8:55:38 AM EDT: you mean the pattern qns?
Roohiya2 6/7/06 8:55:51 AM EDT: oh i understand
Xinliang2 6/7/06 8:56:03 AM EDT: im sorry but i need to go already
Roohiya2 6/7/06 8:56:09 AM EDT: we have to use sq. but in diff patterns
Aza2 6/7/06 8:56:13 AM EDT: its ok
Aza2 6/7/06 8:56:16 AM EDT: bye
Roohiya2 6/7/06 8:56:37 AM EDT: ok xinliang but r u going tomorrow for lessons
Aza2 6/7/06 8:56:44 AM EDT: (gulp) wats recursion?
sophia 6/7/06 8:56:45 AM EDT: yep, bb to xin liang
Xinliang2 6/7/06 8:57:01 AM EDT: im going 4 lessons tmr
Aza2 6/7/06 8:57:01 AM EDT: and induction
Xinliang2 6/7/06 8:57:02 AM EDT: c ya
Xinliang2 6/7/06 8:57:04 AM EDT: (:
sophia 6/7/06 8:57:05 AM EDT: wats that?
Xinliang2 6/7/06 8:57:06 AM EDT: sorry
Aza2 6/7/06 8:57:08 AM EDT: bb
Aza2 6/7/06 8:57:11 AM EDT: its there
Aza2 6/7/06 8:57:24 AM EDT: read in the session II and III section
Aza2 6/7/06 8:57:26 AM EDT: Q 2
Aza2 6/7/06 8:57:32 AM EDT: the last part
Aza2 6/7/06 8:57:38 AM EDT: no prob
sophia 6/7/06 8:57:43 AM EDT: ok... wait
Roohiya2 6/7/06 8:58:06 AM EDT: so do we wrap up this session
Aza2 6/7/06 8:58:32 AM EDT: hang on
Roohiya2 6/7/06 8:58:32 AM EDT: is anyone listening to me?
sophia 6/7/06 8:58:33 AM EDT: eh, its some form of ways to present your workings
sophia 6/7/06 8:58:52 AM EDT: yep, i here
Aza2 6/7/06 8:58:58 AM EDT: the other team is still there
sophia 6/7/06 8:59:01 AM EDT: we need to wrap up the session
Aza2 6/7/06 8:59:13 AM EDT: maybe we should try to start on question 2
Roohiya2 6/7/06 8:59:21 AM EDT: hello ppl i exist
Aza2 6/7/06 8:59:26 AM EDT: or else session 3 will be a mad rush
sophia 6/7/06 8:59:31 AM EDT: hi roohiya
Aza2 6/7/06 8:59:32 AM EDT: we noe tt roo
rtoledosj 6/7/06 8:59:34 AM EDT: You can always agree among yourelves to continue this session on your own.
Roohiya2 6/7/06 8:59:53 AM EDT: lets continue for little more time
sophia 6/7/06 8:59:59 AM EDT: ok
Roohiya2 6/7/06 9:00:08 AM EDT: on a different qn pls
sophia 6/7/06 9:00:16 AM EDT: we've decided to do on rectangles rite?
Aza2 6/7/06 9:00:20 AM EDT: truthfully, i still dont understand wat they want from us... as in do we concentrate on a prob of our own or many problems
rtoledosj 6/7/06 9:00:21 AM EDT: Are you all working from your homes?
Aza2 6/7/06 9:00:30 AM EDT: yup
Roohiya2 6/7/06 9:00:34 AM EDT: yes
sophia 6/7/06 9:00:35 AM EDT: er, ya
Aza2 6/7/06 9:00:46 AM EDT: y?
rtoledosj 6/7/06 9:01:26 AM EDT: If somebody still has to go home from school, that may mean that we really need to end soon.
Roohiya2 6/7/06 9:01:48 AM EDT: sorry?
Aza2 6/7/06 9:01:55 AM EDT: its actually our holidays so i dont think any1 would stay till so late in sch
rtoledosj 6/7/06 9:02:02 AM EDT: The idea is for you to come up with your own problems to explore.
Roohiya2 6/7/06 9:02:12 AM EDT: and it is 9 at night now
Aza2 6/7/06 9:02:14 AM EDT: ok
sophia 6/7/06 9:02:21 AM EDT: yep, i agree too
sophia 6/7/06 9:03:06 AM EDT: anw, shall we try those qn that is non pattern?
Aza2 6/7/06 9:03:14 AM EDT: we could get started on the rectangle and the next session try something else, like 3d
Roohiya2 6/7/06 9:03:36 AM EDT: ok
sophia 6/7/06 9:03:42 AM EDT: hmmm, i dont mind that
sophia 6/7/06 9:03:59 AM EDT: a rectangle has 6 sticks
Roohiya2 6/7/06 9:04:11 AM EDT: ya
Aza2 6/7/06 9:04:13 AM EDT: so that will be fig. 1
sophia 6/7/06 9:04:26 AM EDT: 2rectangles have 10 sticks
sophia 6/7/06 9:04:36 AM EDT: they are stacked
Roohiya2 6/7/06 9:04:47 AM EDT: we need more space in the whiteboard
Aza2 6/7/06 9:04:53 AM EDT: actually they would have more
Aza2 6/7/06 9:05:01 AM EDT: coz they need to look similar
Aza2 6/7/06 9:05:10 AM EDT: if u stack them, they wont look similar
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sophia 6/7/06 9:05:18 AM EDT: can we draw on the board?
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sophia 6/7/06 9:05:31 AM EDT: oh, i see
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Roohiya2 6/7/06 9:05:42 AM EDT: tt's why there i s no space
Aza2 6/7/06 9:05:45 AM EDT: c wat i mean
Aza2 6/7/06 9:05:50 AM EDT: they dont look similar
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sophia 6/7/06 9:05:57 AM EDT: or we make like the sq thingy?
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Aza2 6/7/06 9:06:09 AM EDT: shouldnt it be like this
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Aza2 6/7/06 9:07:16 AM EDT: wat i mean is... fig 1 should have a similar shape to fig 2 and fig 2 to fig 3 etc
Roohiya2 6/7/06 9:07:23 AM EDT: ppl wat r we doing
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sophia 6/7/06 9:07:42 AM EDT: i c....
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rtoledosj 6/7/06 9:08:52 AM EDT: You can erase some of th drawings that you have on the whiteboard to have more space for new drawings.
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Aza2 6/7/06 9:08:58 AM EDT: something like tt
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Aza2 6/7/06 9:09:09 AM EDT: u guys wanna erase the old drawing
Aza2 6/7/06 9:09:14 AM EDT: more space
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sophia 6/7/06 9:09:25 AM EDT: yep
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rtoledosj 6/7/06 9:11:15 AM EDT: You can always look at what the whiteboard was like by using the whiteboard scroll button at the left of the screen. It's that thing which is close to '2005-2006 fraunhofer' at the lower left of the screen.
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Aza2 6/7/06 9:11:35 AM EDT: oh
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rtoledosj 6/7/06 9:12:19 AM EDT: You move that thing up and you see what the whiteboard looked like before you changed it.
sophia 6/7/06 9:12:19 AM EDT: did you see that?
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Aza2 6/7/06 9:12:39 AM EDT: c wat?
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sophia 6/7/06 9:13:16 AM EDT: by scrolling the round buttons, you can see the changes
sophia 6/7/06 9:13:20 AM EDT: done b4
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Aza2 6/7/06 9:13:29 AM EDT: oh
Aza2 6/7/06 9:13:38 AM EDT: cool
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Roohiya2 6/7/06 9:15:25 AM EDT: ok ppl i need to go now
Aza2 6/7/06 9:15:34 AM EDT: ok bye
sophia 6/7/06 9:15:38 AM EDT: ok bb
Roohiya2 6/7/06 9:15:41 AM EDT: bye
sophia 6/7/06 9:15:43 AM EDT: cya
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Roohiya2 leaves the room 6/7/06 9:16:01 AM EDT
Aza2 6/7/06 9:16:23 AM EDT: btw, wat are all those questions in your rooms for?
Aza2 6/7/06 9:16:33 AM EDT: i mean my rooms
rtoledosj 6/7/06 9:16:33 AM EDT: To know the other cool features of this environment, you can click on the tab with the '?/ mark beside the 'Send Mail' tab.
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sophia 6/7/06 9:18:51 AM EDT: the fomula for that one is 6+5+4+3
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Aza2 6/7/06 9:19:01 AM EDT: that one?
Aza2 6/7/06 9:19:04 AM EDT: which one?
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sophia 6/7/06 9:19:37 AM EDT: for ther picture you drew for fig 2
Aza2 6/7/06 9:19:46 AM EDT: oh
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sophia 6/7/06 9:20:25 AM EDT: the no of rectangles is N^2
Aza2 6/7/06 9:20:27 AM EDT: the no. of rectangles is simple
Aza2 6/7/06 9:20:31 AM EDT: yup
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sophia 6/7/06 9:21:31 AM EDT: but i fig 3, the no of sticks is funny, as in the pattern
Aza2 6/7/06 9:22:06 AM EDT: i noe the pattern is very weirdly drawn but i did it in a hurry
Aza2 6/7/06 9:22:11 AM EDT: can u count the no of sticks and check
Aza2 6/7/06 9:22:20 AM EDT: i might have counted wrongly
sophia 6/7/06 9:22:28 AM EDT: i mean the pattern for the number of sticks
Aza2 6/7/06 9:23:07 AM EDT: oh tt
Aza2 6/7/06 9:23:29 AM EDT: u want me to draw fig 4 so tt its easier to spot a pattern?
sophia 6/7/06 9:23:46 AM EDT: yep you can try
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Aza2 6/7/06 9:26:10 AM EDT: all are multiples of 6
sophia 6/7/06 9:26:12 AM EDT: for fig 3 rite, it's 42sticks
Aza2 6/7/06 9:26:19 AM EDT: really
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Aza2 6/7/06 9:27:43 AM EDT: im still getting 36... how?
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sophia 6/7/06 9:27:55 AM EDT: the formula is 2(N)(N+1)+(N)(N+1)
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Aza2 6/7/06 9:28:25 AM EDT: isnt tt the same as 3(N)(N+1)
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sophia 6/7/06 9:28:55 AM EDT: oh, ya
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Aza2 6/7/06 9:30:15 AM EDT: so wats the right no. of matchsticks in fig 3?
sophia 6/7/06 9:30:33 AM EDT: er, i got 42
sophia 6/7/06 9:31:13 AM EDT: theres 4 of the 6 sticks and 4 of the 3sticks
Aza2 6/7/06 9:31:29 AM EDT: u still getting 42... im still getting 36
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Aza2 6/7/06 9:31:35 AM EDT: wait lemme count again
sophia 6/7/06 9:31:53 AM EDT: wait i got 36 too
Aza2 6/7/06 9:32:01 AM EDT: u did?
sophia 6/7/06 9:32:10 AM EDT: sry
Aza2 6/7/06 9:32:24 AM EDT: u noe wat
sophia 6/7/06 9:32:26 AM EDT: i sort of counted wrongly i think
Aza2 6/7/06 9:32:32 AM EDT: its similar to our prev pattern
sophia 6/7/06 9:32:47 AM EDT: in what way?
Aza2 6/7/06 9:33:02 AM EDT: wait
Aza2 6/7/06 9:33:07 AM EDT: ill show on the whiteboard
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Aza2 6/7/06 9:35:03 AM EDT: the pattern for the no. of matchsticks is simply the (no. of squares in the other one) times 6
Aza2 6/7/06 9:35:45 AM EDT: so we have two formulas
sophia 6/7/06 9:36:00 AM EDT: and they are...
sophia 6/7/06 9:36:12 AM EDT: coz i still dont gettit
Aza2 6/7/06 9:36:19 AM EDT: 3(N)(N+1) and 6(N+1)(N/2)
Aza2 6/7/06 9:36:31 AM EDT: which is the same thing
Aza2 6/7/06 9:36:36 AM EDT: nvm
sophia 6/7/06 9:36:40 AM EDT: yep
sophia 6/7/06 9:37:13 AM EDT: any, i got to go now, sry......
Aza2 6/7/06 9:37:26 AM EDT: wat i meant was tt the no. of squares is equal to the no. of GROUPS OF 6 matchsticks
Aza2 6/7/06 9:37:26 AM EDT: ok
Aza2 6/7/06 9:37:31 AM EDT: then even i better go
Aza2 6/7/06 9:38:03 AM EDT: np bb
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sophia 6/7/06 9:38:16 AM EDT: bb
sophia leaves the room 6/7/06 9:38:16 AM EDT
rtoledosj 6/7/06 9:39:30 AM EDT: Ok. Aza2, bye.
Aza2 6/7/06 9:39:50 AM EDT: yup
Aza2 6/7/06 9:39:54 AM EDT: bye
Aza2 leaves the room 6/7/06 9:39:58 AM EDT
rtoledosj leaves the room 6/7/06 9:41:28 AM EDT
tutor joins the room 6/7/06 4:32:28 PM EDT
tutor leaves the room 6/7/06 4:40:39 PM EDT
tutor joins the room 6/7/06 10:03:06 PM EDT
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tutor 6/7/06 10:58:10 PM EDT: tutor sent an email to room members.
Subject: Session 2 feedback
Message:
We have looked at your Session 2 work and we have put our feedback on the whiteboard.
tutor leaves the room 6/7/06 10:58:19 PM EDT

==Session III==
rtoledosj joins the room 6/8/06 7:50:19 AM EDT
Xinliang2 joins the room 6/8/06 8:02:32 AM EDT
sophia joins the room 6/8/06 8:03:06 AM EDT
sophia joins the room 6/8/06 8:04:21 AM EDT
Xinliang2 6/8/06 8:05:40 AM EDT: where is aza?
sophia 6/8/06 8:07:08 AM EDT: i tried to call her but i cant reach her
Xinliang2 6/8/06 8:07:30 AM EDT: oh...then how?
sophia 6/8/06 8:08:52 AM EDT: eh,im not sure leh, as in they are not in school today, so its difficult to contact them
Xinliang2 6/8/06 8:09:42 AM EDT: ok
Xinliang2 6/8/06 8:09:56 AM EDT: so we continue with session 3 ok?
sophia 6/8/06 8:10:04 AM EDT: yep
Xinliang2 6/8/06 8:10:13 AM EDT: alright
Xinliang2 6/8/06 8:10:40 AM EDT: so wad did u discover in the no. of rectangles n sticks
rtoledosj leaves the room 6/8/06 8:10:59 AM EDT
sophia 6/8/06 8:12:06 AM EDT: the no. of sticks for the rectangleis 3N(N+1)
sophia 6/8/06 8:12:27 AM EDT: and the no. of rectangles is N^2
Xinliang2 6/8/06 8:13:05 AM EDT: how do u test it out?
nan joins the room 6/8/06 8:13:06 AM EDT
sophia 6/8/06 8:13:31 AM EDT: we saw the pattern
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jsarmi joins the room 6/8/06 8:14:09 AM EDT
nan 6/8/06 8:14:12 AM EDT: hi, i joined because i noticed ramon left
nan 6/8/06 8:14:22 AM EDT: hi jsarmi
sophia 6/8/06 8:14:24 AM EDT: er, ok...
Xinliang2 6/8/06 8:14:29 AM EDT: hi
nan 6/8/06 8:14:31 AM EDT: we're here in case you have any questions
Xinliang2 6/8/06 8:14:50 AM EDT: thanks
nan 6/8/06 8:14:58 AM EDT: sure
Xinliang2 6/8/06 8:15:14 AM EDT: so now we are going to work on triangles
sophia 6/8/06 8:15:38 AM EDT: orshall wetry with 3D shapes?
jsarmi leaves the room 6/8/06 8:15:44 AM EDT
Xinliang2 6/8/06 8:16:09 AM EDT: hold on
sophia 6/8/06 8:16:31 AM EDT: ok
Xinliang2 6/8/06 8:19:13 AM EDT: im back
Xinliang2 6/8/06 8:19:19 AM EDT: i went to take a phone call
Xinliang2 6/8/06 8:19:21 AM EDT: sorry
sophia 6/8/06 8:19:37 AM EDT: its alright
Xinliang2 6/8/06 8:19:40 AM EDT: the 3d figures are much more challenging
Xinliang2 6/8/06 8:19:50 AM EDT: can we try the triangles?
rtoledosj joins the room 6/8/06 8:19:52 AM EDT
sophia 6/8/06 8:19:58 AM EDT: ok
Xinliang2 6/8/06 8:20:50 AM EDT: so now we find the pattern for the no. of sticks use alright?
sophia 6/8/06 8:21:03 AM EDT: yep
Xinliang2 6/8/06 8:21:15 AM EDT: do u know how to extend the whiteboard space?
rtoledosj 6/8/06 8:21:15 AM EDT: Sorry, my Internet connection disconnected.
Xinliang2 6/8/06 8:21:26 AM EDT: it's alright
sophia 6/8/06 8:21:39 AM EDT: eh nope.\\
Xinliang2 6/8/06 8:21:41 AM EDT: there's no space on the whtieboard left
sophia 6/8/06 8:21:56 AM EDT: we can erase the board
rtoledosj 6/8/06 8:21:59 AM EDT: Thanks! My connection went down.
Xinliang2 6/8/06 8:22:33 AM EDT: rtoledosj and nan, do u know how to extend the whiteboard?
nan 6/8/06 8:22:34 AM EDT: no problem. i will stay in case:-)
rtoledosj 6/8/06 8:22:46 AM EDT: Thnaks.
rtoledosj 6/8/06 8:22:53 AM EDT: Thanks!
sophia 6/8/06 8:23:25 AM EDT: so howdo we extend the board?
Xinliang2 6/8/06 8:23:45 AM EDT: is nan teaching us how to extend the whiteboard?
rtoledosj 6/8/06 8:24:02 AM EDT: The board cannot be extended. :-(
sophia 6/8/06 8:24:26 AM EDT: eh, can we erase the stuffs on the board?
nan 6/8/06 8:24:27 AM EDT: you can't extend the board
nan 6/8/06 8:24:44 AM EDT: what you can do is to delete things or rearrange
rtoledosj 6/8/06 8:24:46 AM EDT: Yes, you can erase the whiteboard.
sophia 6/8/06 8:25:03 AM EDT: ok, thannks
nan 6/8/06 8:25:08 AM EDT: you can always use the bar on the left to scroll up to see the history of the board
nan 6/8/06 8:25:16 AM EDT: every step is preserved
sophia 6/8/06 8:25:16 AM EDT: ok
nan 6/8/06 8:25:23 AM EDT: you're welcome
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Xinliang2 6/8/06 8:26:53 AM EDT: ohhhh
Xinliang2 6/8/06 8:26:55 AM EDT: thanks !!!
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Xinliang2 6/8/06 8:27:23 AM EDT: then are we supposed to erase the feedback too?
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nan 6/8/06 8:27:39 AM EDT: you certainly can
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Xinliang2 6/8/06 8:29:47 AM EDT: sophia, are we erasing the rectangle diagram?
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Xinliang2 6/8/06 8:31:46 AM EDT: sophia, are we going to erase the rectangle diagram?
nan 6/8/06 8:35:41 AM EDT: hi sophia, are you there?
nan 6/8/06 8:36:30 AM EDT: i suspect if she's having technical problem
Xinliang2 6/8/06 8:36:43 AM EDT: nan, how come i cant seem to write on the whiteboard?
Xinliang2 6/8/06 8:36:53 AM EDT: i'll go and call her
nan 6/8/06 8:37:21 AM EDT: can you check if the history bar on the left is scrolled all the way down to the bottom?
nan 6/8/06 8:37:33 AM EDT: which means the status is current?
nan 6/8/06 8:37:52 AM EDT: if it's not, you cannot perform actions on the board
nan 6/8/06 8:37:57 AM EDT: ok
sophia leaves the room 6/8/06 8:39:58 AM EDT
Xinliang2 6/8/06 8:40:22 AM EDT: sophia tries to come in again
nan 6/8/06 8:40:39 AM EDT: i see. what was the problem?
Xinliang2 6/8/06 8:40:45 AM EDT: i see a nice clean whiteboard
Xinliang2 6/8/06 8:41:05 AM EDT: she cant seem to get the latest message
nan 6/8/06 8:41:13 AM EDT: hmm
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sophia joins the room 6/8/06 8:41:58 AM EDT
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rtoledosj 6/8/06 8:42:03 AM EDT: The rectangle problem is still on the whiteboard.
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Xinliang2 6/8/06 8:42:20 AM EDT: i think it's alright
Xinliang2 6/8/06 8:42:25 AM EDT: there's still space
Xinliang2 6/8/06 8:42:29 AM EDT: (:
Xinliang2 6/8/06 8:42:31 AM EDT: (:
rtoledosj 6/8/06 8:42:40 AM EDT: ok.
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nan 6/8/06 8:42:44 AM EDT: hi sophia, sorry we lost you for a little while
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nan 6/8/06 8:42:52 AM EDT: is it working for you now?
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Xinliang2 6/8/06 8:43:26 AM EDT: sophia can you see the message and the drawing?
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sophia 6/8/06 8:43:54 AM EDT: hihihihihihi my board takes such a long time to load
Xinliang2 6/8/06 8:44:04 AM EDT: hi
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sophia 6/8/06 8:45:20 AM EDT: yep i can see
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sophia 6/8/06 8:45:40 AM EDT: i think it sldbe likethat
Xinliang2 6/8/06 8:45:41 AM EDT: ok
Xinliang2 6/8/06 8:45:42 AM EDT:
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Xinliang2 6/8/06 8:45:47 AM EDT: let's start the discussion
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Xinliang2 6/8/06 8:45:50 AM EDT: it's rather late
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nan 6/8/06 8:46:15 AM EDT: sorry about the problem
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nan 6/8/06 8:46:21 AM EDT: i will report that
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sophia 6/8/06 8:47:55 AM EDT: i think the pattern sld be like that, to have similar figures while increasing the number
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Xinliang2 6/8/06 8:48:27 AM EDT: oooh
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Xinliang2 6/8/06 8:48:33 AM EDT: i tink you are right
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Xinliang2 6/8/06 8:48:41 AM EDT: cos my diagram seems so easy
Xinliang2 6/8/06 8:48:42 AM EDT: haha
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Xinliang2 6/8/06 8:50:47 AM EDT: is the pattern for the no. of triangles N^2?
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sophia 6/8/06 8:50:55 AM EDT: yep
sophia 6/8/06 8:51:27 AM EDT: anw, despite my ugly diagram the pattern sld beclear
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Xinliang2 6/8/06 8:51:44 AM EDT: it's not that ugly la
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Xinliang2 6/8/06 8:54:16 AM EDT: sophia, are you finishing the 3rd pattern?
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sophia 6/8/06 8:54:28 AM EDT: eh, trying,
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Xinliang2 6/8/06 8:54:38 AM EDT: i help you!!!
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Xinliang2 6/8/06 8:55:21 AM EDT: is it like that?
sophia 6/8/06 8:55:29 AM EDT: ahhhh, herecomes our pattern 3
Xinliang2 6/8/06 8:55:37 AM EDT: it looks kind of unproportional
Xinliang2 6/8/06 8:55:38 AM EDT: hhaha
sophia 6/8/06 8:55:59 AM EDT: anw, as long as it is clear, will do
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Xinliang2 6/8/06 8:56:35 AM EDT: yup
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sophia 6/8/06 8:58:40 AM EDT: i think the board is slow
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Xinliang2 6/8/06 9:00:06 AM EDT: yeah
Xinliang2 6/8/06 9:00:11 AM EDT: it's not responding
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nan 6/8/06 9:00:41 AM EDT: or very slow
nan 6/8/06 9:01:11 AM EDT: we'll check what the problem could be
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Xinliang2 6/8/06 9:02:47 AM EDT: alright
sophia 6/8/06 9:03:05 AM EDT: yep
Xinliang2 6/8/06 9:03:16 AM EDT: sophia, we can also draw out the 4th pattern
rtoledosj 6/8/06 9:03:23 AM EDT: XInliang and Sophia, are you using a dial-up line?
Xinliang2 6/8/06 9:03:42 AM EDT: no, im not using
sophia 6/8/06 9:03:50 AM EDT: nope, its ADSL cable broadband
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rtoledosj 6/8/06 9:04:42 AM EDT: You're using broadband, too?
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sophia 6/8/06 9:04:51 AM EDT: yep
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Xinliang2 6/8/06 9:05:30 AM EDT: i think im using wireless
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Xinliang2 6/8/06 9:05:37 AM EDT: im not very sure too
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rtoledosj 6/8/06 9:07:05 AM EDT: We are trying to find out why you are experiencing a slowdown.
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rtoledosj 6/8/06 9:07:18 AM EDT: Thank you for the information.
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Xinliang2 6/8/06 9:08:12 AM EDT: you are welcome!!
sophia 6/8/06 9:08:32 AM EDT: welcome
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sophia leaves the room 6/8/06 9:10:00 AM EDT
Xinliang2 6/8/06 9:10:24 AM EDT: what happened to sophia?
rtoledosj 6/8/06 9:11:13 AM EDT: I don't know. Did she mention anything about having to leave early?
Xinliang2 6/8/06 9:11:38 AM EDT: nope
rtoledosj 6/8/06 9:12:09 AM EDT: Oops! It's not early! It's 9:10.
rtoledosj 6/8/06 9:12:31 AM EDT: Sophia's back!
Xinliang2 6/8/06 9:12:36 AM EDT: what country are you from
Xinliang2 6/8/06 9:12:41 AM EDT: yeah it's late
Xinliang2 6/8/06 9:13:00 AM EDT: u are in the same timezone as singapore?
sophia joins the room 6/8/06 9:13:05 AM EDT
rtoledosj 6/8/06 9:13:07 AM EDT: No.
sophia 6/8/06 9:13:27 AM EDT: sry, got connection problem
rtoledosj 6/8/06 9:13:28 AM EDT: It's 9:14am here.
Xinliang2 6/8/06 9:14:01 AM EDT: oooh
Xinliang2 6/8/06 9:14:02 AM EDT: hi sophia
sophia 6/8/06 9:14:14 AM EDT: and, the board is very slow to load
Xinliang2 6/8/06 9:14:30 AM EDT: i got to go very soon
rtoledosj 6/8/06 9:15:16 AM EDT: Okay. our final session will be tomorrow, same time.
Xinliang2 6/8/06 9:15:44 AM EDT: is it alright if i leave early?
rtoledosj 6/8/06 9:16:30 AM EDT: We are actually running late. We should have ended 15 minutes ago.
Xinliang2 6/8/06 9:17:21 AM EDT: alright, then i should get going already
rtoledosj 6/8/06 9:17:34 AM EDT: You might want to make a brief summary of what you did and learned during this session. You can post that on the whiteboard.
Xinliang2 6/8/06 9:17:37 AM EDT: are we supposed to send our discussion?
sophia 6/8/06 9:17:47 AM EDT: ok, nvm, we can try tmr, earlier
rtoledosj 6/8/06 9:17:55 AM EDT: That would help the mentors.
Xinliang2 6/8/06 9:18:05 AM EDT: ok
rtoledosj 6/8/06 9:18:13 AM EDT: Bye, Xinliang!
Xinliang2 6/8/06 9:18:18 AM EDT: sophia, tmr we try to log on 15 min earlier kae?
sophia 6/8/06 9:18:28 AM EDT: ok
nan 6/8/06 9:18:44 AM EDT: that was a great session
nan 6/8/06 9:18:50 AM EDT: thank you guys for coming
nan 6/8/06 9:18:54 AM EDT: and have a good night
Xinliang2 6/8/06 9:19:26 AM EDT: good night
sophia 6/8/06 9:19:36 AM EDT: ok bb
Xinliang2 6/8/06 9:19:36 AM EDT: sophia, is that considered a summary?
Xinliang2 6/8/06 9:19:40 AM EDT: you can edit it.
sophia leaves the room 6/8/06 9:19:40 AM EDT
rtoledosj leaves the room 6/8/06 9:21:06 AM EDT
Xinliang2 6/8/06 9:21:29 AM EDT: Xinliang2 sent an email to mentors.
Subject: session 3
Message:
can you give us some feedback on today's session. im sorry we didn't finish a lot 'cos there's some technical problems going on. thanks anyway!!! (:
nan 6/8/06 9:21:50 AM EDT: great
Xinliang2 leaves the room 6/8/06 9:21:54 AM EDT
nan leaves the room 6/8/06 9:21:58 AM EDT
sophia joins the room 6/8/06 9:21:58 AM EDT
sophia leaves the room 6/8/06 9:25:06 AM EDT
TBryant joins the room 6/8/06 10:34:37 AM EDT
TBryant leaves the room 6/8/06 10:35:06 AM EDT
TBryant joins the room 6/8/06 10:35:11 AM EDT
TBryant leaves the room 6/8/06 10:35:41 AM EDT
TBryant joins the room 6/8/06 10:42:55 AM EDT
TBryant leaves the room 6/8/06 10:48:01 AM EDT
tutor joins the room 6/8/06 9:42:01 PM EDT
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tutor 6/8/06 10:51:36 PM EDT: tutor sent an email to room members.
Subject: Feedback for Session 3
Message:
Feedback for Session 3 has been posted on your room's whiteboard.
tutor leaves the room 6/8/06 10:51:46 PM EDT
sophia joins the room 6/9/06 6:46:48 AM EDT
rtoledosj joins the room 6/9/06 7:40:05 AM EDT

==Session IV==

rtoledosj 6/9/06 7:42:22 AM EDT: Hi Sophia!
sophia 6/9/06 7:43:14 AM EDT: hello
sophia 6/9/06 7:43:31 AM EDT: i went for dinner just now
rtoledosj 6/9/06 7:44:59 AM EDT: You were having technical problems before. Everything ok now?
sophia 6/9/06 7:45:21 AM EDT: yep its ok now
rtoledosj 6/9/06 7:45:46 AM EDT: While we're waiting for the rest, can you describe what happened?
sophia 6/9/06 7:46:54 AM EDT: er, the board seems to be lagging and it took about a few minutes to see teh changes like erasing stuffs from the board
rtoledosj 6/9/06 7:49:31 AM EDT: What about the text box? Was it also lagging?
sophia 6/9/06 7:49:41 AM EDT: yes
sophia 6/9/06 7:49:54 AM EDT: er, as in the chatbox
rtoledosj 6/9/06 7:51:08 AM EDT: Was the lag worse as you stayed longer in the session or was it about the same throughout?
sophia 6/9/06 7:51:33 AM EDT: as i stayed longer in the session
rtoledosj 6/9/06 7:52:57 AM EDT: Yesterday, you had to log out or got logged out several times. Everytime you re-entered did the system become better compared to when you logged out?
sophia 6/9/06 7:53:49 AM EDT: yes, the system became better when i re-entered
rtoledosj 6/9/06 7:55:50 AM EDT: Can you say then, that the earlier session, I mean Session 2, had less lag compared to Session 3?
sophia 6/9/06 7:56:30 AM EDT: yes
rtoledosj 6/9/06 7:57:41 AM EDT: That's very interesting. Now we have a better idea of what seems to be happening.
sophia 6/9/06 7:57:59 AM EDT: er, ya
rtoledosj 6/9/06 7:59:02 AM EDT: Do you know if your companions were having a similar experience with the system?
sophia 6/9/06 8:00:04 AM EDT: erm i'm not sure, but i'm sure that they had technical problems yesterday, as in their board were lagging
rtoledosj 6/9/06 8:00:56 AM EDT: Were you using the same computer for all the sessions?
sophia 6/9/06 8:01:30 AM EDT: yep
Xinliang2 joins the room 6/9/06 8:02:03 AM EDT
sophia 6/9/06 8:02:13 AM EDT: hi
rtoledosj 6/9/06 8:03:01 AM EDT: I recall that you had serious technical problems during the first session, but very few during the second session. Did you make any changes to your computer between the first and the seconsd session?
rtoledosj 6/9/06 8:03:11 AM EDT: Hi Xinliang!
sophia 6/9/06 8:03:55 AM EDT: hang on, i used my home computer in the first session but for the rest ofteh sessions, i used my tablet pc
Xinliang2 6/9/06 8:04:48 AM EDT: it takes so long to load the whiteboard
rtoledosj 6/9/06 8:04:49 AM EDT: Which is the newer PC, the home or tablet?
rtoledosj 6/9/06 8:05:07 AM EDT: You were having problems, too?
sophia 6/9/06 8:05:35 AM EDT: the tablet is newer
rtoledosj 6/9/06 8:05:57 AM EDT: Is it also a more powerful machine?
sophia 6/9/06 8:06:26 AM EDT: er, i'm not sure
rtoledosj 6/9/06 8:06:44 AM EDT: Is the home computer at least three years old?
sophia 6/9/06 8:06:53 AM EDT: yep
rtoledosj 6/9/06 8:07:09 AM EDT: And the tablet is less than a year old?
sophia 6/9/06 8:07:16 AM EDT: yep
rtoledosj 6/9/06 8:07:32 AM EDT: Both are running Windows XP?
sophia 6/9/06 8:07:45 AM EDT: yep
Xinliang2 6/9/06 8:07:47 AM EDT: hello!!
sophia 6/9/06 8:07:57 AM EDT: but different edision
rtoledosj 6/9/06 8:08:02 AM EDT: I guess, we can start.
sophia 6/9/06 8:08:11 AM EDT: ok
rtoledosj 6/9/06 8:08:14 AM EDT: oh.
Xinliang2 6/9/06 8:08:29 AM EDT: ok
sophia 6/9/06 8:08:44 AM EDT: so,shall we start?
rtoledosj 6/9/06 8:08:48 AM EDT: Ok, Sophia, thank you for the info regarding the computers.
rtoledosj 6/9/06 8:08:54 AM EDT: Yes, you can start.
sophia 6/9/06 8:09:04 AM EDT: aha
sophia 6/9/06 8:09:08 AM EDT: *haha
sophia 6/9/06 8:09:30 AM EDT: anw, we stopped on the part where we were doing the triangles
Xinliang2 6/9/06 8:09:43 AM EDT: finding the no of sticks used
sophia 6/9/06 8:10:19 AM EDT: yep
sophia 6/9/06 8:10:34 AM EDT: but i cant see the connection between them
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Xinliang2 6/9/06 8:11:12 AM EDT: sophia do u know where's roohiya and aza?
Xinliang2 6/9/06 8:11:22 AM EDT: didnt' see them in school today too
sophia 6/9/06 8:11:28 AM EDT: i saw aza in the online list
Xinliang2 6/9/06 8:12:22 AM EDT: i asked her to go to our room
Xinliang2 6/9/06 8:12:34 AM EDT: then how about roohiya?
sophia 6/9/06 8:12:43 AM EDT: ok, but she seems not reacting
sophia 6/9/06 8:12:55 AM EDT: shes not online yet
Xinliang2 6/9/06 8:13:05 AM EDT: ok
Xinliang2 6/9/06 8:13:11 AM EDT: let's go back to the topic
sophia 6/9/06 8:13:20 AM EDT: ok
Xinliang2 6/9/06 8:13:27 AM EDT: the no of sticks are in the multiples of 3
sophia 6/9/06 8:13:36 AM EDT: yep
Xinliang2 6/9/06 8:14:32 AM EDT: we have to find a connection between 3 and the pattern no
sophia 6/9/06 8:14:55 AM EDT: yep
Roohiya2 joins the room 6/9/06 8:18:10 AM EDT
sophia 6/9/06 8:18:19 AM EDT: i still cant geddit
Xinliang2 6/9/06 8:18:20 AM EDT: hi
sophia 6/9/06 8:18:29 AM EDT: hi
rtoledosj 6/9/06 8:18:41 AM EDT: Hi Roohiya.
Roohiya2 leaves the room 6/9/06 8:20:16 AM EDT
sophia 6/9/06 8:20:27 AM EDT: the difference in the no. of sticks increases by 3 as the pattern increase
Roohiya2 joins the room 6/9/06 8:20:29 AM EDT
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Xinliang2 6/9/06 8:21:16 AM EDT: we have to find a simpler method
Xinliang2 6/9/06 8:21:34 AM EDT: has it got to do with the no of triangles?
sophia 6/9/06 8:21:53 AM EDT: yep, should be
Roohiya2 6/9/06 8:23:37 AM EDT: may i know wat is happening
sophia 6/9/06 8:24:15 AM EDT: eh, we did the pattern on rectangle and triangles and technical problems happened
Roohiya2 6/9/06 8:24:18 AM EDT: by the way how did u ppl know tt there was a session yesterday?
Xinliang2 6/9/06 8:25:11 AM EDT: we are finding the no of sticks used for triangle
sophia 6/9/06 8:25:28 AM EDT: coz we went to sch yesterday and ms chua told us of the session for yesterday
sophia 6/9/06 8:25:49 AM EDT: then we cant reach aza yesterday
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Roohiya2 6/9/06 8:27:41 AM EDT: the fig so u r trying tiangles
sophia 6/9/06 8:27:53 AM EDT: yep
Roohiya2 6/9/06 8:28:27 AM EDT: do we hv to use the same no. of triangles for each fig.
sophia 6/9/06 8:28:58 AM EDT: eh what do you mean?
Xinliang2 6/9/06 8:30:47 AM EDT: roohiya i don't understand too
Roohiya2 6/9/06 8:31:57 AM EDT: no of triangles will be n^2
sophia 6/9/06 8:32:12 AM EDT: er, ya
Xinliang2 6/9/06 8:32:26 AM EDT: yes
sophia 6/9/06 8:32:50 AM EDT: 3N+3(N+2)
sophia 6/9/06 8:33:40 AM EDT: could be the fomula for the triangle
Xinliang2 6/9/06 8:33:51 AM EDT: let's try out
sophia 6/9/06 8:34:13 AM EDT: but it does not work for pattern 1
Xinliang2 6/9/06 8:35:00 AM EDT: we are always stuck at 1st patterm
Roohiya2 6/9/06 8:36:09 AM EDT: 3(n+1)(n/2)
sophia 6/9/06 8:36:12 AM EDT: as in can that formula work for the rest of the patter?
Roohiya2 6/9/06 8:36:20 AM EDT: is it right
sophia 6/9/06 8:36:28 AM EDT: huh?
Xinliang2 6/9/06 8:37:10 AM EDT: do we need to draw the 5th pattern?
Roohiya2 6/9/06 8:37:24 AM EDT: is tt the right formula
sophia 6/9/06 8:37:28 AM EDT: noneed, its clear enough to spot the pattern
sophia 6/9/06 8:37:50 AM EDT: i think the formula works only at figure 4
sophia 6/9/06 8:38:08 AM EDT: the rest of the patten does not work in that formula
Roohiya2 6/9/06 8:38:11 AM EDT: NO IT DOESN'T IT WORKS!!!!!!!!!
Xinliang2 6/9/06 8:38:24 AM EDT: it doesn't work for 3rd pattern
Xinliang2 6/9/06 8:38:47 AM EDT: it doesn't work in odd no.
Xinliang2 6/9/06 8:38:53 AM EDT: it will give a decimal
Roohiya2 6/9/06 8:38:57 AM EDT: CAN!!!!!!!!!!!!!!
sophia 6/9/06 8:39:09 AM EDT: really?
Roohiya2 6/9/06 8:39:09 AM EDT: IT WORKS!!!!!!!!
Roohiya2 6/9/06 8:39:41 AM EDT: try!!!!!!!!!!!!!!!!!!!
sophia 6/9/06 8:39:51 AM EDT: ok
sophia 6/9/06 8:40:13 AM EDT: anw, since it works, shall we try other patterns? like 3d figures
Xinliang2 6/9/06 8:40:30 AM EDT: congrats roohiya!!!
Xinliang2 6/9/06 8:40:32 AM EDT: yay!!
Roohiya2 6/9/06 8:40:51 AM EDT: 3(n+1)(n/2)
sophia 6/9/06 8:40:53 AM EDT: er, which fomula are you using?
Roohiya2 6/9/06 8:41:05 AM EDT: it is aza's formula
sophia 6/9/06 8:41:18 AM EDT: oh, i see
sophia 6/9/06 8:41:25 AM EDT: it really works anw
Roohiya2 6/9/06 8:42:11 AM EDT: so wat should we do now
sophia 6/9/06 8:42:49 AM EDT: lets try 3Dfigure, shall we?
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Xinliang2 6/9/06 8:43:02 AM EDT: i wrote it down
Xinliang2 6/9/06 8:46:17 AM EDT: so wad are we doing now?
sophia 6/9/06 8:46:32 AM EDT: lets try 3d figs
sophia 6/9/06 8:46:46 AM EDT: like cubes
Roohiya2 6/9/06 8:47:10 AM EDT: for the 3D fig. we find out the no. of faces and wat?
Roohiya2 6/9/06 8:47:43 AM EDT:
sophia 6/9/06 8:47:50 AM EDT: and theno. of cubes and sticks used
Xinliang2 6/9/06 8:48:31 AM EDT: ok but do we need to do a summary on the triangle problem firsst?
Roohiya2 6/9/06 8:48:39 AM EDT: so we which fig. do we use?
sophia 6/9/06 8:48:50 AM EDT: i tot we did the summary?
Roohiya2 6/9/06 8:49:19 AM EDT: tot we did
sophia 6/9/06 8:49:22 AM EDT: erm i think we use the sq
Roohiya2 6/9/06 8:49:49 AM EDT: draw a sq. using a cube?
sophia 6/9/06 8:50:19 AM EDT: i mean draw cube using sqs
Xinliang2 6/9/06 8:50:38 AM EDT: hahaha
Xinliang2 6/9/06 8:50:52 AM EDT: so i erase the board?
sophia 6/9/06 8:51:06 AM EDT: yep
sophia 6/9/06 8:51:14 AM EDT: wait, i go to pee first
Roohiya2 6/9/06 8:51:14 AM EDT: hold on
Roohiya2 6/9/06 8:51:26 AM EDT: ask the facilitator
Xinliang2 6/9/06 8:51:26 AM EDT: yay!!
Xinliang2 6/9/06 8:51:37 AM EDT: ok
sophia 6/9/06 8:52:28 AM EDT: huh?
rtoledosj 6/9/06 8:52:51 AM EDT: You can do with the whiteboard as you please.
sophia 6/9/06 8:53:01 AM EDT: ok
sophia 6/9/06 8:53:10 AM EDT: so, i erase the board
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
sophia 6/9/06 8:56:07 AM EDT: oh no, the board's lagging again
M M M M M M M M M M M M M M M M M M
Roohiya2 6/9/06 8:56:52 AM EDT: the board is clear
Roohiya2 6/9/06 8:57:37 AM EDT: anyone there?
sophia 6/9/06 8:57:46 AM EDT: my board is not clear
Roohiya2 6/9/06 8:57:59 AM EDT: mine is clear
Xinliang2 6/9/06 8:58:21 AM EDT: my board too
sophia 6/9/06 8:58:22 AM EDT: mine's not
Roohiya2 6/9/06 8:58:31 AM EDT: oh
Xinliang2 6/9/06 8:58:35 AM EDT: mine's now
Xinliang2 6/9/06 8:58:46 AM EDT: sophia u haf to drag it to the bottom
Roohiya2 6/9/06 8:58:48 AM EDT: try clearing it
sophia 6/9/06 8:59:21 AM EDT: ok, my board's clear now
M
Roohiya2 6/9/06 8:59:37 AM EDT: lets continue
M M M M M M M M M M M M M M M M M M M M M M M M M M
Xinliang2 6/9/06 9:00:39 AM EDT: ok
M M M M
Xinliang2 6/9/06 9:00:59 AM EDT: are we supposed to stack the squares up?
M M M M M M M M M M M M
sophia 6/9/06 9:01:55 AM EDT: yep, stsck them up into big and bigger cubes
M M M M M M M M
Xinliang2 6/9/06 9:02:27 AM EDT: is that the formula for the no. of sticks used?
M M M
Roohiya2 6/9/06 9:02:47 AM EDT: ppl the formula n^3
sophia 6/9/06 9:02:56 AM EDT: i tot that is forthe one for the very very fitrst type?
Roohiya2 6/9/06 9:02:59 AM EDT: ppl i need to go now
sophia 6/9/06 9:03:05 AM EDT: ok
sophia 6/9/06 9:03:12 AM EDT: bye roohiya
M
Roohiya2 6/9/06 9:03:19 AM EDT: bye
M M M
Roohiya2 6/9/06 9:03:31 AM EDT: try the formula -n^3
M M M M M
sophia 6/9/06 9:03:42 AM EDT: ok
M M
rtoledosj 6/9/06 9:03:50 AM EDT: Oh, we only have a few minutes left, so before you go, I want to ask you some questions.
M M M
sophia 6/9/06 9:04:02 AM EDT: ok
Xinliang2 6/9/06 9:04:03 AM EDT: ok
M M M M
rtoledosj 6/9/06 9:04:20 AM EDT: Would you like to continue working with your team after tonight?
M
sophia 6/9/06 9:04:31 AM EDT: well, i dont mind
M M M M M M M M
Xinliang2 6/9/06 9:06:02 AM EDT: yes
Xinliang2 6/9/06 9:06:03 AM EDT: yes
Xinliang2 6/9/06 9:06:12 AM EDT: (:
rtoledosj 6/9/06 9:06:12 AM EDT: Xinliang, are you having technical problems?
Xinliang2 6/9/06 9:06:22 AM EDT: you mean now?
rtoledosj 6/9/06 9:06:34 AM EDT: yes.
M M
Xinliang2 6/9/06 9:07:41 AM EDT: no, im not.
M M M M
sophia 6/9/06 9:08:00 AM EDT: not me too
M M
rtoledosj 6/9/06 9:08:10 AM EDT: What did you notice during these sessions that seem most interesting to you as far as doing math in a group is concerened?
M
rtoledosj 6/9/06 9:08:12 AM EDT: ok.
M M M M
Xinliang2 6/9/06 9:08:55 AM EDT: the questions that we encountered are much challenging than those we faced in school
sophia 6/9/06 9:09:02 AM EDT: we seems to be able to come up with the solutions faster for questions like these
Xinliang2 6/9/06 9:09:15 AM EDT: cos in school, we only deal with the concepts and applying it to problems
Xinliang2 6/9/06 9:09:42 AM EDT: but these sessions let me face more challenging questions that you at first thought are easy
Xinliang2 6/9/06 9:09:44 AM EDT: yupp
sophia 6/9/06 9:10:32 AM EDT: yep me too
M M M M
Xinliang2 6/9/06 9:11:35 AM EDT: haha
Xinliang2 6/9/06 9:11:45 AM EDT: i have to go
sophia 6/9/06 9:12:30 AM EDT: haha, ok anw, bye xinliang
M
sophia 6/9/06 9:13:08 AM EDT: well i've got to go too bye!
sophia leaves the room 6/9/06 9:13:11 AM EDT
Xinliang2 6/9/06 9:13:24 AM EDT: bye!!!
Xinliang2 leaves the room 6/9/06 9:13:26 AM EDT
sophia joins the room 6/9/06 9:13:46 AM EDT
sophia leaves the room 6/9/06 9:14:38 AM EDT
rtoledosj leaves the room 6/9/06 9:15:43 AM EDT
jsarmi joins the room 6/9/06 9:19:16 AM EDT
jsarmi 6/9/06 9:19:53 AM EDT: Hi, Roohiya!
jsarmi 6/9/06 9:20:04 AM EDT: Is your team done?
nan joins the room 6/9/06 9:20:24 AM EDT
nan leaves the room 6/9/06 9:21:52 AM EDT
rtoledosj joins the room 6/9/06 9:22:47 AM EDT
rtoledosj 6/9/06 9:23:40 AM EDT: My computer got disconnected.
rtoledosj 6/9/06 9:24:08 AM EDT: Roohiya left earlier.
rtoledosj 6/9/06 9:24:30 AM EDT: I wasn't able to finish interviewing them.
rtoledosj leaves the room 6/9/06 9:28:21 AM EDT
jsarmi leaves the room 6/9/06 9:39:07 AM EDT
Roohiya2 leaves the room 6/9/06 9:53:15 AM EDT
TBryant joins the room 6/9/06 7:04:22 PM EDT
TBryant leaves the room 6/9/06 7:06:06 PM EDT
TBryant joins the room 6/10/06 6:36:24 PM EDT
TBryant leaves the room 6/10/06 6:38:00 PM EDT
TBryant joins the room 6/12/06 4:41:46 PM EDT
TBryant leaves the room 6/12/06 4:43:38 PM EDT
tutor joins the room 6/12/06 10:56:02 PM EDT
tutor leaves the room 6/12/06 11:03:36 PM EDT
tutor joins the room 6/13/06 9:00:04 AM EDT
tutor leaves the room 6/13/06 9:01:14 AM EDT
tutor joins the room 6/13/06 9:05:38 AM EDT
tutor leaves the room 6/13/06 9:07:30 AM EDT
tutor joins the room 6/13/06 9:44:15 AM EDT
tutor 6/13/06 10:11:30 AM EDT: tutor sent an email to room members.
Subject: Feedback for Session 4 Message: Feedback has been posted in your room.
tutor leaves the room 6/13/06 10:11:30 AM EDT
TBryant joins the room 6/13/06 6:52:00 PM EDT
TBryant leaves the room 6/13/06 6:53:48 PM EDT
tutor joins the room 6/14/06 1:08:44 PM EDT
tutor leaves the room 6/14/06 1:20:14 PM EDT
tutor joins the room 6/14/06 1:50:06 PM EDT
M M
tutor joins the room 6/14/06 2:11:02 PM EDT
tutor leaves the room 6/14/06 2:24:43 PM EDT
TBryant joins the room 6/14/06 2:27:12 PM EDT
TBryant leaves the room 6/14/06 2:37:24 PM EDT
tutor joins the room 6/16/06 9:21:46 PM EDT
tutor leaves the room 6/16/06 9:26:09 PM EDT

Dataset2/D2T2S2n

Jsarmi — Thu, 24 Jan 2008 03:29:04 GMT

Jsarmi:

Noticings on Team B's Session II

The team members start orienting to "yesterday's stuff" from reading the feedback but soon, such orientation is very much their own and a lot of relevancies from that prior work emerge of their interactions. One that seems specially interesting to me, is the "re-use" of prior group reasoning procedures as in the case of "breaking figures down" into sub-components to figure out number of sticks and squares. That reasoning strategy was central to their work on Session I and it re-appears here in Session II:

bwang8 5/10/06 7:30:07 PM EDT: ok, how do we figure that out
p M
bwang8 5/10/06 7:30:17 PM EDT: 3*3 blocks
p M
Quicksilver 5/10/06 7:30:26 PM EDT: Break it down
Aznx 5/10/06 7:30:27 PM EDT: I'd say look for a pattern.
p M
Aznx 5/10/06 7:30:33 PM EDT: and yes, break it down.

There is no magic, however. They need to work out what the "breaking down" of their 3D figure means, and how to use "yesterday's work" today. Interestingly at the end, when they get to work on what they would put on the Wiki, Aznx states that "technically" they got the same result in this session as in the previous one:

Aznx 5/10/06 8:04:53 PM EDT: We technically had the same result.
Quicksilver 5/10/06 8:05:07 PM EDT: Whaddya mean?
Quicksilver 5/10/06 8:05:21 PM EDT: oh as yesterday?
Aznx 5/10/06 8:05:31 PM EDT: Yeah.
Aznx 5/10/06 8:05:36 PM EDT: And today.
Quicksilver 5/10/06 8:05:40 PM EDT: Still...
Aznx 5/10/06 8:05:43 PM EDT: Well today was really a discussion.

Dataset2/NotesFromDataSessions

Jsarmi — Thu, 10 Jan 2008 21:39:32 GMT

Jsarmi:

We need a new word for turn
We need a new concept of sequence in "reading's work"

make something the topic of the moment

Tasking:
who they are with the respect to what they are to do

the initiation of the inquiry work, are there elements
that can be identified in how this is done?
Can they be recognized in other initiations?

Participation Frameworks

Jsarmi — Tue, 11 Dec 2007 03:59:38 GMT

Jsarmi:

http://iib-wiki.cogsci.rpi.edu/index.php?title=David_Kirsh

Participation Frameworks in CMC
http://209.85.165.104/search?q=cache:QfdqK_c1rTYJ:gretel.econ.surrey.ac.uk/staff/ngilbert/ngpub/paper91_NG.pdf+participation+frameworks+for+computer+supported&hl=en&ct=clnk&cd=1&gl=us

Organizing Participation in Interaction: Doing Participation Framework

http://mathforum.org/wiki/VMTStudents/VMTStudents?action=browse&diff=1&id=RowsOfTheTable&diffrevision=6&revision=2

http://mathforum.org/wiki/VMT?Session010906

The theory of participation framework comes from Goffman?
Goffman, E. (1979). Footing. Semiotica, 25(1), 1-29. Reprinted in Goffman, E. (1981). Forms of talk. Philadelphia: University of Pennsylvania Press.

Duranti, A. (1997). Units of participation. Linguistic anthropology (pp.280-331). Cambridge University Press.

Goodwin, C. Notes on the Organization of Engagement http://www.sscnet.ucla.edu/clic/cgoodwin/publish.htm
Notice how he defines participation (and the role of "social positions")

Participation

I investigate Participation as a temporally unfolding process through which separate parties demonstrate to each other

their ongoing understanding of the events they are engaged in by building actions that contribute to the further progression

of these very same events. Thus a hearer is not just a structural category, an addressee, but someone who displays detailed

analysis of, and stance toward, the unfolding structure of the talk in progress through visible embodied displays.

Speakers take such displays into account as they organize their own actions. Moreover, parties in interaction build action

from the social positions they occupy. This approach to participation, with its focus on analysis displayed through temporally

unfolding action, differs from approaches that proceed by constructing typologies of different kinds of participants.

Self Regulation

Jsarmi — Sun, 09 Dec 2007 19:39:32 GMT

Jsarmi: /* Creating Interactive Sociocultural Environments for Self-Regulated Learning */

http://en.wikipedia.org/wiki/Self-regulated_learning

The concept of academic self-regulation and its relationship to learning has been widely explore (Ruban, McCoach, McGuire, & Reis, 2003). According to Zimmerman, (1989) self-regulation refers to â��the degree that individuals are metacognitively, motivationally, and behaviorally active participants in their own learning processâ�� (p. 329). Zimmerman (1989) identifies the hallmarks of academic self-regulation to include academic time management, practice, mastery of learning methods, goal-directedness, and a sense of self-efficacy.

Self-regulation refers to the use of processes that activate and sustain thoughts, behaviors, and affects in order to attain goals (Schunk & Zimmerman, 1997). In other words, it refers to taking charge of our own learning by coordinating the thinking skills described in this chapter. Self-regulation has three components:

::* '''Self-observation'''. Deliberate attention to specific aspects of one's own behaviors.
::* '''Self-judgment'''. Comparing one's current progress toward a goal with a standard.
::*'''Self-reaction'''. Making evaluative responses to judgments of one's own performance.

Zimmerman (1994) conceptualizes self-regulation as comprising four dimensions or areas in which students can self-regulate their activities:
:*(a) motives for learning or performing
:*(b) methods used
:*(c) performance outcomes or target behaviors, and
:*(d) environmental resources used.
To be self-regulated it is not necessary that one exert control over all dimensions; such complete control would be rare in educational settings. Rather, these are four areas in which self-regulation is possible.

==Conceptual Analysis of the Dimensions of Academic Self-Regulation==
----
<pre>
Scientific Psychological Task Self-Regulatory Self-Regulatory
Questions Dimensions Conditions Attributes Processes
</pre>
----
<pre>
Why? Motive Choose to Intrinsically or Self-goals,
participate self-motivated self-efficacy,
values,attributions, etc.

How? Method Choose method Planned or Strategy use,
automatized relaxation, etc.

What? Performance Choose Self-aware of Self-monitoring,
outcomes performance performance self-judgment, action control,
outcomes outcomes volition, etc.

Where? Environmental Control social Envirorunentally Envirorunental structuring,
(social) and physical socially help seeking, etc.
setting sensitive and
resourceful
</pre>
----

The question of what deals with students' efforts to self-regulate their academic performance outcomes. The third column in this table specifies the task conditions necessary for a student to self-regulate the particular psychological dimension in question. The question of where or with whom addresses students' efforts to self-regulate their physical and social environment in order to learn.
Constructivist explanations ( Paris & Byrnes, 1989) have focused on students constructing supportive environments using their own personal theory of academic tasks, whereas social cognitive theorists have emphasized seeking social models and assistance ( Schunk, 1989; ZimmerÂman, 1989).

There is evidence that a major cause of underachievement is the inability of students to self-control themselves effectively ( Krouse & Krouse, 1981). Borkowski and Thorpe (in Schulz and Zimmerman, 1994) review this body of research indicating that underachievers are more impulsive, have lower academic goals, and are less accurate in assessing their abilities; furthermore, they are more self-critical and less self-efficaÂcious about their performance and tend to give up more easily than achievers.

In summary, academic self-regulation includes skills such as the following (McCombs, 1989; Schunk, 1994; Zimmerman, 1994):

::*Valuing learning and its anticipated outcomes
::*Setting performance goals
::*Planning and managing time
::*Holding positive beliefs about one's abilities
::*Attending to and concentrating on instruction
::*Effectively organizing, rehearsing, and encoding information
::*Setting up a productive work environment
::*Using social resources effectively
::*Focusing on positive effects
::*Making useful attributions for success and failure

According to Zimmerman self-judgment is essential. He states (1989) that "self-judgment refers to students' responses that involve systematically comparing their performance with a standard or goal" (p. 333).

Recently, researchers have begun to look at issues of self-regulation and its relationship with success in online learning environments (Zerr, 2007; Whipp & Chiarelli, 2004). Yet studies in this area remain few and far between (Whipp & Chiarelli 2004), and a call for more research has been issued (Hodges, 2005). It is in response to that call that this study was undertaken.

==Self Regulation and Brain Research==

With the advent of new and more sophisticated methods of brain research it has become possible to establish relationships between the development of self-regulation and the maturation of particular areas of the brain. It was found, for example, that relatively low levels of self-regulation in preschool age children are associated with the children not yet utilizing the areas of the brain responsible for planning and reflection (Bronson, 2000). Recent research on the brain seems to indicate that self-regulation is tied to the development of the prefrontal prefrontal /pre·fron·tal/ (-fron´t'l) situated in the anterior part of the frontal lobe or region.
pre·fron·tal (pr-fr cortex which is not only important for the development of control over emotions, but also that of focused attention as well as planning and monitoring of cognitive behaviors (Davidson et. al., 2006). There is evidence that positive emotionality and negative emotionality induce different patterns of activation of the prefrontal cortex (Davidson, Jackson, & Kalin, 2000) and that this can affect levels of attention (Davidson, 1999). The fact that the same area of the brain is responsible for emotional control and for the metacognitive functions further supports the idea of the interconnection between social-emotional self-regulation and cognitive self-regulation (Blair, 2002).

==Vygotsky's view of self-regulation==

Vygotsky's view on self-regulation is based on his general ideas of cultural- historical nature of human development. For Vygotsky, self-regulation is not a single trait or even a combination of traits but rather a critical development signaling emergence of uniquely human set of competencies "higher mental functions". While not using the word "'self-regulation" to describe higher mental functions, Vygotsky described them though as deliberate, intentional, or volitional behaviors, as something that humans have control of Acquiring higher mental functions allows children to make a critical transition from being "slaves to the environment" to becoming "masters of their own behavior". This process requires children to master specific cultural tools--including language and other symbolic systems--which they can use to gain control over their physical, emotional, and cognitive functioning.

As it is true for all higher mental functions, children's self-regulatory abilities originate in social interactions and only later become internalized and independently used by children (Vygotsky, 1978). This means that self-regulation is not something that emerges spontaneously as the child matures but is instead taught formally or informally within the social context. Classroom presents one of the possible contexts; family and peer group provide alternative contexts for learning self-regulation. In the case when none of the social contexts support the development of self-regulatory behaviors, children continue to operate as "slaves to the environment" being guided by ever-changing external stimulation and incapable of intentional actions.

For Vygotsky, there are three critical conditions necessary for development of self-regulatory behaviors in children. First, to develop any higher mental function on the intra-subjective (individual) plane, children first have to experience it on the inter-subjective (shared) plane (Vygotsky 1978). In regard to self-regulatory behaviors--social as well as cognitive- it means that children need to have an opportunity to engage in other-regulation. Other-regulation implies that children act both as subjects of another person's regulatory behaviors (as is the case of many of their interactions with adults) and as actors regulating other person's behaviors (as might happen in the interaction with peers or younger children). A second necessary condition for emergence of self-regulation is children's learning of specific cultural tools that would allow them to eventually use self-regulatory behaviors independently. Among first such tools children learn is self-talk or "private speech". When children engage in private speech to themselves, the same words that adults once used to regulate children's behaviors, are now used by children themselves for the purposes of self-regulation. Studies of private speech have found a direct link between children's use of private speech and their self-regulatory abilities (Berk & Landau, 1993; Berk & Spuhl, 1995; Winsler, Diaz, Atencio, McCarthy, & Chabay, 2000).

The last condition is young children's engagement in well-developed make-believe play. Vygotsky's famous quote about a child standing "a head taller than himself' when engaged in highly imaginative sociodramatic play can definitely be applied to self-regulatory behaviors--in social-emotional as well as in cognitive realm. Being the "leading activity" for preschool- and kindergarten-aged children (Vygotsky, 1967; Leont'ev, 1978), play provides opportunities for children to practice self-regulatory components of multiple mental functions--from fulfilling their desires in a symbolic form while at the same time delaying gratification to beginning to develop reflective competencies while taking multiple perspectives (Elkonin, 1978).

==Creating Interactive Sociocultural Environments for Self-Regulated Learning==

Ronald W. Henderson & Linda Cunningham
University of California, Santa Cruz

What a child can do in cooperation today he can do alone tomorrow. Therefore
the only good kind of instruction is that which marches ahead of development
and leads it. -- Vygotsky ( 1962, p. 104)

==Self-Regulated Learning & Metacognition==

Flavell (1976) first invented the term metacognition. He defined metacognition as one's knowledge regarding one's own cognition as well as control and monitor one's own cognition. The terms self-regulated learning and metacognition are interchangeable in the current discussion.

A self-regulated leaner is aware when she knows a fact or has a skill and when she does not. She views acquisition as a systematic and controllable process, and she accepts greater responsibility for her achievement. In other words, She is the initiator of the learning process. Self-regulated learning has played a part in behavioral theory, cognitive theory, social cognitive theory, and constructivism theory. In behavioral theory, regulation is through external reinforcement. In cognition theory, self-regulation is equivalent to metacognition, knowing about and regulating cognition. Social cognition theory views self-regulation as combining self-observation, self-judgment, and self-reaction. Constructivism theory perceives individuals as active agents who construct and reconstruct their knowledge (Davidson, K., 1995) .

Self-regulation plays a crucial role in all phases of learning and cross-domains. Schoenfeld (1987) states that self-regulation has the potential to increase the meaningfulness of students' classroom learning, and the creation of a "mathematics culture "in the classroom best fosters metacognition. Schoenfeld (1983) showed that many problem-solving errors are due to metacognitive failure rather than lack of basic mathematics knowledge. He further insists that all metacognitive strategies are illustrated in action, should be developed by students, not declared by the teachers. Study metacognitive strategies are important as well, in reading to learn and can be applied to enhance text processing ( Grow, 1996a). To teach students to become active, motivated, self-regulated learners is a continuing issue in education. Authentic and meaningful classroom activities that are relevant to real-life situations are likely to engender students' cognitive activity and conceptual change (transfer). Scaffolding, dual instructions (verbal persuasion and modeling), and teaching appropriate cognitive strategies are believed to have positive impact on increasing students' efficacy.

==References==
:* Ruban, L., McCoach, B., McGuire, J., & Reis, S., (2003) The differential impact of academic self-regulatory methods on academic achievement among university students with and without learning disabilities. Journal of Learning Disabilities, 36(3), 268-284.
:* Whipp J. & Chiarelli S. (2004) Self-regulation in a web-based course: a case study. Educational Technology Research and Development, 52(4) 5-23.
:* Zerr, R., (2007) A Quantitative and Qualitative Analysis of the Effectiveness of Online Homework in First-Semester Calculus. The Journal of Computers in Mathematics and Science Teaching, 26(1), 55-74.
:* Zimmerman, B. J. (1989). A social cognitive view of self-regulated academic learning. Journal of Educational Psychology, 81, 329â��339.
:* Zimmerman B. J., & Schunk D. H. (Eds.). ( 1989). Self-regulated learning and academic achievement: Theory, research, and practice. New York: Springer-Verlag
:* Zimmerman, B. J. (1994) Dimensions of Academic Self-Regulation: A Conceptual Framework for Education. In D. H. Schunk, D. H. & B. J. Zimmerman (Eds.) Self-regulation of Learning and Performance: Issues and Educational Applications. Hillsdale, New Jersey Hove, UK, Lawrence Erlbaun Associates. p. 3-
:* Schunk, D. H., Zimmerman, B. J. (Eds.). (1994) Self-regulation of Learning and Performance: Issues and Educational Applications.
Hillsdale, New Jersey Hove, UK, Lawrence Erlbaun Associates.
:* Hodges, C. (2005). Self-Regulation in web based courses: a review and the need for Research. Quarterly Review of Distance Education, 6(4), 375-384.

Dataset2/D2TASS

Jsarmi — Wed, 05 Dec 2007 17:03:55 GMT

Jsarmi: /* Final action: the rest on the Wiki */

=Group Trajectory=
Session 1: Dyad from same school, technical problems, f2f work produces some reported results
Session 2: Feedback attended to
Session 3:
Session 4:

==Group composition: Stable/ Technical Problems==

Session 1: tc ro (TP)
Session 2: tc ro
Session 3: tc ro (TP)
Session 4: tc ro

(TP) Technical Problems

==Session I==

Work done F2F is reported to the chat... how is this "reporting" deployed? Initially Tc attempts a direct dialog style:

tcmath 5/9/06 5:12:43 PM EDT: So, Rook, we have the fact that squares is defined as a function of N
by the partial sum quadratic for the sequence 1,2,3,4,5....

This whiteboard textbook was created by tcmath before the previous message:

sequence:1,2,3,4,5
partial sum sequence:1,3,6,10,15
Function is quadratic, so these eqautions are true:
a1^2+b1+c=1

but later, because of technical problems, the style changes to a plural narrative:

jsarmi 5/9/06 5:19:46 PM EDT: It seems as if the system is giving Rook a lot of trouble, isn't it, tcmath?
jsarmi 5/9/06 5:21:41 PM EDT: tcmath?
tcmath 5/9/06 5:24:36 PM EDT: I'm done for now
tcmath 5/9/06 5:24:48 PM EDT: I was working with Rook since his computer wasn't working
jsarmi 5/9/06 5:24:57 PM EDT: I see
tcmath 5/9/06 5:25:16 PM EDT: We figured out the equation for squares, and we should easily solve it for sticks as well in the same manner

This lat posting works like a "projection/plan" which includes a report of what was done. This posting is deceptively simple. It is a report of what was done framed as "figuring out" but such achievement (i.e. the equation for the squares) is not recap, nor placed on the whiteboard. The projection made of what can be done in the future with two qualifications: level of difficulty (easily) and manner (the same way). It is presented to an unspecified recipient, most likely, the moderator who has been giving out instruction on the task and asking for the status of Rook's participation.

tcmath 5/9/06 5:25:16 PM EDT: We figured out the equation for squares, and we should easily solve it for sticks as well in the same manner.

==Wiki posting for Session I?==
It isn't clear that results were posted between Sessions I and II. Most likely, in Session II the team posted results for both sessions. Some results are posted to the "rows of the table" page. Interestingly, their results differ with what Team B posted in the same page (almost next to it) by other teams. There is uptake of this triggered by the facilitator during Session II.
For example:

Row 3

Team name: B
Row 3: 28, 10

Team name: A
Row 3: 18, 6

Team name:
Row 3:

==Feedback==
(No Feedback in between sessions)

==Session II==

Technical problems seemed to be resolved. Dyad must be in same room or connected otherwise, no greetings. Tc starts with this message after which the board is CLEARED of everything that was posted in the previous session.

tcmath 5/11/06 5:04:13 PM EDT: Okay. You must agree that the squares is defined by the equation squares=1/2N^2+1/2N.

Rook attempts to paste a table of values into a textbox but the formatting does not work too well and he ends up with a long list instead. Interestingly, this list lacks values that may have been posted to the wiki already? E.g., The values for N=4 and N=5 which in the wiki read "Team name: A Row 4: 28, 10 / Team name: A Row 5: 40, 15", and in Rooks texbox: "4 ? ? / 5 ? ?". Perhaps they created these values in the second session since they map their equation: N^2 + 3*N?

===Are we doing Session 1 still? Lack of coordination?:===

tcmath 5/11/06 5:09:53 PM EDT: I'm setting up the problem on the whiteboard
p M M M
tcmath 5/11/06 5:10:08 PM EDT:
p M M M M
Rook 5/11/06 5:11:18 PM EDT: Did you solve the sticks as function of N yet?
Rook 5/11/06 5:11:35 PM EDT: I think the equation is x^2+3x
Rook 5/11/06 5:11:50 PM EDT: Found the equation...
tcmath 5/11/06 5:11:54 PM EDT: The seperate lines here represent the sticks you would "add" when N increases by 1.
p M M
Rook 5/11/06 5:12:11 PM EDT: What are you doing?
p M M
Rook 5/11/06 5:12:17 PM EDT: !!
Rook 5/11/06 5:12:40 PM EDT: Are we doing Session 1 still?
tcmath 5/11/06 5:12:43 PM EDT: Okay. The top 4 sticks are there by default; you have to have them.

===Linking Sequences: Squares then Sticks===
How do they constitute the two to be related?

tcmath 5/11/06 5:26:20 PM EDT: So, for squares we found the partial sum equation for the sequence 1,2,3,4,5... Now we find it for the sequence 2n+2 (after distribution)

===Then we will be done===
Definitively in the same room but conversing/coordinationg on the chat. Notice long gaps between postings

tcmath 5/11/06 5:28:30 PM EDT: Here, you can use my TI-84 to do the whole regression thing and I'll do it algebraically on paper. Tell me your results.
Rook 5/11/06 5:29:34 PM EDT: oh...
Rook 5/11/06 5:30:36 PM EDT: x^2+3X
tcmath 5/11/06 5:31:51 PM EDT: Then we're done with the pattern:

===Typing on the Wiki===

tcmath 5/11/06 5:42:32 PM EDT: we're here--we're just typing up our patterns observed on VMT Wiki

===Reading the Wiki, Finding the "next" topic===

jsarmi 5/11/06 5:47:28 PM EDT: Well.. any ideas suggested by the notes from other groups in the Wiki?
tcmath 5/11/06 5:48:02 PM EDT: Well, they figured out the same thing for squares, but their approach was unique for the sticks.
tcmath 5/11/06 5:48:33 PM EDT: We used the same technique for both teh sticks and the squares (partial sums on a sequence), while they used two different ones.
jsarmi 5/11/06 5:48:41 PM EDT: how about the values of the table?
Rook 5/11/06 5:49:02 PM EDT: they got the same
Rook 5/11/06 5:49:33 PM EDT: and we checked with the other groups--same answers...
tcmath 5/11/06 5:49:38 PM EDT: They were ahead one row, though, starting with row 4 since it was the first row without a given answer.
Rook 5/11/06 5:49:53 PM EDT: on the 1st website (VMT Wiki)
jsarmi 5/11/06 5:50:12 PM EDT: Oh... I see
tcmath 5/11/06 5:50:31 PM EDT: For our discussion: I think that mathematiciancs would usually generalize a lot, finding a method that fit the problem even if initial values were changed.
Rook 5/11/06 5:50:46 PM EDT: Yeah
Rook 5/11/06 5:50:54 PM EDT: that's the next topic

===Our method would still work===

tcmath 5/11/06 5:51:39 PM EDT: For example, if every column in the diagram increased by 2 instead of 1.
Rook 5/11/06 5:52:20 PM EDT: I think that the polygons/figures have to be regular to have a chance at this problem, of course--or else there's really no pattern
Rook 5/11/06 5:52:39 PM EDT: Assume that the rest of the answers would just be doubled?
tcmath 5/11/06 5:52:57 PM EDT: If this happened, then our method would still work becuase we would determine the original sequence and then generalize it in a closed form, quadratic equation, for the partial sums.
Rook 5/11/06 5:53:02 PM EDT: The 2 wouldn't make a difference really
Rook 5/11/06 5:53:22 PM EDT: Yeah, or solve it as written, jumping by 2...
Rook 5/11/06 5:53:37 PM EDT: so, it should also work for n-gons that are regular
tcmath 5/11/06 5:54:18 PM EDT: Probably not for three since the sticks really depends on the number of squares we're increasing by. In ours, we had 4 in our equation, while if we increased by three, that number would be 10, I think.
Rook 5/11/06 5:54:34 PM EDT: Yeah, the equation, such as the initial starting point, would have to change to fit more or less starting sticks

===Projecting===

tcmath 5/11/06 5:58:42 PM EDT: We should try looking at the specific case of, say pentagons.
p M
Rook 5/11/06 5:59:11 PM EDT: Yeah
Rook 5/11/06 5:59:18 PM EDT: though do you have to leave?
tcmath 5/11/06 5:59:28 PM EDT: That'll have to wait till next time. I have to leave.
I wonder if we could even replicate the problem with regular pentagons?
Rook 5/11/06 5:59:45 PM EDT: mb in our spare time we could look at it and talk next session

=Feedback=

Dear tcmath and Rook,

We were very interested in the way you combined several approaches to find the formula
for the pattern of growth of sticks and squares. Using a regression method and thinking about
the difference between one step of the pattern and the next seem to work very nicely.
You also posted very complete descriptions of your ideas on the Wiki.

In your previous session you started to explore what the patterns would look like with other polygons and in 3-D,
and you made a couple of conjectures about them (e.g. “the methods for solving general situations like this would be the same”).
For the next step we will encourage you to continue thinking about the different approaches and the problems
that you can discover of your own and that are interesting to pursue.

-The VMT Team

=Session III=

The feedback talks about 3D so Rook orients to it:

tcmath 5/16/06 5:04:24 PM EDT: The 3-d seems like a good place to start.

Noticed that Rook had made some "projected" observations about 3D in the previous session:

Rook 5/11/06 5:58:40 PM EDT: but 3-D might include solving it in "2-D", such as seeing the patterns
on one "dimension" of the 3-D figures, and combing the formulats into one
equation for the 3-D problem

Tcmath reports on work they did in between. Because of technical problems they had to "talk" in person and report in the chat:

tcmath 5/16/06 5:06:04 PM EDT: We started talking about 3d after the last session and decided
that the method would just be double: The original sequence would be the 2-d problem
tcmath 5/16/06 5:08:51 PM EDT: This is true becuase if the problem is a pyramid, expanding n cubes in each direction,
then the number of squares starts with this pattern, then is the same pattern for n-1,
then n-2, all the way to one cube.
jsarmi 5/16/06 5:10:12 PM EDT: tcmath... you may want to wait until Rook gets here so that you can both discuss
the ideas you are posting
tcmath 5/16/06 5:11:36 PM EDT: Okay. we'll just talk (in person) and then type up what we said.

==A projectable (pentagons) recovered but discarded?==

They decide that Rook will type in parenthesis his ideas

jsarmi 5/16/06 5:22:41 PM EDT: (BTW, Once you read the feedback you can delete it so that you can work on the whiteboard freely)
tcmath 5/16/06 5:25:08 PM EDT: The feedback seems to indicate that we should work on 3d., since pentagons tesselate in a weird way (in 5 directions instead)
jsarmi 5/16/06 5:25:42 PM EDT: This is for you to decide... you can go in any direction that seems promising to you.
tcmath 5/16/06 5:25:59 PM EDT: Rook: if it's 2-D; assume that you add 2, then 3...figures every time...
tcmath 5/16/06 5:26:39 PM EDT: 3D seems like a good place to continue, since cubes are a lot like squares.
tcmath 5/16/06 5:27:42 PM EDT: [every side/plane is similar to the squares problem]
tcmath 5/16/06 5:28:06 PM EDT: [since we already figured out the equations for squares]
tcmath 5/16/06 5:30:00 PM EDT: 3d goes like this: the base has 1/2N^2+1/2N cubes, as we figured out in the squares problem, and each level above it has 1/2(N-1)^2+1/2(N-1), and so on.

==Reportable: Same method as before, Algebra==

tcmath 5/16/06 5:41:10 PM EDT: ANYhoo, the 3d partial sum equation is probably a cubic (I think the patter n is, the partial sum equation has a degree one higher than the sequence it is partial-summing)
jsarmi 5/16/06 5:41:30 PM EDT: ok
tcmath 5/16/06 5:42:22 PM EDT: We'll use the same method as we did last time, with algebra

==Wiki writing: a table==

Rook 5/16/06 5:51:34 PM EDT: I'm going to make a table for the data value for a the cube sequences
jsarmi 5/16/06 5:51:40 PM EDT: sure... probably better to concentrate on the math than fighting the computers... sorry about that
jsarmi 5/16/06 5:54:51 PM EDT: a table on the whitebaord?
Rook 5/16/06 5:57:47 PM EDT: on Wiki
jsarmi 5/16/06 6:00:56 PM EDT: I see
Rook leaves the room 5/16/06 6:04:27 PM EDT

Then, abrupt ending

==Feedback==

Dear tcmath and Rook:
We are sorry that you ran into technical problems last time. You tried to work with one computer but
that must have been awkward. Despite that, it seemed to us that you were able to start exploring a
3-D pattern based on your notes posted on the Wiki. Do you need to specify which 3-D pattern you are investigating?
Is it similar to the ones that other teams are exploring?

We hope that this time you will be able to collaborate via the system and continue
this work or explore other interesting math question you create. -The VMT team

This feedback message gets deleted very early on Session IV by tcmath. Rook claims he knows how to get it from the history

==Session IV==
The whitebaord stays clear for the most of the session after Tcmath erases everything, until a critical point when tcmath wants to "take a look" at something on the whitebaord

====Lets continue + Wiki====

Rook 5/18/06 5:25:41 PM EDT: o.k., let's continue the cubes version of the problem
Rook 5/18/06 5:25:44 PM EDT: tcmath
jsarmi 5/18/06 5:26:15 PM EDT: hopefully tcmath is just distracted with the Wiki and not having computer problems
Rook 5/18/06 5:26:31 PM EDT: I'll make a chart of the faces as function of N...
tcmath 5/18/06 5:27:40 PM EDT: Okay. I'm posting all of our ideas, since we came up with a lot of them. When I'm done, you can post your ideas on the wiki as you come up with them.

Rook 5/18/06 5:31:52 PM EDT: R you done posting?
Rook 5/18/06 5:31:54 PM EDT: tcmath
tcmath 5/18/06 5:32:09 PM EDT: Yeah. Its long, but its our work.

===I figured it out... everything in 3D has a strong correlation to the original squares problem===
Rook 5/18/06 5:34:50 PM EDT: so far, for N={1,2} I've gotten Faces={6,14}
Rook 5/18/06 5:34:54 PM EDT: it looks similar...
tcmath 5/18/06 5:35:19 PM EDT: I figured it out! (the faces). Its just 4*(1/2n^2+1/2n)
Rook 5/18/06 5:35:39 PM EDT: that makes sense!
Rook 5/18/06 5:35:55 PM EDT: the faces should be similar to the squares problem
Rook 5/18/06 5:36:05 PM EDT: it's just "magnified" times 4!
tcmath 5/18/06 5:36:41 PM EDT: I'll explain. There are two flat faces which are the full pyramid,
and one which is 3d from one angle, and that same side has another 1/2n^2+1/2n squares viewable
from a different abgle.
tcmath 5/18/06 5:36:51 PM EDT: Does this make any sense?
Rook 5/18/06 5:37:22 PM EDT: you mean the "opposite" side of the cube pyramid?
tcmath 5/18/06 5:37:34 PM EDT: Exactly. Its intuitive, not mathematical as one might expect.
However, we do notice that everything in 3D has a strong orrelation to the original squares problem

===Wait a minute...I'll look at it on the whiteboard===

tcmath 5/18/06 5:43:20 PM EDT: Wait a minute...I'll look at it on the whiteboard;
I think the actual formula is 2.5N^2+2.5N+1, or 5(1/2N^2+1/2N)+1, the extra 1 for the top face.
p M M M M M M M
Rook 5/18/06 5:44:08 PM EDT: (i get the four pyramids now: I was counting wrong)
p M M M M
tcmath 5/18/06 5:44:46 PM EDT: So the whiteboard now shows one view, a flat view of the 3d figure
p M M
Rook 5/18/06 5:45:14 PM EDT: where?
Rook 5/18/06 5:45:16 PM EDT: I don't see it
tcmath 5/18/06 5:45:43 PM EDT: You need to slide the slider on the left down to the bottom.
p M M
Rook 5/18/06 5:45:57 PM EDT: I think it just took some time...

===Something correlates===

Rook 5/18/06 5:48:30 PM EDT: something with the sticks in the original problem correlate to the number of faces in the cubes
tcmath 5/18/06 5:48:33 PM EDT: Yes, you're right. I think the ofrmula I came up with needs some adjustments.
Rook 5/18/06 5:48:50 PM EDT: the faces is similar to the sticks in the original
Rook 5/18/06 5:49:02 PM EDT: however, there are 6 faces compared to 4 sticks
Rook 5/18/06 5:49:16 PM EDT: and the faces increase by 8, then 10, then 12...
Rook 5/18/06 5:49:25 PM EDT: while the sticks are 6,8,10...
tcmath 5/18/06 5:50:09 PM EDT: We probably should use that method, with partial sums
tcmath 5/18/06 5:50:09 PM EDT: We probably should use that method, with partial sums.
Rook 5/18/06 5:50:41 PM EDT: yeah...
Rook 5/18/06 5:50:59 PM EDT: I think it's really the same equation, with slight addition modifications...
p M
Rook 5/18/06 5:51:21 PM EDT: what's the sticks original equation again?
Rook 5/18/06 5:51:42 PM EDT: let's see

==Final action: the rest on the Wiki==

tcmath 5/18/06 5:58:58 PM EDT: I'm leaving. Rook will put the rest of our ideas on the wiki
...
Rook 5/18/06 6:01:51 PM EDT: I think I'll quickly post what we found out just as tcmath was leaving (I checked with him in "life") on Wiki, I think I also have to leave in a minute

===Squares, Sticks, Cubes and Faces===
Interestingly, this group did not see a problem with working on a problem that was too similar to the original one, as other groups did. It almost seems that it was exciting for them to figure out that the same results applied in some parts of it. For other groups this was a reason not to approach the problem at all. In addition, this group broke the cube into "faces" which led them to reuse prior findings but did not break the "faces" into sticks. In other words, in the original pattern 2D (squares) was divided into 1D (sticks) but for their pyramid, 3D (cube) was only divided into 2D (faces).

Dataset1/Gdo

Jsarmi — Wed, 05 Dec 2007 15:08:20 GMT

Jsarmi:

==Session III==

109 gdog: so where's the origin
117 gdog: ok
122 gdog: how do u delete
132 gdog: yes
148 gdog: you can't have a curvbed line on this grid
167 gdog: k
173 gdog: ..................
191 gdog: it's just ur computer clock
218 gdog: yea
225 gdog: lol
243 gdog: how are there 5 possibilites?
255 gdog: y 8 possibilitees?
257 gdog: i'm confuzzled salso
259 gdog: wait what's wrong with it
263 gdog: o i see
264 gdog: how'd u come up with that?
269 gdog: how'd u get infinite series
270 gdog: o
275 gdog: ?
277 gdog: a turn?
284 gdog: OK
285 gdog: think that might work
288 gdog: can u show me
289 gdog: i still dont get how there ar e8
291 gdog: .
292 gdog: .....
295 gdog: thought smthing was wrong
307 gdog: i think there are 9, i might have miscounted
308 gdog: lte me check again
310 gdog: wait
311 gdog: it's 8
312 gdog: i miscounted
334 gdog: i gotta go
341 gdog: kk
345 gdog: i think the main thing was discussion
350 gdog: not sre
352 gdog: he was the brains tonight

==Session III

Vygotsky On Time

Jsarmi — Wed, 05 Dec 2007 04:03:16 GMT

Jsarmi:

The child, with the help of speech, creates a time field that is just as perceptible and real to him as the visual one….He can view changes in his immediate situation from the point of view of past activities, and he can act in the present from the viewpoint of the future.

With the help of the indicative function of words," says Vygotsky (1978), "the child begins to master his attention, creating new structural centers in the perceived situation" (p.35). The child, however, can with the help of speech do even more: he [sic] can create "a time field that is just as perceptible and real to him as the visual one. The speaking child has the ability to direct his attention in a dynamic way. He can view changes in his immediate situation from the point of view of past activities, and can act in the present from the viewpoint of the future" (p.36). Thus what is internalized when a certain way of looking at a visual field is internalized, is a deliberately organized way of seeing and acting is constituted from a set of elementary, spontaneous forms, 'called' out in an orchestrated sequence by a set of initially explicit verbal 'instructions'.

The child’s field of attention embraces not one but a whole series of potential perceptual fields.

The possibility of combining elements of the past and present visual fields (for instance, tool and goal) in one field of attention leads in turn to a basic reconstruction of another vital function, memory. Through verbal formulations of past situations and activities, the child frees himself from the limitations of direct recall; he succeeds in synthesizing the past and present to suit his purposes.

With the development of these quasi-needs, the child’s emotional thrust is shifted from a preoccupation with the outcome to the nature of the solution.

Voluntary activity…a product of the historical-cultural development of behavior and…a unique feature of human psychology.

Voluntary activity, more than highly developed intellect, distinguishes humans from the animals which stand closest to them.

Preference for Agreement

Jsarmi — Tue, 04 Dec 2007 19:23:44 GMT

Jsarmi:

==On Agreements and Disagreements.==

One particular research focus here has been the issue of how disagreements in assessment are negotiated within a
conversation. Pomerantz (1984) argues that '''in a majority of contexts in which assessments are being offered, the typical conversational turn preference structure is one of agreement preferred, disagreement dispreferred'''. Pomerantz’s underlying assumption here is that participants orient to agreement with one another as comfortable, supportive, reinforcing, perhaps as being sociable and as showing that they are like-minded. Disagreements, on the other hand, are oriented to as being ‘uncomfortable, unpleasant, difficult, risking threats, insult, or offence’ (Pomerantz, 1984: 77). When a recipient’s agreement or disagreement with a prior assessment is due, any disagreement is normally marked: the co-participant will preface disagreement with delays such as no immediately forthcoming talk or indicators of reluctance such as ‘uh’ and ‘well’ used as prefaces or patterns of weak agreement followed by disagreement. More
recently, Kotthoff (1993) has suggested that this may be moderated in that, once a dissent-turn sequence has been displayed, co-participants may in turn display concessions which result in the dispute being reframed.

:* Kotthoff, H. (1993) ‘Disagreement and Concession in Disputes: On the Context Sensitivity
of Preference Structures’, Language in Society 22: 193–216.

:* Pomerantz, A. (1984) ‘Agreeing and Disagreeing with Assessments: Some Features of
Preferred/Dispreferred Turn Shapes’, in J.M. Atkinson and J. Heritage (eds) Structures
of Social Action: Studies in Conversation Analysis, pp. 57–101. Cambridge: Cambridge
University Press.

:* Pomerantz, A. (1986) ‘Extreme Case Formulations: A Way of Legitimizing Claims’,
Human Studies 9: 219–29.

Situated Symbolic

Jsarmi — Sat, 01 Dec 2007 14:59:28 GMT

Jsarmi:

Vera, A.H. & Simon, H.A. (1993) Situated Action: A Symbolic Interpretation. Cognitive Science, 17, 7-48.

Dataset2/D2TCSS

Jsarmi — Thu, 29 Nov 2007 18:57:02 GMT

Jsarmi: /* Wouldn't this work? */

==Group Trajectory==
Session 1:
Session 2: Feedback attended to
Session 3:
Session 4:

==Group composition: Stable==

Session 1: js dc ot ss(L)
Session 2: js ot qw
Session 3: js(E) ot qw
Session 4: js ot ss(!) qw

(L) Late (E) Leave Early (!) Very Little Participation
(*) js knows ss: e.g. Jason 5/11/06 7:07:52 PM EDT: ssjnish says that his client is still loading
ot knows dc: e.g. 137 5/11/06 7:21:25 PM EDT: I think David forgot today... Our teacher didn't remind us.

==Session I==

They join within seconds:

Jason joins the room 5/9/06 6:24:03 PM EDT
davidcyl joins the room 5/9/06 6:24:04 PM EDT
137 joins the room 5/9/06 6:24:15 PM EDT

===We did this in class===
Notice how it is 137 who ends up posting the formula

Jason 5/9/06 6:25:44 PM EDT: ooh we just did this in math class about a week ago! :-)
p M M M
azemel 5/9/06 6:25:54 PM EDT: if you have any questions, just ask
Jason 5/9/06 6:25:55 PM EDT: well, not the exact thing, but sequences and series
p M M
Jason 5/9/06 6:26:03 PM EDT: anyhow
p M M M M M M M
Jason 5/9/06 6:26:21 PM EDT: so do we see how the number of sticks grows in a sequence?
davidcyl 5/9/06 6:26:25 PM EDT: ok i've drawn n=4,5,6
Jason 5/9/06 6:26:29 PM EDT: 4(+6) = 10
Jason 5/9/06 6:26:36 PM EDT: 10(+8) = 18
p M M
Jason 5/9/06 6:26:48 PM EDT: i'm guessing 18(+10) = 28 for the next one, according to this pattern
davidcyl 5/9/06 6:27:32 PM EDT: the nth pattern has n more squares than the (n-1)th pattern
davidcyl 5/9/06 6:27:55 PM EDT: basically it's 1+2+..+(n-1)+n for the number of squares in the nth pattern
137 5/9/06 6:28:16 PM EDT: so n(n+1)/2
davidcyl 5/9/06 6:28:24 PM EDT: and we can use the gaussian sum to determine the sum: n(1+n)/2
davidcyl 5/9/06 6:28:36 PM EDT: 137 got it

===Recursive or Explicit?===
Notice that Jason ASKS and david offers his opinion. See Session II

davidcyl 5/9/06 6:29:31 PM EDT: well to find the number of sticks:
davidcyl 5/9/06 6:29:39 PM EDT: let's look on the board
p M M M
Jason 5/9/06 6:29:54 PM EDT: should we use a recursive or explicit definition for it
p M M
davidcyl 5/9/06 6:30:20 PM EDT: i don't think we need recursion

===Lost Proposal?===
137 posts these formulas which seem to be for the number of sticks and mentions overlaps but there is no follow up. Davidcyl and Jason seem to be engaged in figuring it out step by step.

137 5/9/06 6:28:43 PM EDT: and 2(1+2+3...n-1) overlaps
137 5/9/06 6:29:05 PM EDT: so n(n+1)/2-n(n-1)/2?

===Horizontal and Vertical===
As in Team B

(david circles horizontal lines in a pattern diagram on the whiteboard)
davidcyl 5/9/06 6:32:21 PM EDT: 137: i'm separating the sticks into vertical and horizontal sticks
davidcyl 5/9/06 6:30:33 PM EDT: it's simpler to express it as 1+2+...+n

===Not Shared===
Disoriented, then MY formula

Jason 5/9/06 6:32:28 PM EDT: # sticks = N*(3+N)
davidcyl 5/9/06 6:32:30 PM EDT: wait what are you working on?
Jason 5/9/06 6:32:32 PM EDT: wait lemme check
davidcyl 5/9/06 6:32:35 PM EDT: (to 137)
137 5/9/06 6:32:46 PM EDT: Great. Confused.
Jason 5/9/06 6:33:03 PM EDT: 137 are you talking about # sticks or squares
137 5/9/06 6:33:09 PM EDT: Sticks.
Jason 5/9/06 6:33:18 PM EDT: ok
davidcyl 5/9/06 6:33:21 PM EDT: i would think it's 2(n(1+n)/2) + n + n
Jason 5/9/06 6:33:23 PM EDT: well i think my formula works
Jason 5/9/06 6:33:33 PM EDT: provided that you have a value for N

but later (after an interruption)

davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n)
davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right
Jason 5/9/06 6:35:16 PM EDT: :-)
Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares

but where is 137?

===Ssjnish joins ===
ssjnish joins the room 5/9/06 6:34:25 PM EDT

===Didn't we do that?===

davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n)
davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right
Jason 5/9/06 6:35:16 PM EDT: :-)
Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares
davidcyl 5/9/06 6:35:42 PM EDT: ok let's complete the table
Jason 5/9/06 6:35:46 PM EDT: if you take the change in the change of the number of squares, it's constant
137 5/9/06 6:36:10 PM EDT: Didn't we do that?
(points to Jason's message on 6:35:36 PM)
davidcyl 5/9/06 6:36:19 PM EDT: yes
Jason 5/9/06 6:36:27 PM EDT: oh, sorry i guess i must've not caught that
davidcyl 5/9/06 6:36:33 PM EDT: look up
(points to davidcyl 5/9/06 6:28:24 PM EDT: ''and we can use the gaussian sum to determine the sum: n(1+n)/2'')
Jason 5/9/06 6:36:33 PM EDT: could someone post it in a text box on the whiteboard
davidcyl 5/9/06 6:36:38 PM EDT: sure
azemel 5/9/06 6:36:40 PM EDT: be sure that SSJNISH is up to speed folks
(Textbox created)

===A summary for Ssjnish===
Notice the diffeence between We've figured out and I divided

davidcyl 5/9/06 6:38:30 PM EDT: basically, we've figured out that the number of squares in the nth pattern is 1 + 2 + ... + n
p M
137 5/9/06 6:38:33 PM EDT: It was blinding.
p M M M M
davidcyl 5/9/06 6:39:26 PM EDT: then, to find the number of sticks, I divided the figure into "vertical sticks" (|) and "horizontal sticks" (--)
Jason 5/9/06 6:39:41 PM EDT: the formulas are on the Whiteboard
azemel 5/9/06 6:39:56 PM EDT: don't forget to post your ideas to the wiki when you think it's time!
davidcyl 5/9/06 6:40:15 PM EDT: the number of vertical sticks is (1 + 2 + 3 + ... + n)+ n, and the number of horizontal sticks is the same
p M

===Ssjnish asks for an explanation===
This is interesting because it prompts a form of "bridging" in a sense

ssjnish 5/9/06 6:45:11 PM EDT: just to clarify sumthing, i am not overwhelmingly good at math as u guys seem to be,
so it may take me more time than u guys to understand sumthing..
azemel 5/9/06 6:45:44 PM EDT: can you tell us what's puzzling you?
Jason 5/9/06 6:46:07 PM EDT: are we allowed to post images on the wiki? I could just download TeX real quick and get the
summation notation in a small graphic
ssjnish 5/9/06 6:46:12 PM EDT: the derivation of the number of squares
Jason 5/9/06 6:46:21 PM EDT: oh
Jason 5/9/06 6:46:31 PM EDT: so you see in the list a column for "N"
Jason 5/9/06 6:46:50 PM EDT: when n=1, we have 1 square; for n=2, 3; and for n=3, 6
Jason 5/9/06 6:47:00 PM EDT: we came up with a formula to find the total number of squares for any number N
Jason 5/9/06 6:47:16 PM EDT: the purpose of the formula is so that you don't have to draw out the squares and count them
ssjnish 5/9/06 6:47:39 PM EDT: um yes
ssjnish 5/9/06 6:47:41 PM EDT: i know
ssjnish 5/9/06 6:47:51 PM EDT: but how did u get that formula
Jason 5/9/06 6:48:00 PM EDT: oh
azemel 5/9/06 6:48:11 PM EDT: i believe so
Jason 5/9/06 6:48:12 PM EDT: uh, basically you try to find a pattern in the total number of squares first
Jason 5/9/06 6:48:47 PM EDT: we found a formula for that which we'll post on the wiki
p M
davidcyl 5/9/06 6:49:00 PM EDT: if you look at the patterns row by row, it's 1 + 2 + 3 + 4 + however many rows there are
davidcyl 5/9/06 6:49:24 PM EDT: so for the nth pattern, we can say there are 1 + ... + n squares
Jason 5/9/06 6:49:27 PM EDT: if N rows: 1+2+3+...N
Jason 5/9/06 6:49:57 PM EDT: so then we incorporated the formula for finding the sum of an arithmetic series
davidcyl 5/9/06 6:50:12 PM EDT: there's a formula for finding the sum of consecutive integers, which (when starting from 1) is: n(n+1)/2
137 5/9/06 6:50:17 PM EDT: so you use gaussian sum to get n(n+1)/2
Jason 5/9/06 6:50:25 PM EDT: that's it
davidcyl 5/9/06 6:50:35 PM EDT: and as Jason said, it works for arithmetic sequences in general
ssjnish 5/9/06 6:50:51 PM EDT: hmm...

===Davidcyl Announces the Wiki===
In a sense saying, it is done, check it out.

davidcyl 5/9/06 7:03:59 PM EDT: http : //mathforum.org/wiki/VMTStudents/?PatternsOfTheSticks

but notice that 137 says that "they did"

azemel 5/9/06 7:09:41 PM EDT: I assume you posted your results to the wiki, right?
azemel 5/9/06 7:09:53 PM EDT: I don't think you can
137 5/9/06 7:09:54 PM EDT: They did.

interesting

===Moderator's Closing===

azemel 5/9/06 7:08:04 PM EDT: well, if you're done with the sticks problem as it stands,
then this might be a time to stop. there will be another problem on Thursday
p M M
azemel 5/9/06 7:08:24 PM EDT: remember, 7 pm, Thursday, same room

=Feedback=
Dear 137, davidcyl, Jason, and ssjnish,
It seemed to us that you had a very productive first session exploring the given pattern of sticks and squares. We were especially interested in the variety of strategies you used, such as constructing the next steps of the pattern on the whiteboard, separating the pattern in horizontal and vertical lines (other teams did that as well!) and deriving a formula for that sum.

As far as working as a math team, you built on each other’s ideas and tried to work with them in interesting ways. We find it very important that ssjnish felt comfortable asking the team to explain in detail the reasoning for the work completed (e.g. ssjnish 5/9/06 6:47:51 PM EDT: but how did u get that formula?), and that as a team you provided that explanation. It looked useful to us when your group tested together the formula you found. One question that was left unexplored was whether a recursive function shows better how the number of sticks and square grow. Someone offered that as a possibility but you opted for using a summation notation. We notice when ideas or questions are stated in a group but not discussed. What do you think about that situation and how groups deal with it?

For the next step we will encourage you to think more about the different approaches and the problems that you can discover on your own which you find interesting to pursue.

The VMT team.
(Feel free to delete this note once everyone has read it)

=Session II=

===Catching up Qw===
Notice how Jason uses the formulas left on the whiteboard in his report to QW. Notice how Qw gest involved and asks a question "how do you get n(1+n)/2. Jason explanation is "that is the formula" basically.

Jason 5/11/06 7:18:07 PM EDT: ok, so with this aside-- i guess we should discuss our feedback from the last session
jsarmi 5/11/06 7:18:34 PM EDT: make sure you bring qwertyuiop up to speed
Jason 5/11/06 7:18:41 PM EDT: ok
Jason 5/11/06 7:19:35 PM EDT: for the problems last session, we came up with formulas to find the values for the columns
qwertyuiop 5/11/06 7:20:02 PM EDT: in the view topic thing?
Jason 5/11/06 7:20:03 PM EDT: You can see them to the left of this text; our formula for the total number
of sticks or squares for any number N is given
Jason 5/11/06 7:20:09 PM EDT: yes
qwertyuiop 5/11/06 7:20:12 PM EDT: ok
Jason 5/11/06 7:20:17 PM EDT: that was the problem we were given
Jason 5/11/06 7:20:39 PM EDT: remains of our discussion is on the whiteboard and online wiki
137 5/11/06 7:21:25 PM EDT: I think David forgot today... Our teacher didn't remind us.
p M
jsarmi 5/11/06 7:22:35 PM EDT: I see... hopefully he will join you next Tuesday
qwertyuiop 5/11/06 7:23:35 PM EDT: n=3 is 3+2+1 squares, n=4 is 4+3+2+1 squares... how did you get n(1+n)/2
Jason 5/11/06 7:23:42 PM EDT: oh
Jason 5/11/06 7:23:53 PM EDT: that's the formula for finding a series of consecutive numbers
Jason 5/11/06 7:24:08 PM EDT: 1+2+3+4+...n = ((n)(n+1))/2

===Recursive Function (Again?) and the Feedback ===
Noticed how 137 uses "again" but qwerty, who is new, just asks plainly what is it (earlier he got a very different response with "how did you get it" )

Jason 5/11/06 7:26:32 PM EDT: so apparently there's something with a recursive sequence that we should discuss
137 5/11/06 7:26:55 PM EDT: What was a recursice sequence again?
qwertyuiop 5/11/06 7:27:03 PM EDT: recursive sequence?

...

Jason 5/11/06 7:27:18 PM EDT: i think that an explicit formula is better, but a recursive one would show how the number of squares/sticks increases as N increases
Jason 5/11/06 7:27:35 PM EDT: it's something like this:
Jason 5/11/06 7:27:45 PM EDT: a(n) = 5+ a(n-1)
Jason 5/11/06 7:27:53 PM EDT: where the things in parentheses are supposed to be subscripts
Jason 5/11/06 7:28:07 PM EDT: so a recursive formula relies on the value of a previous function
137 5/11/06 7:28:09 PM EDT: Ah, I see.
Jason 5/11/06 7:28:19 PM EDT: thus, you must specify something first, like a(1) = 4
qwertyuiop 5/11/06 7:28:29 PM EDT: i get it
Jason 5/11/06 7:28:54 PM EDT: great :-)
qwertyuiop 5/11/06 7:30:07 PM EDT: for the number of squares, would that be: a(n)=n2-1
137 5/11/06 7:30:15 PM EDT: so a(1)=1, a(n)=n+a(n-1)...

...

137 5/11/06 7:33:06 PM EDT: b(1)=4, b(n)=b(n-1)+4(n)-(n-1)-(n-1), b is the number ofr sticks...
137 5/11/06 7:33:30 PM EDT: So b(n)=b(n-1)+2n+2?
Jason 5/11/06 7:33:51 PM EDT: assuming only (n-1) is a subscript?

...

Jason 5/11/06 7:35:13 PM EDT: did u check that
Jason 5/11/06 7:35:39 PM EDT: looks correct
Jason 5/11/06 7:35:45 PM EDT: how did you get it?

Noticed that this "how did you get it" is in essence the same question that QW asked at the beginning but the answer does not bring the "narrative" of the team (we did this last time and then this, and you can find it in the wiki and in the textboxes)

Jason 5/11/06 7:35:45 PM EDT: how did you get it?
137 5/11/06 7:36:23 PM EDT: There are n-1 overlaps here...
137 5/11/06 7:36:24 PM EDT: Wait.
p M M M
137 5/11/06 7:36:36 PM EDT: Those.
137 5/11/06 7:36:43 PM EDT: And n-1 here:
qwertyuiop 5/11/06 7:36:45 PM EDT: those?
p M M M M
Jason 5/11/06 7:36:57 PM EDT: what do you mean by :"overlaps"
137 5/11/06 7:37:17 PM EDT: They're counted twise; they belong to two boxes.
p M M M M M
Jason 5/11/06 7:38:13 PM EDT: are you guys still talking about that formula?

===I liked the "original" one===
and back to why recursive function is better? (Jason)

Jason 5/11/06 7:41:48 PM EDT: well this requires you to first calculate number of squares;
i think the formulas for each of these should be seperate
Jason 5/11/06 7:41:58 PM EDT: i liked the original formula
Jason 5/11/06 7:42:05 PM EDT: in my quick checking it worked
137 5/11/06 7:42:06 PM EDT: So did I...
137 5/11/06 7:42:18 PM EDT: The first one seeemed simpler.
Jason 5/11/06 7:42:39 PM EDT: but this one has a nice explanation :-)
Jason 5/11/06 7:42:43 PM EDT: i mean
qwertyuiop 5/11/06 7:42:54 PM EDT: we already have the square formula; just include it: n(1+n)+n2
Jason 5/11/06 7:43:16 PM EDT: yup
qwertyuiop 5/11/06 7:43:41 PM EDT: that looks like the same thing as n*(N+3) at a glance...
Jason 5/11/06 7:43:51 PM EDT: so speaking of formulas, we got both explicit and recursive definitions for sticks/squares;
explicit is easier while recursive shows how each step grows from the previous

Notice, by "we got" does he mean "in both sessions" "all who have worked here". At that point the recursive functions have not been placed on the whiteboard but qwertyop quickly adds one of them to it:

----------------------------------
| Formula for total # of squares: |
| |
| n(1+n)/2 |
| a(n)=n+a(n-1) |
| |
----------------------------------

===Other problems to do?===

qwertyuiop 5/11/06 7:48:37 PM EDT: are there other problems to do?
137 5/11/06 7:48:51 PM EDT: I do not think so...
Jason 5/11/06 7:48:58 PM EDT: well
Jason 5/11/06 7:49:03 PM EDT: we are supposed to come up with some
qwertyuiop 5/11/06 7:49:10 PM EDT: ok...
Cynthia 5/11/06 7:49:13 PM EDT: did you view the topic for tonight, session 2
Jason 5/11/06 7:49:17 PM EDT: WHAT IF? Mathematicians do not just solve other people's problems - they also explore little worlds
of patterns that they define and find interesting. Think about other mathematical problems related to the problem with the sticks.
For instance, consider other arrangements of squares in addition to the triangle arrangement (diamond, cross, etc.). What if
instead of squares you use other polygons like triangles, hexagons, etc.? Which polygons work well for building patterns like
this? How about 3-D figures, like cubes with edges, sides and cubes? What are the different methods (induction, series, recursion,
graphing, tables, etc.) you can use to analye these different patterns?
--->(Taken from the topic)
Cynthia 5/11/06 7:49:45 PM EDT: thanks, jason
137 5/11/06 7:50:07 PM EDT: Let's try diamonds first..

===The "each square with 2 sides" thing doesn't work as neatly here===
This is something that QW had said earlier when speaking about "overlap" ( qwertyuiop 5/11/06 7:39:02 PM EDT: might be easier if you think of each square corisponding to 2 sides-the right and bottom sides, and then add the upper left border)

Jason 5/11/06 7:53:52 PM EDT: ok
Jason 5/11/06 7:53:57 PM EDT: sorry for the delay on my part
137 5/11/06 7:54:03 PM EDT: So the number of squares is n^2 +4, where n is a side length
qwertyuiop 5/11/06 7:54:12 PM EDT: the "each square with 2 sides" thing doesn't work as neatly here
Jason 5/11/06 7:54:13 PM EDT: if we look at rows, its 1, 3, 5, 3, 1

===How did you get that===
This is the third "how did you get that" of the session. It required a second call for an uptake.

qwertyuiop 5/11/06 7:54:28 PM EDT: how did you get that?
Jason 5/11/06 7:54:29 PM EDT: by side length you mean...
p M M M
137 5/11/06 7:54:50 PM EDT: The orange.
(...)
Jason 5/11/06 7:55:52 PM EDT: can you explain how you got that formula?

137 attempts a number of diagrams but seems to have trouble with coloring. Later QW posts a formula for Number of sides. Jason rembers that 137 had posted a formula earlier and points to it (this one)

qwertyuiop 5/11/06 8:00:57 PM EDT: i think NumberOfSides=NumberOfSquares*2+SideLength*3-2
p M M
Jason 5/11/06 8:01:29 PM EDT: wait-- you gave a formula earlier
p M
Jason 5/11/06 8:01:34 PM EDT: lemme see if i can find it
p M
qwertyuiop 5/11/06 8:01:42 PM EDT: because it's like the first shape, but with 3 other edges
p M
Jason 5/11/06 8:01:55 PM EDT: this one
p M M M M M M
Jason 5/11/06 8:02:12 PM EDT: oh but you're talking about # of sides

later with more diagrams, 137 posts that "he screwed up somewhere" and Jason makes another observation:

Jason 5/11/06 8:08:18 PM EDT: the fact that, when the squares are arranged in a diamond shape result in 1+3+5+3+1
total squares in the diagram to the left, remind me of pascal's triangle
Jason 5/11/06 8:08:35 PM EDT: just a thought... not sure if it'll work

Then QW makes a proposal "using your previous method" which they agree works:

qwertyuiop 5/11/06 8:08:35 PM EDT: using your previous method: SideLenght^2 + (SideLength-1)^2
qwertyuiop 5/11/06 8:08:51 PM EDT: does that work?
qwertyuiop 5/11/06 8:10:06 PM EDT: the part in front of the plus is the large, rotatewd 45 square and
the part after it is the smaller, not rotated squared
qwertyuiop 5/11/06 8:10:59 PM EDT: um... hello?
137 5/11/06 8:11:03 PM EDT: Hi.
Jason 5/11/06 8:11:17 PM EDT: well, looking at the center diagram with the orange boxed
qwertyuiop 5/11/06 8:11:18 PM EDT: but does that work?
Jason 5/11/06 8:11:20 PM EDT: boxes
Jason 5/11/06 8:11:24 PM EDT: you'd be 1 off
Jason 5/11/06 8:11:41 PM EDT: nvm, my arithmetic skills faltered ther
Jason 5/11/06 8:11:42 PM EDT: e
p M M
Jason 5/11/06 8:11:59 PM EDT: there
qwertyuiop 5/11/06 8:12:03 PM EDT: checking for SideLenght=3...
Jason 5/11/06 8:12:35 PM EDT: works
qwertyuiop 5/11/06 8:12:36 PM EDT: yes, it works
Jason 5/11/06 8:12:52 PM EDT: cool, so should we call this a formula

And the forth "how do you get it" of the session:

137 5/11/06 8:12:57 PM EDT: I don't get why though...
Jason 5/11/06 8:13:29 PM EDT: i dont either
p M M M M
qwertyuiop 5/11/06 8:14:10 PM EDT: I used your previous method: take the (orange) side; that^2 gives part of the shape...
qwertyuiop 5/11/06 8:15:03 PM EDT: the rest happens to be a square with a side length of one less, therfore th "(SideLength-1)^2"
qwertyuiop 5/11/06 8:15:10 PM EDT: does that make sense?
Jason 5/11/06 8:15:42 PM EDT: i get it!
Jason 5/11/06 8:15:43 PM EDT: clever :)
qwertyuiop 5/11/06 8:15:48 PM EDT: 137?
137 5/11/06 8:15:56 PM EDT: Now I do.

===3D but time runs out===
and the moderator suggests working on the Wiki

qwertyuiop 5/11/06 8:22:40 PM EDT: to make it more 3D, you could continue the pattern along the new dimension
qwertyuiop 5/11/06 8:22:57 PM EDT: not sure how you would draw that...
Jason 5/11/06 8:23:38 PM EDT: well going back to our session problems
Jason 5/11/06 8:23:38 PM EDT: What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns?
Jason 5/11/06 8:23:57 PM EDT: i'd say series (recursive or explicit) for many of them
Jason 5/11/06 8:24:49 PM EDT: anyone else?
qwertyuiop 5/11/06 8:24:59 PM EDT: induction?
Jason 5/11/06 8:25:58 PM EDT: what's that
...

Notice "last time" but no incidence in problem solving

Cynthia 5/11/06 8:26:13 PM EDT: so i'm wondering if this is a good time to figure out the information that you are going to post to the wiki?
Jason 5/11/06 8:26:30 PM EDT: hmm
qwertyuiop 5/11/06 8:26:30 PM EDT: the equations...
Jason 5/11/06 8:26:55 PM EDT: well im not sure if we formulated too many questions to post, but i guess yeah we can write up our formulas and how we got them
qwertyuiop 5/11/06 8:28:25 PM EDT: there are 4, I think: number of squares and number of sides for both diamonds and the first problem
Jason 5/11/06 8:28:47 PM EDT: alright
Jason 5/11/06 8:29:05 PM EDT: last time we designated one person to write up the wiki...
do you guys want to do that again or should we all assign each other some part to write
qwertyuiop 5/11/06 8:29:35 PM EDT: we could just do it here
Jason 5/11/06 8:29:47 PM EDT: do what here
qwertyuiop 5/11/06 8:29:59 PM EDT: write it

==Feedback II==
Dear Jason, 137, davidcyl, ssjnish, and qwertyuiop

Last time you had a very creative session where you explored a number of new ideas
related to the sticks and squares problem. We found it interesting how you worked
as a team to clarify what a recursive formula is and how to find one for the sticks and squares.
We also noticed that you concluded that "an explicit formula is better, but a recursive
one would show how the number of squares/sticks increases as N increases".
We wondered what other teams working on the problem might think about this idea
so maybe you want to post it to the Wiki?

Your exploration of the diamond shape was also very interesting to us, and your posting to the Wiki
should be helpful to other teams thinking about similar cases. For the next step
we will encourage you to continue thinking about the problems that you can discover on your own
and that are interesting to pursue, and also to explore the different approaches to solve them.
BTW, remember that you can load the old chat messages by clicking on the double arrow icon
above the chat scroll bar. You can look through the history of the whiteboard by using the scroll bar
all the way on the left (be sure to scroll all the way down to the present in order to draw anything new.)

-The VMT team.

==Session III==
Noticed that this session's feedback does not really contain any statements about things "you should have done different". A couple of suggestions for things to post on the wiki are followed up eventually but there is really no other direct discussion about the feedback. One could say that there is uptake because the suggestion of working on problems the group finds interesting is, indeed, what they do

===we do what we did last time again?===

137 5/16/06 7:04:41 PM EDT: So we do what we did last time again?
nan 5/16/06 7:04:47 PM EDT: yes

===Triangular Numbers===
137 creates a hexagonal grid on the whiteboard but it doesn't look too good so he asks somebody else to try it. QW does it:

qwertyuiop 5/16/06 7:14:51 PM EDT: triangles are done
137 5/16/06 7:15:08 PM EDT: So do you want to first calculate the number of triangles in a hexagonal array?

They work on this grid for a while and come to the idea of triangular numbers. This is something that Team B also worked withbut for which there is no group-to-group exchange. First both QW and 137 make references to things they had contributed in the previous session: "each polygon corrisponds to 2 sides" and the 1-3-5 pattern. Only QW does it explicitly with a reference to LAST TIME and quotes:

Jason 5/16/06 7:20:02 PM EDT: so... should we try to find a formula i guess
Jason 5/16/06 7:20:22 PM EDT: input: side length; output: # triangles
qwertyuiop 5/16/06 7:20:39 PM EDT: It might be easier to see it as the 6 smaller triangles.
137 5/16/06 7:20:48 PM EDT: Like this?
p M M M
qwertyuiop 5/16/06 7:21:02 PM EDT: yes
Jason 5/16/06 7:21:03 PM EDT: yup
p M M
qwertyuiop 5/16/06 7:21:29 PM EDT: side length is the same...
Jason 5/16/06 7:22:06 PM EDT: yeah
Jason 5/16/06 7:22:13 PM EDT: so it'll just be x6 for # triangles in the hexagon
137 5/16/06 7:22:19 PM EDT: Each one has 1+3+5 triangles.
Jason 5/16/06 7:22:23 PM EDT: but then we're assuming just regular hexagons
qwertyuiop 5/16/06 7:22:29 PM EDT: the "each polygon corrisponds to 2 sides" thing we did last time doesn't work for triangles

later 137 proposes a formula and JS offers support with an objection:

137 5/16/06 7:24:49 PM EDT: And there are n terms so... n(2n/2)
137 5/16/06 7:25:07 PM EDT: or n^2
Jason 5/16/06 7:25:17 PM EDT: yeah
Jason 5/16/06 7:25:21 PM EDT: then multiply by 6
137 5/16/06 7:25:31 PM EDT: To get 6n^2
Jason 5/16/06 7:25:39 PM EDT: but this is only with regular hexagons... is it possible to have one
definite formula for irregular hexagons as well

So they do some more work and triangular numbers emerge

qwertyuiop 5/16/06 7:33:54 PM EDT: I don't see the pattern yet...
137 5/16/06 7:34:01 PM EDT: We're ignoring the bottom one?
p M M M
qwertyuiop 5/16/06 7:34:29 PM EDT: no, 3 is only for side length 2.
137 5/16/06 7:34:52 PM EDT: And I think the'y;re all triangular numbers.
p M M M
qwertyuiop 5/16/06 7:35:17 PM EDT: "triangular numbers"?
p M M M M M M
Jason 5/16/06 7:35:37 PM EDT: you mean like 1, 3, 7, ...
Jason 5/16/06 7:35:39 PM EDT: ?
137 5/16/06 7:35:59 PM EDT: Like 1,3,6,10,15,21,28.
qwertyuiop 5/16/06 7:36:02 PM EDT: the sequence is 1, 3, 6...
137 5/16/06 7:36:30 PM EDT: Numbers that can be expressed as n(n+1)/2, where n is an integer.
qwertyuiop 5/16/06 7:36:45 PM EDT: ah

===Team B Asks a Question===

nan 5/16/06 7:48:49 PM EDT: (we got a question for you from another team, which was posted in the lobby:
nan 5/16/06 7:48:53 PM EDT: Quicksilver 7:44:50 PM EDT: Hey anyone from team c, our team needs to know what n was in your equations last week
Jason 5/16/06 7:49:04 PM EDT: oh
137 5/16/06 7:49:15 PM EDT: The length of a side.
qwertyuiop 5/16/06 7:49:16 PM EDT: was n side length?
Jason 5/16/06 7:49:33 PM EDT: are you talking about the original problem with the squares
137 5/16/06 7:49:48 PM EDT: I think nan is.
qwertyuiop 5/16/06 7:49:58 PM EDT: i think it's squares and diamonds
Jason 5/16/06 7:49:58 PM EDT: oh
Jason 5/16/06 7:50:12 PM EDT: then if you look in the topic description, theres a column for N;
Jason 5/16/06 7:50:14 PM EDT: thats what it is
nan 5/16/06 7:50:17 PM EDT: ok, quicksilver said they got it
Jason 5/16/06 7:50:25 PM EDT: so yes it is # sides
nan 5/16/06 7:50:26 PM EDT: thanks guys

===Collecting Formulas on Textbox===
Jason leaves first, but Qw and 137 continue to work:

...
qwertyuiop 5/16/06 8:06:20 PM EDT: it's x3 for the 3 colinear sets, then x6 for 6 triangles in a hexagon... where's the 9 and 2?
qwertyuiop 5/16/06 8:06:28 PM EDT: oh
137 5/16/06 8:06:38 PM EDT: So 18/2.
137 5/16/06 8:06:50 PM EDT: A.K.A. 9
qwertyuiop 5/16/06 8:07:08 PM EDT: (n(n+1)/2)x3x6
137 5/16/06 8:07:15 PM EDT: Yeah.
qwertyuiop 5/16/06 8:07:27 PM EDT: which can be simplified...
137 5/16/06 8:07:46 PM EDT: To 9n(n+1)
qwertyuiop 5/16/06 8:08:04 PM EDT: that's it?
137 5/16/06 8:08:12 PM EDT: -6n.
137 5/16/06 8:08:24 PM EDT: So 9n(n+1)-6n
qwertyuiop 5/16/06 8:08:34 PM EDT: i'll put it with the other formulas...

There is a bit of collision while editing the texbox but at the end it looks like this:

SIDES:
N(N+3)
diamond:
(n^2+(n-1)^2)*2+n*3-2
hexagon w/ triangles:
9n(n+1)-6n

POLYHEDRA:
square
n(n-1)/2
diamond:
n^2+(n-1)^2
hexagon w/ triangles
6n^2

===The hypercube: Imagine our first problem with a grid of squares.... Resume here next time ===

qwertyuiop 5/16/06 8:15:02 PM EDT: If you have a square, it extends to make a grid that fills a plane. A cube fills a space. A simaller pattern of hypercubes fills a "hyperspace".
p M M
137 5/16/06 8:15:19 PM EDT: The heck?
137 5/16/06 8:15:29 PM EDT: That's kinda confusing.
p M M M M M
qwertyuiop 5/16/06 8:15:43 PM EDT: So, how many planes in a hyper cube latice of space n?
p M M M M M M M
137 5/16/06 8:16:05 PM EDT: Er...
qwertyuiop 5/16/06 8:16:07 PM EDT: instead of "how many lines in a grid of length n"
qwertyuiop 5/16/06 8:16:17 PM EDT: does that make any sense?
137 5/16/06 8:16:30 PM EDT: No. No offense, of course.
qwertyuiop 5/16/06 8:16:43 PM EDT: ok... let me think...
p M M M M M M
qwertyuiop 5/16/06 8:17:19 PM EDT: Imagine our first problem with a grid of squares.
p M M
137 5/16/06 8:17:31 PM EDT: Right.
p M M
qwertyuiop 5/16/06 8:18:07 PM EDT: The squares are 2 dimensional and they can be arranged in a grid to tessalate over a plane. The plane is also 2 dimensional.
p M
137 5/16/06 8:18:41 PM EDT: Right.
qwertyuiop 5/16/06 8:18:54 PM EDT: If you use 3 dimensional cubes, they can be arranged to fill a 3 dimensional space.
137 5/16/06 8:19:17 PM EDT: And that structure's 4 dimensional?
qwertyuiop 5/16/06 8:19:25 PM EDT: If you have hypercubes, they can be arranged to fill a 4 dimensional "hyperspace"
qwertyuiop 5/16/06 8:19:36 PM EDT: what's 4D?
137 5/16/06 8:19:46 PM EDT: ?
nan 5/16/06 8:20:04 PM EDT: you may want to make your ideas available on the wiki before you go
nan 5/16/06 8:20:09 PM EDT: which may take some time
137 5/16/06 8:20:24 PM EDT: Actually, I only have around 10 minutes left.
...
(Moderator prompts to stop and work on the wiki)
...
137 5/16/06 8:21:33 PM EDT: So how the heck are we supposed to calculate the number of four-dimentional figures?
nan 5/16/06 8:21:42 PM EDT: do you want to stop here and start putting ideas on wiki?
qwertyuiop 5/16/06 8:21:47 PM EDT: ok
137 5/16/06 8:21:52 PM EDT: Sure.
qwertyuiop 5/16/06 8:22:09 PM EDT: resume from here next time?
p M M
nan 5/16/06 8:22:17 PM EDT: sure
137 5/16/06 8:22:19 PM EDT: Ya.

===Wiki===

qwertyuiop 5/16/06 8:22:48 PM EDT: We have the 2 hexagon equations to put on the wiki.
p M M
137 5/16/06 8:23:04 PM EDT: Right.
p M M M
qwertyuiop 5/16/06 8:23:18 PM EDT: Where's the wiki again?
p M
nan 5/16/06 8:23:30 PM EDT: open "view topic"
137 5/16/06 8:23:31 PM EDT: Somewhere in the View topic button
p M
nan 5/16/06 8:23:41 PM EDT: there's link
qwertyuiop 5/16/06 8:23:54 PM EDT: I see it.
137 leaves the room 5/16/06 8:24:28 PM EDT
qwertyuiop 5/16/06 8:25:02 PM EDT: i'll write it.

==Feedback III==

Dear Team C: We noticed that you continued working on your idea of a pattern of
“hexagons made of triangles” and you discussed some possible formulas for the number of sides and triangles.
There is a sense in your conversation that at the end you ran out of time to fully check and discuss
these formulas, so if you want to do that today, that would be ok. If you feel that you understand that pattern
already and that your notes on the Wiki are good for others to understand your ideas, you can explore other patterns
that you find interesting. You could also explore some of the ideas presented by other groups on the Wiki.
When revisiting the idea of a hypercube and a pattern in 4-dimensions wee also noticed that you were looking
for the relationship between similar patterns in different dimensions, and that made us think of a number
of interesting ideas. Enjoy your fourth session! -The VMT Team

== Session IV ==
Jason missed the last part of Session III, so asks to be caught up. Differentiates between "keep thinking" and "start"
ss is coming back after missing 2 sessions and participates very little in this final session.

===Keep thinking... or start?===

qwertyuiop 5/18/06 7:06:22 PM EDT: do we want to keep thinking about the hexagon thing or start on the hypercube?
p M M M M M M M
Jason 5/18/06 7:06:43 PM EDT: well if we want to start on the hypercube i'll need to first fully
understand the concept of the fourth dimension
p M M M M M M
qwertyuiop 5/18/06 7:07:05 PM EDT: what needs clairifying?
p M M M M M
Jason 5/18/06 7:07:12 PM EDT: everything, pretty much
ssjnish 5/18/06 7:07:19 PM EDT: same here
qwertyuiop 5/18/06 7:07:30 PM EDT: ok... imagine a cube
(Moves objects on the Whiteboard to make space)
qwertyuiop 5/18/06 7:07:56 PM EDT: it tessalates in a grid to fill a 2 dimensional plane
p M M M M M M M M M M
qwertyuiop 5/18/06 7:08:39 PM EDT: it's made of 4 parts (sides) of one dimension lower than itself (1 dimensional lines)
qwertyuiop 5/18/06 7:08:49 PM EDT: does that make sense so far?
p M M M
137 5/18/06 7:09:08 PM EDT: Yeah.
p M M M M M M M M
Jason 5/18/06 7:09:42 PM EDT: hmm
p M
qwertyuiop 5/18/06 7:10:01 PM EDT: a cube is made of 6 parts one dimension lower than itself (6 2 dimensional faces) and can be arranged to fill a 3 dimensional space
Jason 5/18/06 7:10:03 PM EDT: well u guys can go ahead with the hypercube if you want, i probably wont be able to contribute much though
137 5/18/06 7:10:20 PM EDT: Neither will I.
qwertyuiop 5/18/06 7:10:36 PM EDT: we could just do a cube
Jason 5/18/06 7:10:45 PM EDT: ok, that'll probably be a bit easier :-)
qwertyuiop 5/18/06 7:11:01 PM EDT: i'll start drawing

===The first problem and the hypercube + Like last time===

qwertyuiop 5/18/06 7:14:09 PM EDT: on the first problem, the pattern continued in 2 dimensions (up and left) so this should continue in 3 (along each axis)
qwertyuiop 5/18/06 7:14:18 PM EDT: does that make sense?
Jason 5/18/06 7:14:31 PM EDT: yea
137 5/18/06 7:14:32 PM EDT: Yes.
...
137 5/18/06 7:20:31 PM EDT: I think we should just look at it in 3 groups of parallel lines like last time.

===Triangular numbers===
Notice the reapearance of the definition of triangular numbers

Jason 5/18/06 7:26:29 PM EDT: can you get the next level for these cubes
Jason 5/18/06 7:26:38 PM EDT: then we might be able to start seeing a pattern
p M M M M M
qwertyuiop 5/18/06 7:27:20 PM EDT: I think that's n=4.
137 5/18/06 7:27:34 PM EDT: The number of cubes is the sum of n consecutive triangular numbers...
qwertyuiop 5/18/06 7:27:49 PM EDT: triangular?
qwertyuiop 5/18/06 7:27:49 PM EDT:
Jason 5/18/06 7:27:57 PM EDT: woah
Jason 5/18/06 7:28:15 PM EDT: (reacting to the diagram i mean)
137 5/18/06 7:28:22 PM EDT: Numbers that are the sum of counstecutibe numbers starting from 1...
Jason 5/18/06 7:28:43 PM EDT: how many cubes are in that diagram that you just posted?
qwertyuiop 5/18/06 7:28:45 PM EDT: counstecutible?
137 5/18/06 7:28:57 PM EDT: consecutive.
137 5/18/06 7:29:07 PM EDT: Sry.
qwertyuiop 5/18/06 7:29:09 PM EDT: 1 min
137 5/18/06 7:29:34 PM EDT: 10+6+3+1=20.

===The evolution of Whiteboard Notes===
It is interesting that this team keeps all its results in a single textbox on the whiteboard. In the wiki, there is more explanation but on the whiteboard it is a place to keep all the formulas organized and, as new formulas/results are added, some of the existing labels are changes to represent the "expanding" notions that they are working with. For example, in the original problem, there were sticks and squares as the "primary" elements but they labeled them "squares" and "sides" which worked for both the original pattern and their diamond pattern, however, when they work with the hexagon made up of triangles, they changed squares to "POLYHEDRA" and recorded that hexagons as "hexagon/w triangles". This is how the formula for the number of cubes in their piramid gets recorded in that textbox:

SIDES:
square:
N(N+3)
diamond:
(n^2+(n-1)^2)*2+n*3-2
hexagon w/ triangles:
9n(n+1)-6n

POLYHEDRA:
square
n(n-1)/2
diamond:
n^2+(n-1)^2
hexagon w/ triangles
6n^2
cubes in pyramid shape:
f(n)=f(n-1)+x(X+1)/2

Now that they are working with cubes, they can use, sticks, squares ("faces"), and cubes.

===Like we said earlier===
Earlier in Session II

qwertyuiop 5/18/06 7:41:25 PM EDT: or do we want to put that function in a different form?
Jason 5/18/06 7:41:35 PM EDT: i think that form is good
Jason 5/18/06 7:41:49 PM EDT: like we said earlier, recursiveness=easy to track pattern of growth

===Wouldn't this work?===
OT points to his earlier posting indicating a reuse of something they did in last session on the hexagon.
Notice that "overlap" resurfaces as a relevant concern.

137 5/18/06 7:41:52 PM EDT: Wouldn't this work? [Points to: I think we should just look at it in 3 groups of parallel lines like last time.]
137 5/18/06 7:42:06 PM EDT: Each cube has 2 pointing each direction.
137 5/18/06 7:42:11 PM EDT: Wait.
137 5/18/06 7:42:13 PM EDT: 4.
qwertyuiop 5/18/06 7:42:28 PM EDT: i think so [Points to: Wouldn't this work?]
qwertyuiop 5/18/06 7:43:38 PM EDT: the overlap is different depending on wether the cube is on the outside of the shape or on the inside

Later QW makes a series of very interesting graphs that form a proposal for how to calculate the number of edges and posts:

qwertyuiop 5/18/06 7:48:21 PM EDT: an idea: Each cube is assigned to 3 edges. Then add the edges on the diagonalish face.
qwertyuiop 5/18/06 7:48:44 PM EDT: does that make sense?
137 5/18/06 7:48:58 PM EDT: Not really...
qwertyuiop 5/18/06 7:49:13 PM EDT: let me think how to explain it...
Jason 5/18/06 7:49:13 PM EDT: well some would be the same
p M M M
qwertyuiop 5/18/06 7:51:36 PM EDT: oops
p M
qwertyuiop 5/18/06 7:52:44 PM EDT: see those 3 highlighted edges?
Jason 5/18/06 7:53:32 PM EDT: yeah
Jason 5/18/06 7:53:37 PM EDT: theyre in red
qwertyuiop 5/18/06 7:54:09 PM EDT: those would be the edges assigned to that cube (the cube at the bottom corner)
qwertyuiop 5/18/06 7:54:15 PM EDT: still make sense?

qwertyuiop 5/18/06 8:02:49 PM EDT: so the first part of the equation would be 3 times the number of cubes
qwertyuiop 5/18/06 8:03:12 PM EDT: I cn't think how to get the other part, though.

but unfortunately time runs out and the moderator closes the session with some questions.

===Usually....===

qwertyuiop 5/18/06 8:09:15 PM EDT: Usually when I work in a group, I don't do much. Here, I had a lot more to say.

End

ToRead

Jsarmi — Thu, 29 Nov 2007 16:42:55 GMT

Jsarmi:

==To Reads==
* [http://www.apa.org/monitor/oct03/sins.html The Seven Sins of Memory] by Daniel Sachter

* [http://mitpress.mit.edu/catalog/item/default.asp?tid=10684&ttype=2 The Complementary Nature] by J. Scott & David Engstrom

* [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=4679 Dynamic Patterns]: The Self-Organization of Brain and Behavior by J. Kelso
* [[http://www.jstor.org/cgi-bin/jstor/printpage/00014273/sp030002/03x0027a/0?frame=noframe&dpi=3&userID=90763528@drexel.edu/01cce4405b00501cd48b0&backcontext=page&backurl=/cgi-bin/jstor/viewitem/00014273/sp030002/03x0027a/0%3fframe%3dnoframe%26dpi%3d3%26userID%3d90763528@drexel.edu/01cce4405b00501cd48b0%26config%3d%26PAGE%3d0&action=download&config=jstor Getting It Together]]: Temporal Coordination and Conflict Management in Global Virtual Teams. Mitzi M. Montoya-Weiss; Anne P. Massey; Michael Song. The Academy of Management Journal, Vol. 44, No. 6. (Dec., 2001), pp. 1251-1262.

* [[http://www.journals.uchicago.edu/cgi-bin/resolve?id=doi:10.1086/339566 Time in Action]] Charles Goodwin

* [[http://www.journals.uchicago.edu/cgi-bin/resolve?id=doi:10.1086/427120 Explorations in the Deictic Field]] William Hanks

==Find==

TWO GREAT ELECTRONIC BOOKS AT DREXEL:

:*Context and appropriateness [electronic resource] micro meets macro / edited by Anita Fetzer.
::Philadelphia : J. Benjamins Pub. Co., 2007.

:*Rethinking sequentiality [electronic resource] linguistics meets conversational interaction
::edited by Anita Fetzer and Christiane Meierkord
::Amsterdam ; Philadelphia : John Benjamins Pub. Co., c2002.

ALSO

:*Dynamics of Groups and Teams: Groups as Complex Action Systems
::Joseph E. McGrath and Franziska Tschan
::Chapter 3 (p. 50-) in Handbook of Organizational Change and Innovation
::Edited by Marshall Scott Pole and Andrew H. Van de Ven
::Published 2004 by Oxford University Press US ISBN 0195135008

People

Jsarmi — Thu, 29 Nov 2007 16:32:00 GMT

Jsarmi:

Some people whose ideas, I track (sometimes):

:* [http://darkwing.uoregon.edu/~harrow/ Holly Arrow]
:* [http://www.visi.com/~snowfall/ Tom Erickson]
:* [http://www.cis.drexel.edu/faculty/gerry/ Gerry Stahl]
:* [http://del.icio.us/jsarmi/Alterman Alterman]
:* [http://del.icio.us/jsarmi/Amidon Amidon]
:* [http://del.icio.us/jsarmi/dieberger dieberger]
:* [http://del.icio.us/jsarmi/gomez gomez]
:* [http://del.icio.us/jsarmi/Halverson Halverson]
:* [http://del.icio.us/jsarmi/Hoadley Hoadley]
:* [http://cogsci.ucsd.edu/~kirsh/ David Kirsh]
:* [http://del.icio.us/jsarmi/lakoff lakoff]
:* [http://del.icio.us/jsarmi/schuler schuler]
:* [http://del.icio.us/jsarmi/Stahl Stahl]
:* [http://del.icio.us/jsarmi/Viegas Fernanda Viegas]
:* [http://garfield.library.upenn.edu/classics.html Eugene Garfield]
:* [http://www.psy.cmu.edu/~siegler/publications-all.html Robert Siegler]
:* [http://www.pitt.edu/~chi/Publications%20page.htm Micki Chi]
:* [http://www.msu.edu/~jwalther/ Joseph Walther]

:* [http://www.37signals.com/ 37 Signals]

Apps/CoverL1

Jsarmi — Wed, 28 Nov 2007 18:47:41 GMT

Jsarmi:

:'''Johann W. Sarmiento'''
:iSchool at Drexel University
:2601 Pennsylvania Ave, #508 Philadelphia, PA 19130
:1 - 215 - 888 - 0603
:jsarmi@drexel.edu - jsarmi@gmail.com

:November 25, 2007

:Chair, Learning Science Search Committee
:Graduate School of Education
:University of Pennsylvania
:3700 Walnut St.
:Philadelphia, PA 19104

:Dear Chair and Members of the Learning Science Search Committee:

:I am delighted to apply for the faculty position in Learning Sciences/Learning Technologies at the University of Pennsylvania Graduate School of Education, as advertised in the Chronicle of Higher Education. The field of the Learning Sciences has been my central area of research and development work for close to fifteen years and one which, I strongly believe, is uniquely positioned to make significant contributions to both foundational learning theory and innovative educational practice. As an avid participant of the International Society of the Learning Sciences and the Computer-supported Collaborative Learning community of practice, I feel strongly connected to these two fields and to their crucial role in understanding and shaping human and social development. My interdisciplinary background, track record of funded research and publications, and ample expertise in K-12 learning technologies would allow me to make significant contributions to the development of the new specialization in Learning Technologies in Education at the Graduate School of Education as well as to complement and strengthen the high-quality work conducted in other related programs.

:Building on my applied research experiences and extending them to anticipate the evolving field of learning technologies, my current research agenda intertwines three major strands of work. First, as a foundation to all my work, I engage in design-based research aimed at iteratively evolving the design of technology-supported learning environments while, at the same time, advancing aspects of socio-cultural learning theory by studying through mixed methods the forms of learning that emerge from activity in such new learning contexts. Second, my work explores the design and study of collaborative knowledge-building environments that contribute to content learning in K-12 contexts (e.g. mathematics and science learning) as well as to adult professional development and to the development of communities of practice. Finally, I investigate the enabling role of technology-supported strategies for assessing learning and supporting data-driven decision making in educational contexts.

:My most recent work is situated in the field of Computer-supported Collaborative Learning (CSCL) and focuses on investigating the role of learning technologies in promoting and supporting sustained collaborative knowledge building in mathematics. For instance, in my dissertation work I investigate, from a socio-cultural perspective, the ways that rich and sustained interactions in a virtual environment contribute to the construction of math knowledge and the development of a diverse community of practice over time. This NSF-funded work takes place within the context of the Virtual Math Teams (VMT) project at the Math Forum (http://mathforum.org), a well established online community which promotes technology-mediated interactions among teachers of mathematics, students, mathematicians, staff members and others interested in learning, teaching and doing mathematics. My analysis has shown that in longitudinal collaborative knowledge building, learners are faced with the challenge of "bridging" multiple episodes of activity, multiple collectivities, and multiple perspectives -a non trivial and possibly very consequential undertaking. Studying bridging has revealed linkages among group meaning-making efforts, across episodes of interaction over time, and across phases of individual understanding. This work has also pointed out aspects of the online environment that can promote and support bridging in knowledge building. The VMT project has been an extraordinary opportunity to forge collaborative relationships with colleagues and collaborators within the U.S. and abroad including researchers in the CSCL workgroup of the International Society of the Learning Sciences, the European research network Kaleidoscope, and the Laboratory for Interactive Learning Technologies at the University of Hawaii, among others.

:Before joining the Virtual Math Teams project, I served as the director of the Advanced Technologies for Learning (ATL) laboratory at the Center for Research in Human Development and Education at Temple University. The ATL's program of applied research focused on the effective integration of learning technologies to diverse K-12 content areas, professional development, and data-driven decision making. This work, funded by the U.S. Department of Education, provided me with ample opportunities to study and implement multiple ways in which learning technologies can contribute to systemic K-12 reform in complex urban contexts as well as at different levels of the educational system, from the individual classroom to the school building and scaling up to the district and regional levels. One of the most crucial challenges we addressed was the implementation of learning technologies that were closely aligned with existing curriculum frameworks and yet expanded the possibilities of disadvantaged learners towards active learning, inquiry and reflection, and collaborative knowledge building. In addition, our research and development work on Reflection Connection, an online environment for teacher professional development and collaborative knowledge building, showed how iterative cycles of collaborative planning, action, and reflection anchored on samples of student work can lead to pre-service and in-service teachers becoming more reflective practitioners. This work was also a career-shaping opportunity to participate in large-scale interdisciplinary research and field work integrating perspectives and contributions from educators, psychologists, educational administrators, sociologists, statisticians, and information technology professionals.

:Given the nature of my research and development work, I have always found that my own teaching is a most propitious setting to apply and advance my personal knowledge of human learning and instruction. As described in my curriculum vitae, I have significant instructional experience in a wide range of topics and contexts. From after-school informal programs to undergraduate and graduate level University courses, I have always approached teaching as a unique opportunity to "design" a learning environment that is sound, rich, and engaging and where the principles of the Learning Sciences are applied effectively. In addition, I approach teaching as an opportunity to expand theories of learning and to involve students in the communities of practice directly concerned with learning, education, and the relevant content areas. This approach has been received very positively in repeated occasions and has provided me with evidence that this is a solid foundation for a learner-centered and active learning environment. My teaching interests include areas such as Design and Evaluation of Learning Environments, Computer-supported Collaborative Learning in Math and Science, Technology-supported, Data-driven Decision Making, Learning in Online Communities and Virtual Worlds, Design-Research Methods in the Learning Sciences, and Socio-cultural Psychology. Furthermore, I approach my participation in curriculum planning and general organizational support activities, with the same interest and enthusiasm.

:In closing, I would like to reiterate that I regard the position in Learning Sciences and the Graduate School of Education at the University of Pennsylvania as exceptional opportunities for me to contribute to the highest quality of research and teaching activity. Enclosed is my Curriculum Vitae as well as information on academic references. I would welcome the opportunity to interview with the members of the search committee and discuss the results you can expect from me as a member of your faculty. If you require additional materials or any other information, I would be glad to supply it.

:Sincerely,

:Johann W. Sarmiento
:[encl. Curriculum Vitae, Academic References]

Grant Sources

Jsarmi — Tue, 27 Nov 2007 20:34:26 GMT

Jsarmi:

==Office of Educational Technology of the U.S. Department of Education==

:Grant Program for Statewide, Longitudinal Data Systems
:Evaluating State Education Technology Programs
:Enhancing Education Through Technology

http://www.ed.gov/about/offices/list/os/technology/edgrants.html

==National Science Foundation==

Discovery Research K-12 (DR-K12)
http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=500047&org=DRL&from=home

Information Technology Experiences for Students and Teachers (ITEST)
http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5467&org=DRL

Developmental and Learning Sciences (DLS)
Division of Behavioral and Cognitive Sciences
http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=8671

Research on Learning in Formal and Informal Settings (DRL)

==Science of Learning Centers==
http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5567&org=SBE

:Center of Excellence for Learning in Education, Science, and Technology (CELEST)
:Center for Learning in Informal and Formal Environments (LIFE)
:Pittsburgh Science of Learning Center for Robust Learning (PSLC)
:Spatial Intelligence and Learning Center (SILC)
:[[http://tdlc.ucsd.edu/portal/ The Temporal Dynamics of Learning Center]] (TDLC)
:Visual Language and Visual Learning Center (VL2)

Dataset2/D2TBSS

Jsarmi — Tue, 20 Nov 2007 18:07:30 GMT

Jsarmi: /* Sharedness */

=Group Trajectory=
Session 1: Bwang divided the figure into horizontal and vertical lines, Formulas for both sticks and squares were produced,
The values for N=4, 5, and 6 were agreed upon and posted to the Wiki. Quicksilver offers an explanation of how
the pattern grows but it is not discussed
Session 2: Feedback attended to
Session 3:
Session 4:

==Group composition: Stable==

Session 1: bw qs az
Session 2: bw qs az
Session 3:
Session 4:

(L) (N)

==Session I==

bwang8 5/9/06 6:23:18 PM EDT: hi
Aznx 5/9/06 6:23:23 PM EDT: Hi
Quicksilver 5/9/06 6:23:28 PM EDT: hey
Aznx 5/9/06 6:23:35 PM EDT: So we can't have our own friends?
bwang8 5/9/06 6:23:40 PM EDT: nope
bwang8 5/9/06 6:23:49 PM EDT: lol
Quicksilver 5/9/06 6:23:52 PM EDT: hey three of us are from miller
Gerry 5/9/06 6:23:55 PM EDT: Hi everyone!

Gerry 5/9/06 6:24:59 PM EDT: Today's session is mainly to get to know the VMT system

Gerry 5/9/06 6:29:12 PM EDT: You can click on the button at the top that says "View Topic" to see the math problem
bwang8 5/9/06 6:29:32 PM EDT: ok
bwang8 5/9/06 6:29:50 PM EDT: are we suppose to solve it now?
Gerry 5/9/06 6:30:13 PM EDT: Then you can click on the button in the little window that appears to open the topic in another big growser window
Gerry 5/9/06 6:30:36 PM EDT: browser*
Aznx 5/9/06 6:30:40 PM EDT: It didn't open.
Aznx 5/9/06 6:30:52 PM EDT: Now it did.
Aznx 5/9/06 6:31:32 PM EDT: So, are we supposed to work together?
bwang8 5/9/06 6:31:49 PM EDT: yeah
bwang8 5/9/06 6:31:50 PM EDT: ok
Gerry 5/9/06 6:31:54 PM EDT: Exactly!
Aznx 5/9/06 6:32:04 PM EDT: Aditya, you there?
bwang8 5/9/06 6:32:05 PM EDT: you can divide the thing into two parts
Aznx 5/9/06 6:32:10 PM EDT: Let's start this thing.
(bwang draws the third iteration of the pattern splitted in 2 diagrams dividing the horizontal and vertical lines)
...
Quicksilver 5/9/06 6:32:58 PM EDT: what are the lines for?
Aznx 5/9/06 6:33:01 PM EDT: go to view topic
bwang8 5/9/06 6:33:05 PM EDT: so you can see we only need to figur one out to get the total stick

===intersubjectivity===
good example of how whiteboar actions and chat are mutually informative,
but also how the sequential production of the conversation is used as a resource for making sense of the conversation.
This is all tentative, and the group works it out. What are the lines for?
Instructability: There is always a content and a procedural side to everything we do:
Saying "you can divide the thing into two parts" informs the others about how his subsequent actions are to be read.
Those whiteboard actions inform the meaning of that posting as well.

bwang8 5/9/06 6:33:32 PM EDT: 1+2+3+........+N+N
bwang8 5/9/06 6:33:38 PM EDT: times that by 2
Quicksilver 5/9/06 6:33:40 PM EDT: Never mind I figured it out..
Aznx 5/9/06 6:34:01 PM EDT: Can we collaborate this answer even more?
Aznx 5/9/06 6:34:05 PM EDT: To make it even simpler?
bwang8 5/9/06 6:34:15 PM EDT: ok
Aznx 5/9/06 6:34:16 PM EDT: Because I think we can.
bwang8 5/9/06 6:34:50 PM EDT: ((1+N)*N/2+N)*2
bwang8 5/9/06 6:34:58 PM EDT: that's the formula, right?
Aznx 5/9/06 6:35:15 PM EDT: How did you come up with it?
bwang8 5/9/06 6:35:16 PM EDT: for total sticks
bwang8 5/9/06 6:35:34 PM EDT: is a common formual
bwang8 5/9/06 6:35:40 PM EDT: formula
Aznx 5/9/06 6:35:46 PM EDT: Yeah, I know.
bwang8 5/9/06 6:35:59 PM EDT: and just slightly modify it to get this
(whiteboard)
Aznx 5/9/06 6:36:31 PM EDT: Aditya, you get this right?
(bwang corrects his drawing so that the horizontal lines orient in the same way that the original problem drawing)

bwang8 5/9/06 6:38:38 PM EDT: The number of squares is just (1+N)*N/2 (points to his formula posted at 6:34:50 PM)

Gerry 5/9/06 6:38:52 PM EDT: I put BWang's formula on the whiteboard
(whiteboard)
Aznx 5/9/06 6:39:45 PM EDT: So how do we submit this?
Quicksilver 5/9/06 6:40:26 PM EDT: We are still in the process
Quicksilver 5/9/06 6:40:38 PM EDT: We are discussing
Gerry 5/9/06 6:40:41 PM EDT: you can complete the table for different N and put that on the wiki

The practice of moving formulas to the whiteboard is not picked up, so the formula for the number of squares never makes it on to the whiteboard.

Quicksilver 5/9/06 6:46:50 PM EDT: Are we Team B?
Aznx 5/9/06 6:46:55 PM EDT: TEAM B
bwang8 5/9/06 6:47:02 PM EDT: i am done
Aznx 5/9/06 6:47:06 PM EDT: I think's its case sensitive.
Aznx 5/9/06 6:47:11 PM EDT: Alright, my turn.
Gerry 5/9/06 6:47:25 PM EDT: Nice!
bwang8 5/9/06 6:47:27 PM EDT: is mine in the correct format

Aznx 5/9/06 6:49:34 PM EDT: The number of squares is 15.
Gerry 5/9/06 6:49:47 PM EDT: You might want to draw the table on the whiteboard to make sure you all agree
(table being constructed on the whiteboard by bwang)
Quicksilver 5/9/06 6:51:00 PM EDT: There are 15 squares and 44 sticks for n=5?
(correction 4 instead of 3 and the values for n=5 just mentioned by Quicksilver added by bwang)
bwang8 5/9/06 6:52:03 PM EDT: isn't it 40
bwang8 5/9/06 6:52:18 PM EDT: (15+5)*2
(correction 40 instead of 44 by bwang)

Interesting... This an application of ((1+N)*N/2+N)*2 -> ((1+5)*5/2+5)*2) -> (15+5)*2 = 40

Later they have on the whiteboard two tables and one textbox which contain overlap but disagree in one number. In two, number of sticks for N=5 is 44 in the rest it is 40, so they try to coordinate this. Quicksilver does not seem responsive and later he posts this long chat message:

Quicksilver 5/9/06 7:00:39 PM EDT: Well, anyway, you can see a pattern that the amount of squares increases by the n. For the
sticks, The bottom row's square on the right has 2 new sticks. All the squares in the new row
to the left of it have 3 new sticks. So, If te row has 5 squares, 4 of the squares have 3 sticks,
the last on only has two. For the enitre Figure, you would add the amount to the previous ammount

After that technical problem the moderator sort of closes down the session:

Gerry 5/9/06 7:04:43 PM EDT: Maybe we should stop for today
Aznx 5/9/06 7:04:48 PM EDT: Alright.
jsarmi 5/9/06 7:04:50 PM EDT: Quicksilver... why don't you go ahead and close this window and try to enter again
Gerry 5/9/06 7:05:10 PM EDT: and let jsarmi help Quicksilver get ready to Thursday
jsarmi 5/9/06 7:05:27 PM EDT: (BTW, this room will now show up in the "My Rooms" tab not on the "Limited Access" one)
Quicksilver leaves the room 5/9/06 7:05:43 PM EDT
Gerry 5/9/06 7:05:48 PM EDT: You made a lot of progress already.
Aznx 5/9/06 7:05:53 PM EDT: So do we leave?
Aznx 5/9/06 7:06:01 PM EDT: And when do we come back?
...
Gerry 5/9/06 7:06:51 PM EDT: I think we will have the next session at the same time on Thursday.
You will come into the same room and start where you left off today
jsarmi 5/9/06 7:07:06 PM EDT: that's correct... same time, same team, same room
bwang8 5/9/06 7:07:12 PM EDT: ok
Quicksilver 5/9/06 7:07:15 PM EDT: I have a dentis't appointment...I don't think I can come
Aznx 5/9/06 7:07:16 PM EDT: Same time on Thursay...got it!
bwang8 5/9/06 7:07:37 PM EDT: but aren't we done now with this problem
Aznx 5/9/06 7:07:47 PM EDT: Yeah
Aznx 5/9/06 7:07:56 PM EDT: So I guess we would start on the second problem?
bwang8 5/9/06 7:08:05 PM EDT: ok
Quicksilver 5/9/06 7:08:16 PM EDT: Did you guys discuss the problem like it said to?
Aznx 5/9/06 7:08:21 PM EDT: Yeah.
Quicksilver 5/9/06 7:08:22 PM EDT: i didn't get half the messages'
Quicksilver 5/9/06 7:08:24 PM EDT: so i dont know
bwang8 5/9/06 7:08:25 PM EDT: yeah

Because Quicksilver can't make it on Thursday , they reschedule their session for the next day:

Quicksilver 5/9/06 7:09:45 PM EDT: Can we just reschedule for wednesday or something?
jsarmi 5/9/06 7:11:03 PM EDT: If it works out for everyone, you could re-schedule... is that an option?
Aznx 5/9/06 7:11:23 PM EDT: Wednesday should work for me.
Quicksilver 5/9/06 7:11:31 PM EDT: it works for me
Aznx 5/9/06 7:11:43 PM EDT: bwang?
bwang8 5/9/06 7:11:50 PM EDT: yes
Quicksilver 5/9/06 7:11:59 PM EDT: So this time tomorrow then
Quicksilver 5/9/06 7:12:11 PM EDT: in place of thursdays
bwang8 5/9/06 7:12:14 PM EDT: wednesday, 6-7 central?
Aznx 5/9/06 7:12:34 PM EDT: Same time as today.
Quicksilver 5/9/06 7:12:38 PM EDT: Yeah
bwang8 5/9/06 7:12:44 PM EDT: ok
Aznx 5/9/06 7:12:45 PM EDT: Except it's Wednesday instead of Thursday.
....
Aznx 5/9/06 7:13:37 PM EDT: So will we start on a new problem?
jsarmi 5/9/06 7:13:43 PM EDT: Is it clear to everyone???
Aznx 5/9/06 7:13:46 PM EDT: Tomorrow?
Quicksilver 5/9/06 7:13:48 PM EDT: Yes.
bwang8 5/9/06 7:13:59 PM EDT: ok
jsarmi 5/9/06 7:14:11 PM EDT: Some of you are on Central time and some of you on Pacific time, so do not get confused...
same time as today
bwang8 5/9/06 7:14:17 PM EDT: ok
Quicksilver 5/9/06 7:14:25 PM EDT: Ok. See you tomorrow then.

==Feedback==

VMT Feedback

We were very interested in the approach that divided the figure into
the horizontal lines and the vertical lines and the quickness with
which formulas fell out of that approach. It seemed as though you
also were paying attention to each other's work and quickly reached
agreement. You handled the technology of the chat environment and the
wiki easily.

We also noticed two places in the chat where some kinds of
conversation did not happen. There was a point where 44 was posted as
the number of sticks and 40 was offered as a correction. There was no
discussion of how 44 was calculated. At another moment, Quicksilver
posted an explanation of the pattern of growth that was not discussed.

There was a sense in which you indicated that your work was done when
you had at least one answer for the questions in the problem. For the
next step we will encourage you to think more about the different
approaches and the problems that you can discover on your own and
that are interesting to pursue.

==Session II==

Gerry 5/10/06 7:02:03 PM EDT: You have some feedback and a new Topic
Aznx 5/10/06 7:02:13 PM EDT: Has everyone read the feedback?
Quicksilver 5/10/06 7:02:17 PM EDT: yup
Quicksilver 5/10/06 7:02:25 PM EDT: NOw we have to discuss
bwang8 5/10/06 7:02:28 PM EDT: yes
Quicksilver 5/10/06 7:03:01 PM EDT: Well,, the part about converstaion not happening is because of me
Quicksilver 5/10/06 7:03:06 PM EDT: my computer was lagging....
Quicksilver 5/10/06 7:03:12 PM EDT: but that's out of our hands
Aznx 5/10/06 7:03:17 PM EDT: So, I think we should focus on discussing on each step more.
Quicksilver 5/10/06 7:03:30 PM EDT: and explain every answer thoroughly
Aznx 5/10/06 7:03:40 PM EDT: Even if the answer was "obvious."
bwang8 5/10/06 7:03:48 PM EDT: ok
Quicksilver 5/10/06 7:03:49 PM EDT: like i gave a wrong answer, but my explanations didn't come up
on the computer because of the lag
Quicksilver 5/10/06 7:03:58 PM EDT: so thats one thing
Quicksilver 5/10/06 7:04:12 PM EDT: maybe think of more ways of doing the same problem?
Aznx 5/10/06 7:04:21 PM EDT: Yeah.

===They try to start an activity===
Two proposals, looking at today's topic and talking about Quicksilvers wrong idea:

Quicksilver 5/10/06 7:04:50 PM EDT: Now did you two read today's topic?
bwang8 5/10/06 7:05:08 PM EDT: what was your pattern of growth, quicksiler
Quicksilver 5/10/06 7:06:20 PM EDT: i think it was something about the amount of squares that increased with each row....and how one of the new squares had 3 new sticks while the other new ones had 2 new sticks
p M
bwang8 5/10/06 7:06:41 PM EDT: oh, ok
(Quicksilver starts to draw squares with sticks to illustrate his talk to which he refers to in his next chat message)
Quicksilver 5/10/06 7:07:07 PM EDT: i drew some sqaures
Quicksilver 5/10/06 7:07:19 PM EDT: the left one had three new sticks
Quicksilver 5/10/06 7:07:33 PM EDT: the right one has a new stick on the bottom and on the right
Quicksilver 5/10/06 7:07:39 PM EDT: the top one is from an old square
Gerry 5/10/06 7:07:40 PM EDT: It was at 7:00:39 -- to get the old messages, click on the icon above here with the two circular arrows
(this messages points to a message from the previous day's session, unclear if they followed the link?)
(the feedback textbox is deleted from the whiteboard)
Quicksilver 5/10/06 7:09:25 PM EDT: yea that's wrong
Aznx 5/10/06 7:09:33 PM EDT: So let's brainstorm through some problems that we think are challenging.

===Aznx goes back to his idea of orienting to a new task===
Instead of quicksilver's error to which bwang and quicksilver oriented, others agree:

Quicksilver 5/10/06 7:09:40 PM EDT: yes...new topic
bwang8 5/10/06 7:09:42 PM EDT: ok
Quicksilver 5/10/06 7:10:20 PM EDT: 3-d figures?
(quicksilver adds sticks to the 2 squares he drew earlier to make them 3-D)

===Projecting===
Later on, Aznx adds a third 3D square and calls them a "row of blocks". Aznx makes some "projections" of what they could do:

Aznx 5/10/06 7:11:06 PM EDT: I think we should discuss on the different methods.
Aznx 5/10/06 7:11:24 PM EDT: So that we can easily apply our thoughts quickly when seeing a problem.
Quicksilver 5/10/06 7:11:30 PM EDT: Yes....but we must find a question or problem to investigate
Aznx 5/10/06 7:11:37 PM EDT: Yeah.
p M M
Aznx 5/10/06 7:11:50 PM EDT: I think we should start off with a conjecture, that we need to prove.
p M M M
Aznx 5/10/06 7:12:03 PM EDT: Not a hard one, but one that can be challenging.
Quicksilver 5/10/06 7:12:17 PM EDT: Maybe a row of blocks
Quicksilver 5/10/06 7:12:27 PM EDT: likethis
Aznx 5/10/06 7:12:44 PM EDT: What about them?
Quicksilver 5/10/06 7:12:59 PM EDT: The amount of sticks may increase in a pattern?
bwang8 5/10/06 7:13:01 PM EDT: The problem from yesterday, but only 3-d

===The problem from yesterday! BUT different.===
Notice no reference to members! (They are stable!) and this is taken by Quicksilver to be a negative assessment, a complaint! BUT ONLY?

Quicksilver 5/10/06 7:13:07 PM EDT: yea i guess
Quicksilver 5/10/06 7:13:09 PM EDT: not that good

He repairs the offer, bwang accepts, he mitigates it, bwant escalates, aznx endorses it, quicksilver mitigates put down:

Quicksilver 5/10/06 7:13:18 PM EDT: maybe a pyramind
bwang8 5/10/06 7:13:24 PM EDT: yeah
Quicksilver 5/10/06 7:13:30 PM EDT: although that's hard to draw
bwang8 5/10/06 7:13:35 PM EDT: pryamind is good
Aznx 5/10/06 7:13:36 PM EDT: Yeah, I liked that.
Quicksilver 5/10/06 7:13:36 PM EDT: but we shoudl be able to managt
Quicksilver 5/10/06 7:13:36 PM EDT: e
(Quicksilver draws a 2d version of a stack of cubes in pyramid shape and marks it as "side view")

Yesterday is still a problem:

bwang8 5/10/06 7:14:56 PM EDT: isn't this the same as yesterday problem
Quicksilver 5/10/06 7:15:03 PM EDT: Really?
Aznx 5/10/06 7:15:10 PM EDT: Except it's 3-D.
Quicksilver 5/10/06 7:15:12 PM EDT: no it's three d

===What can we use that we ALREADY KNOW:===
Interesting:

Aznx 5/10/06 7:16:45 PM EDT: So, how should we approach this?
Aznx 5/10/06 7:16:54 PM EDT: What can we use that we already know?
Quicksilver 5/10/06 7:16:57 PM EDT: Layer by layer shown in a chart?
bwang8 5/10/06 7:17:01 PM EDT: well we can divide it into a front and a back
Aznx 5/10/06 7:17:02 PM EDT: I'd suggest yesterday's problem.
bwang8 5/10/06 7:17:10 PM EDT: yeah
bwang8 5/10/06 7:17:22 PM EDT: using the formula from yesterday's problem
bwang8 5/10/06 7:17:32 PM EDT: we can figure the front and back easily
Quicksilver 5/10/06 7:17:36 PM EDT: this
(Points to the formula from Session I which is still on the whiteboard)

Notice here Projections again, in this case very collaboratively constructed:
"break it down" is something they used in Session I.

bwang8 5/10/06 7:27:55 PM EDT: the last level have 9
Quicksilver 5/10/06 7:28:07 PM EDT: yeah
p M M M M M
bwang8 5/10/06 7:28:28 PM EDT: so we will just have to figure out how many sticks make up 3 by 3 blocks
p M M M M M
Aznx 5/10/06 7:29:06 PM EDT: Yes.
p M
Aznx 5/10/06 7:29:15 PM EDT: After that, we go up to Nth step.
Quicksilver 5/10/06 7:29:20 PM EDT: Yes
p M M M M M M M M M M M
bwang8 5/10/06 7:30:07 PM EDT: ok, how do we figure that out
p M
bwang8 5/10/06 7:30:17 PM EDT: 3*3 blocks
p M
Quicksilver 5/10/06 7:30:26 PM EDT: Break it down
Aznx 5/10/06 7:30:27 PM EDT: I'd say look for a pattern.
p M
Aznx 5/10/06 7:30:33 PM EDT: and yes, break it down.
p M
Aznx 5/10/06 7:30:40 PM EDT: What other possible ways are there?
Aznx 5/10/06 7:30:44 PM EDT: That we know of?
bwang8 5/10/06 7:30:52 PM EDT: top, middle and bottom
p M M M M M M
bwang8 5/10/06 7:31:29 PM EDT: top and bottom are 3 by 3 squares
Quicksilver 5/10/06 7:31:33 PM EDT: whoops i drew it wrong

==="Yesterday stuff:"===

bwang8 5/10/06 7:32:27 PM EDT: do you mind if i erase some yesterday stuff?
Quicksilver 5/10/06 7:32:34 PM EDT: yea u can do it
Diagrams and other materials (e.g. table) are deleted, the formula is kept and then
a "decomposed" diagram with horizontal and vertical sticks for a 3x3 grid is created by bwang (as he did in S1!)
...
bwang8 5/10/06 7:33:57 PM EDT: when they combine
bwang8 5/10/06 7:34:05 PM EDT: they make a 3 by 3 square
Quicksilver 5/10/06 7:34:08 PM EDT: yes
Quicksilver 5/10/06 7:34:14 PM EDT: so just count these
bwang8 5/10/06 7:34:28 PM EDT: and the equation for it is 2N(N+1)
bwang8 5/10/06 7:34:35 PM EDT: right?
p M M
bwang8 5/10/06 7:34:58 PM EDT: N is the level
Quicksilver 5/10/06 7:34:59 PM EDT: I don't know
Aznx 5/10/06 7:35:04 PM EDT: Prove it.
Quicksilver 5/10/06 7:35:11 PM EDT: Where did you get it?
Aznx 5/10/06 7:35:16 PM EDT: I'll help you as you go along.
Aznx 5/10/06 7:35:27 PM EDT: I kind of get it, but not clearly.
bwang8 5/10/06 7:35:27 PM EDT: i mean just from the top and bottom 3 by 3 squares
Aznx 5/10/06 7:35:44 PM EDT: Where did the 2 come from?
bwang8 5/10/06 7:35:54 PM EDT: this is 3(3+1) (reference to the whitebaord)

===Sharedness===

Interesting explanation of bwang8's formula. Is it shared now?
Was it just in bwang's problem space before? Was it in everbody's problem space but positioned differently?
With different meanings?

Bwang had sugested that their pyramid can be broken down into "top, middle and bottom" and that the "top and bottom are 3 by 3 squares" Then bwang draws a "broken down" version of a 3 by 3 square that looks like this on the whiteboard:

_ _ _
_ _ _ | | | |
_ _ _ | | | |
_ _ _ | | | |

Then he follows up with this explanation:

bwang8 5/10/06 7:33:57 PM EDT: when they combine
bwang8 5/10/06 7:34:05 PM EDT: they make a 3 by 3 square
Quicksilver 5/10/06 7:34:08 PM EDT: yes
Quicksilver 5/10/06 7:34:14 PM EDT: so just count these
bwang8 5/10/06 7:34:28 PM EDT: and the equation for it is 2N(N+1)
bwang8 5/10/06 7:34:35 PM EDT: right?
(bwang manipulates some objects on the whiteboard, invisible)
bwang8 5/10/06 7:34:58 PM EDT: N is the level
Quicksilver 5/10/06 7:34:59 PM EDT: I don't know
Aznx 5/10/06 7:35:04 PM EDT: Prove it.
Quicksilver 5/10/06 7:35:11 PM EDT: Where did you get it?
Aznx 5/10/06 7:35:16 PM EDT: I'll help you as you go along.
Aznx 5/10/06 7:35:27 PM EDT: I kind of get it, but not clearly.
bwang8 5/10/06 7:35:27 PM EDT: i mean just from the top and bottom 3 by 3 squares
Aznx 5/10/06 7:35:44 PM EDT: Where did the 2 come from?
bwang8 5/10/06 7:35:54 PM EDT: this is 3(3+1) (Points to the left side of his diagram, the array of horizontal lines)

Claim Markings:

Quicksilver 5/10/06 7:36:05 PM EDT: ok
Aznx 5/10/06 7:36:05 PM EDT: Ah.
Quicksilver 5/10/06 7:36:07 PM EDT: i c
Aznx 5/10/06 7:36:08 PM EDT: I get it.

Bwang aknowledges, moves on:

bwang8 5/10/06 7:36:10 PM EDT: ok
bwang8 5/10/06 7:36:10 PM EDT: ok
bwang8 5/10/06 7:36:32 PM EDT: so now we get the top and bottom
bwang8 5/10/06 7:36:40 PM EDT: we need to find the middle

But this "sharedness" is contingent, not cumulative! For example... in this passage both Quicksilver and bwang create different graphics and at the end, they use it to understand each other's views:

Quicksilver 5/10/06 7:37:14 PM EDT: i don't understand something
Quicksilver 5/10/06 7:37:15 PM EDT:
Quicksilver 5/10/06 7:37:15 PM EDT:
Quicksilver 5/10/06 7:37:15 PM EDT:
Quicksilver 5/10/06 7:37:19 PM EDT: sorry\\
Quicksilver 5/10/06 7:37:28 PM EDT: um...what do you mean it is the top and bottom
bwang8 5/10/06 7:37:37 PM EDT: oh
Quicksilver 5/10/06 7:37:39 PM EDT: it is a pyramid with a flat face right
p M
bwang8 5/10/06 7:37:47 PM EDT: let me explain
(''Quicksilver and Bwang, each, create a drawing. Bwang's is 3D, Quicksilver's 2D with colors'')
Quicksilver 5/10/06 7:38:38 PM EDT: This face could go againts a wall(this is a top view) [''Points to his drawing'']
bwang8 5/10/06 7:38:48 PM EDT: it is just a way to divide the problem
(''Quicksilver colors a part of his diagram in yellow'')
Quicksilver 5/10/06 7:39:05 PM EDT: so the yellow is the top level?
(Quicksilver creates a yellow 3 by 3 grid of squares, Bwang marks lines in his original diagram with scribbles)
bwang8 5/10/06 7:39:45 PM EDT: we are just focusing on the bottommost level
Aznx 5/10/06 7:39:54 PM EDT: Yeah.
bwang8 5/10/06 7:40:04 PM EDT: and all those edges with scribble on it are the top
Quicksilver 5/10/06 7:40:18 PM EDT: So this is against the floor underneath the other two levels [''Points to his yellow 3 by 3 grid'']
bwang8 5/10/06 7:40:35 PM EDT: yes
Quicksilver 5/10/06 7:40:43 PM EDT: ok...continue then

Q: Is "coloring" (like "labeling") a a more "persistent" diectic?
(Note: the use of whiteboard references is very sophisticated here)
How do the 2 diagrams stand in relation to each other, their authors and other participants

bwang8 5/10/06 7:41:02 PM EDT: all the vertical lines are consider the middle [''Points to his diagram'']]
Quicksilver 5/10/06 7:41:21 PM EDT: ok
bwang8 5/10/06 7:41:32 PM EDT: and the rest are the bottom
bwang8 5/10/06 7:41:48 PM EDT: which has the same number of sticks as the top
p M M

===Explaining to others and to oneself===
Also, bwang, who is "explaining" is also monitoring the intelegibility of his own explanation, and complains about it:

bwang8 5/10/06 7:42:51 PM EDT: my explanation is pretty bad
bwang8 5/10/06 7:43:01 PM EDT: do you understand?
Quicksilver 5/10/06 7:43:12 PM EDT: enough to go on with the problem
Aznx 5/10/06 7:43:12 PM EDT: I understand it.

Bwang posts this equation on the whiteboard, not on the chat:

top/bottom: 2n(n+1)
middle: (n+1)^2

==="recursive equation/function" appears===

bwang8 5/10/06 7:46:30 PM EDT: so we can use recursive equation to figure out n 3d pryamind
bwang8 5/10/06 7:46:36 PM EDT: stick number
bwang8 5/10/06 7:46:42 PM EDT: lol
bwang8 5/10/06 7:46:48 PM EDT: bad grammar
(bwang scribles on the whiteboard: Sum (n=1, n) = 4n(n+1) + (n+1)^2

Later he clarifies how is that this is a "recursive function"

Quicksilver 5/10/06 7:50:18 PM EDT: It goes up by one every time because n=1 rite?
bwang8 5/10/06 7:50:38 PM EDT: no, n start at 1
Quicksilver 5/10/06 7:50:46 PM EDT: oh yeah!!!
bwang8 5/10/06 7:50:46 PM EDT: this is a recursive function
Quicksilver 5/10/06 7:50:46 PM EDT:
bwang8 5/10/06 7:51:26 PM EDT: when n=1, plug 1 into the right equation\\
Quicksilver 5/10/06 7:51:40 PM EDT: 12?
bwang8 5/10/06 7:51:58 PM EDT: when n=2, plug 2 into the right equation and add the equation when n=1
Quicksilver 5/10/06 7:52:13 PM EDT: Oh...so u add the thing that came before
bwang8 5/10/06 7:52:17 PM EDT: yes
bwang8 5/10/06 7:52:31 PM EDT: 12 is right (points to Quicksilver's 7:51:40 PM)

===Transition to the Wiki===
What to put, who/how to put it.

Quicksilver 5/10/06 7:57:45 PM EDT: so we have to go to the wiki now
...
Quicksilver 5/10/06 8:01:03 PM EDT: so our equation
Quicksilver 5/10/06 8:01:11 PM EDT: no first lets state our problem
bwang8 5/10/06 8:01:49 PM EDT: The number of sticks to make a N level pryamind
bwang8 5/10/06 8:02:04 PM EDT: ?
Aznx 5/10/06 8:02:17 PM EDT: Yeah, that's our question.
Quicksilver 5/10/06 8:02:56 PM EDT: Err...
Quicksilver 5/10/06 8:03:03 PM EDT: I kind of put somethingt different
Quicksilver 5/10/06 8:03:04 PM EDT:
Quicksilver 5/10/06 8:03:09 PM EDT: But it's similar
Aznx 5/10/06 8:03:24 PM EDT: Wait, do we all have to put it in?
Aznx 5/10/06 8:03:30 PM EDT: Only one of us right?

Today's result was "technically" the same as yesterday but today was "really" a discussion

Quicksilver 5/10/06 8:04:03 PM EDT: you guys can add on
Quicksilver 5/10/06 8:04:08 PM EDT: i just put the basic
Quicksilver 5/10/06 8:04:20 PM EDT: Maybe share our results?
Aznx 5/10/06 8:04:53 PM EDT: We technically had the same result.
Quicksilver 5/10/06 8:05:07 PM EDT: Whaddya mean?
Quicksilver 5/10/06 8:05:21 PM EDT: oh as yesterday?
Aznx 5/10/06 8:05:31 PM EDT: Yeah.
Aznx 5/10/06 8:05:36 PM EDT: And today.
Quicksilver 5/10/06 8:05:40 PM EDT: Still...
Aznx 5/10/06 8:05:43 PM EDT: Well today was really a discussion.
Quicksilver 5/10/06 8:05:46 PM EDT: we should say that'
...
Quicksilver 5/10/06 8:06:39 PM EDT: That may mean these types of problems all are similar in one way

====We should write it out here====

The "natural" person to write their findings on the Wiki might be bwang since he is the one who was driving the process and explaining things to others, but he says he is "bad with words". So Quicksilver suggests that they do it together. In reality, he does it by himself almost, which is a great display of his level of engagement with prior group activity:

Aznx 5/10/06 8:06:55 PM EDT: Wait, who is submitting?
Aznx 5/10/06 8:06:57 PM EDT: bwang?
bwang8 5/10/06 8:06:59 PM EDT: tell them the intervals between levels
Aznx 5/10/06 8:07:06 PM EDT: or quicksilver, or me?
bwang8 5/10/06 8:07:08 PM EDT: sorry, i am bad with words
Quicksilver 5/10/06 8:07:14 PM EDT: So am i
Aznx 5/10/06 8:07:15 PM EDT: Not to worry.
Aznx 5/10/06 8:07:21 PM EDT: We should write it out
Aznx 5/10/06 8:07:22 PM EDT: here
Quicksilver 5/10/06 8:07:24 PM EDT: Aznx to the rescue lol
Aznx 5/10/06 8:07:26 PM EDT: Together
Quicksilver 5/10/06 8:07:30 PM EDT: sure
Aznx 5/10/06 8:07:30 PM EDT: No not that
Quicksilver 5/10/06 8:07:34 PM EDT: a conclusion
Aznx 5/10/06 8:07:34 PM EDT: Yeah lol
bwang8 5/10/06 8:07:36 PM EDT: yeah
Aznx 5/10/06 8:07:51 PM EDT: So first, we started off with the basic problem.
Aznx 5/10/06 8:07:57 PM EDT: and changed it to a 3-D problem
Aznx 5/10/06 8:08:02 PM EDT: to make it more challenging
Quicksilver 5/10/06 8:08:04 PM EDT: Yea
Aznx 5/10/06 8:08:22 PM EDT: then we divided the top, bottom, and middle area down, to make the problem simpler for us
Aznx 5/10/06 8:08:42 PM EDT: Then, we recognized the 2N(N+1) pattern in the middle area
Quicksilver 5/10/06 8:08:44 PM EDT: That was one strategy\\
Aznx 5/10/06 8:08:54 PM EDT: that's our second: finding a pattern
Quicksilver 5/10/06 8:08:55 PM EDT: dividing it
Quicksilver 5/10/06 8:08:59 PM EDT: yes
Aznx 5/10/06 8:09:07 PM EDT: Finally, we used the recursion method to figure out the obttom area,
Quicksilver 5/10/06 8:09:15 PM EDT: obttom?
bwang8 5/10/06 8:09:16 PM EDT:
Aznx 5/10/06 8:09:19 PM EDT: So that's three strategies right there.
Aznx 5/10/06 8:09:32 PM EDT: I meant bottom
...

===retrospective-prospective===
Later, Quicksilver still assigns the task to bwang. Also, here there is a '''retrospective-prospective''' move: The feedback said X, we can do that next time

Aznx 5/10/06 8:10:32 PM EDT: I think bwang should put it in, since he's more familiar with the recursion method and how to use it than we are,
Aznx 5/10/06 8:10:36 PM EDT: Agreed?
Quicksilver 5/10/06 8:10:51 PM EDT: Today's topic siad go to the wiki and share the most intersting math problems that your group chose to work on
Quicksilver 5/10/06 8:10:59 PM EDT: agreed
Quicksilver 5/10/06 8:11:15 PM EDT: but we do understand it now
Quicksilver 5/10/06 8:11:18 PM EDT: that's important
Aznx 5/10/06 8:11:28 PM EDT: Well, we should just say we wanted to explore yesterday's problem more.
Quicksilver 5/10/06 8:11:29 PM EDT: maybe we can apply it next time...who knows?
Aznx 5/10/06 8:11:32 PM EDT: Yes, we do.
bwang8 5/10/06 8:11:32 PM EDT: ok
bwang8 5/10/06 8:12:06 PM EDT: we can use the strategy we used to solve this problem to solve future problems
bwang8 5/10/06 8:12:31 PM EDT: the method is important
bwang8 5/10/06 8:12:36 PM EDT: not the answer
Aznx 5/10/06 8:12:48 PM EDT: Yup.
Quicksilver 5/10/06 8:12:49 PM EDT: definiteyly
Aznx 5/10/06 8:12:56 PM EDT: Always learned that whereever I learned math. =P

Interestingly, here they find it relevant to talk about things that they "learned." How did they do that? For what purpose?

bwang8 5/10/06 8:13:05 PM EDT: we learn that divide the problem up can make it simpler and easier to solve
Quicksilver 5/10/06 8:13:09 PM EDT: so bwang...are you updating the wiki?
Quicksilver 5/10/06 8:13:14 PM EDT: yea
Aznx 5/10/06 8:13:21 PM EDT: we also learned finding a pattern is a good step
Quicksilver 5/10/06 8:13:39 PM EDT: yes and we could have also started with a simpler problem
Quicksilver 5/10/06 8:13:42 PM EDT: in fact...we did
Aznx 5/10/06 8:13:43 PM EDT: and recursion can be usually used when solving for a pattern, after finding the designated pattern of course
Quicksilver 5/10/06 8:13:48 PM EDT: yesterday's problem was simpler
Aznx 5/10/06 8:13:52 PM EDT: yes, we did!
Aznx 5/10/06 8:14:00 PM EDT: so we actually used 4 strategies =D
Quicksilver 5/10/06 8:14:12 PM EDT: yes
Aznx 5/10/06 8:14:34 PM EDT: We also tried to look at the problem from different views, although it's not really a strategy.

The moderator kind of "closes" down the session by bringing up next session:

Gerry 5/10/06 8:15:46 PM EDT: So, can you all come back here at the same time next Tuesday?

===What gets on the Wiki===
An elaborate narrative of what they did (to which they will add after the other 2 sessions)

To investigate the number of sticks in a flat faced pyramid with n levels with 1 block increase in length and width per level.
Also, to find as many approaches and put them to use. We eventually found 4 different strategies and applied them, such as divide
the problem up, finding a basic pattern, and use recursion to solve problems. We also found a formula, its origins, and how to use it.

f(n)=4n(n+1)+(n+1)^2+f(n-1) and f(0)=0.
We first determine the number of squares in each level of the pyramid, 1 cubes in first level, 4 cubes in second level, 9 cubes in
third level, and so on. Then we divide each level into 3 parts, the top, the bottom and the middle. The top is the same as the
bottom part. They are just a bunch of squares in square format. When divided top or bottom into vertical or horizontal, the
equation for # of sticks is n(n+1). Times that by 2 and you get a top or bottom, and times it by 2 again to get the total for top
and bottom. The result is 4n(n+1). Then there is the middle which are straight columns, and they are n+1 by n+1 on the side, so
(n+1)^2. The equation for each level is 4n(n+1)+(n+1)^2, and use a recursive fuction and you can get the total sticks for the pyramid.

==Feedback II==

VMT Feedback on Session #2

You can load the old chat messages by clicking on the double arrow icon above the chat scroll bar.
You can look through the history of the whiteboard by using the scroll bar all the way on the left
(be sure to scroll all the way down to the present in order to draw anything new.)

You did a great job of defining a challenging problem and solving it by using a combination of methods
that were well suited to the problem. And you shared what you did with the other groups in the wiki.

You noticed that stating the problem and making it clear to everyone is a big part of working on a problem.
In going to 3-D, you selected a particular kind of pyramid. How would your problem change if you had two flat sides,
with each layer in a corner of the layer underneath, so that some cube faces and edges (sticks) were shared between layers?

Can you explain your formula for the number of sticks so that someone in a different group can see how you got it
by breaking each layer into its top surface, bottom and middle and then counting the horizontal
and vertical sticks separately?

Do you understand how team C got its formulae for the diamond pattern of squares?
What if they had a diamond pattern of diamonds (just rotate the squares 45 degrees)?

What shapes make mathematically interesting patterns in 2-D or in 3-D?

==Session III==

They take on the feedback mention of a "corner pyramid" but it gest too confusing so they make a bid to postpone it:

Aznx 5/16/06 7:24:08 PM EDT: Should we just go onto a different problem for now?
Quicksilver 5/16/06 7:24:20 PM EDT: This is todays problem isn't it?
Quicksilver 5/16/06 7:24:25 PM EDT: Discuss last week?
Quicksilver 5/16/06 7:24:50 PM EDT: And more problems I guess..
Aznx 5/16/06 7:24:55 PM EDT: Yeah
Aznx 5/16/06 7:25:05 PM EDT: WE can come back to this on Thursday

===Recovering last session's materials: we keep it and move onto a different sequence===

Aznx 5/16/06 7:26:08 PM EDT: This was our formula for this problem last time correct? [''Points to whiteboard's formula'']
bwang8 5/16/06 7:26:13 PM EDT: yeah
Quicksilver 5/16/06 7:26:13 PM EDT: Yes
Aznx 5/16/06 7:26:21 PM EDT: So how about we keep it
Quicksilver 5/16/06 7:26:29 PM EDT: Yes
Aznx 5/16/06 7:26:31 PM EDT: And move onto a different sequence?
p M M M

Who had mentioned squares???

Aznx 5/16/06 7:26:47 PM EDT: How about squares?
Aznx 5/16/06 7:26:52 PM EDT: As you had mentioned?
Quicksilver 5/16/06 7:26:55 PM EDT:
Aznx 5/16/06 7:26:56 PM EDT: bwang you have any ideas?
Quicksilver 5/16/06 7:27:01 PM EDT: These basically were squares
p M M
bwang8 5/16/06 7:27:24 PM EDT: squares of what?
p M M M
Quicksilver 5/16/06 7:27:45 PM EDT: The cubes were basically squares
Aznx 5/16/06 7:28:22 PM EDT: I'm sure we can come up with other sequences.
Quicksilver 5/16/06 7:28:41 PM EDT: How did team C get its formula for the diamonds?

===How do we access that [Team C's] formula===

Quicksilver 5/16/06 7:28:41 PM EDT: How did team C get its formula for the diamonds?
Quicksilver 5/16/06 7:28:46 PM EDT: How do we access that?
Aznx 5/16/06 7:29:00 PM EDT: Well, let's look at their problem.
bwang8 5/16/06 7:29:05 PM EDT: open browser
p M M M
bwang8 5/16/06 7:29:13 PM EDT: and click on the link
Quicksilver 5/16/06 7:29:14 PM EDT: oh nevrmind
p M
Quicksilver 5/16/06 7:29:15 PM EDT: i got it
bwang8 5/16/06 7:29:19 PM EDT: ok
p M M M M
Aznx 5/16/06 7:29:48 PM EDT: Wait, I think I messed up.

===How did they derive it?===

bwang8 5/16/06 7:33:30 PM EDT: how did they derive it
Aznx 5/16/06 7:33:50 PM EDT: There's the formula
bwang8 5/16/06 7:33:57 PM EDT: (n^2+(n-1)^2)*2+n*3-2
bwang8 5/16/06 7:34:08 PM EDT: n^2+(n-1)^2
Aznx 5/16/06 7:34:18 PM EDT: The 3n has to do with the growing outer layer of the pattern I think.

From Team's C Wiki:

We also found formulas for a diamond-like arangement of the squares:
sides:
(n^2+(n-1)^2)*2+n*3-2
squares:
n^2+(n-1)^2

Later on, Quicksilver who might know somebody in Team C (xander?) attempts to ask Team C directly, what they meant by N, through Nan but at some point he withdraws the question, aparently

{| class="wikitable" border="1" cellpadding="2"
|-
|
:bwang8 5/16/06 7:43:33 PM EDT: what is n in their equation
:p M M M M
:Aznx 5/16/06 7:43:56 PM EDT: Good question
:Aznx 5/16/06 7:44:01 PM EDT: I don't know. :P
:p M M
:Quicksilver 5/16/06 7:44:10 PM EDT: Sides, sticks or squares?
:p M
:Aznx 5/16/06 7:44:14 PM EDT: Gerry?
:Quicksilver 5/16/06 7:44:17 PM EDT: let ask xander
:p M M M M M M M M M M M M M M M M M M M M M M
:Gerry 5/16/06 7:45:18 PM EDT: I assume N is the stage in the pattern
:Aznx 5/16/06 7:45:29 PM EDT: What do you mean?
:Quicksilver 5/16/06 7:45:35 PM EDT: That is twelve extra squares in a five by five square
:Aznx 5/16/06 7:45:39 PM EDT: I'm confused how the pattern grows
:Aznx 5/16/06 7:45:50 PM EDT: Oh, I get it now
:Aznx 5/16/06 7:45:56 PM EDT: I was on the right track =P
:Gerry 5/16/06 7:45:59 PM EDT: Just like in the original problem on the Topic
:Gerry 5/16/06 7:47:12 PM EDT: Stage N=1 is one square
:Gerry 5/16/06 7:47:27 PM EDT: Stage N= 2 is a cross of 5 squares
:Quicksilver 5/16/06 7:47:37 PM EDT: Ok
:Gerry 5/16/06 7:48:00 PM EDT: Stage N=3 is the bigger figure with 13 squares
:Quicksilver 5/16/06 7:48:08 PM EDT: Stage N=3 is a cross of 9 squares or 13?
:Aznx 5/16/06 7:48:23 PM EDT: 13
:Aznx 5/16/06 7:48:32 PM EDT: i tihnk
:Quicksilver 5/16/06 7:48:42 PM EDT: Because those extra four are tricky
:Gerry 5/16/06 7:48:46 PM EDT: you could define the sequence either way
:Quicksilver 5/16/06 7:48:54 PM EDT: yeah
:Quicksilver 5/16/06 7:49:01 PM EDT: but it has to be constant
:Gerry 5/16/06 7:49:05 PM EDT: which did they do? Which is more interesting mathematically?
:Aznx 5/16/06 7:49:29 PM EDT: 13
:Aznx 5/16/06 7:49:34 PM EDT: is much more interesting =P
:Quicksilver 5/16/06 7:49:34 PM EDT: it doesn't actually have to be constant but it has to have some kind of patter
:bwang8 5/16/06 7:49:53 PM EDT: ok
:Aznx 5/16/06 7:50:23 PM EDT: Now what do we do?
:Quicksilver 5/16/06 7:50:33 PM EDT: this
:bwang8 5/16/06 7:50:38 PM EDT: (2n-1)^2= the # of squares in the big square
|
:nan 5/16/06 7:48:49 PM EDT: (we got a question for you from another team, which was posted in the lobby:
:nan 5/16/06 7:48:53 PM EDT: Quicksilver 7:44:50 PM EDT: Hey anyone from team c, our team needs to know what n was in your equations last week
:Jason 5/16/06 7:49:04 PM EDT: oh
:137 5/16/06 7:49:15 PM EDT: The length of a side.
:qwertyuiop 5/16/06 7:49:16 PM EDT: was n side length?
:Jason 5/16/06 7:49:33 PM EDT: are you talking about the original problem with the squares
:137 5/16/06 7:49:48 PM EDT: I think nan is.
:qwertyuiop 5/16/06 7:49:58 PM EDT: i think it's squares and diamonds
:Jason 5/16/06 7:49:58 PM EDT: oh
:Jason 5/16/06 7:50:12 PM EDT: then if you look in the topic description, theres a column for N;
:Jason 5/16/06 7:50:14 PM EDT: thats what it is
:nan 5/16/06 7:50:17 PM EDT: ok, quicksilver said they got it
:Jason 5/16/06 7:50:25 PM EDT: so yes it is # sides
:nan 5/16/06 7:50:26 PM EDT: thanks guys
|}

===Le'ts explain it together right here===
This is something Aznx did in Session II also when team members were refusing the task of writing on the Wiki.
(Aznx to the rescue)

Aznx 5/16/06 8:03:11 PM EDT: Le'ts explain it together right here

but bwang has to leave and Qs and Az struggle with creating an explanation, so they '''project''' it to next session:

====then lets pick it up next time when bwang can explain it====

Aznx 5/16/06 8:05:21 PM EDT: I'm not sure if we got the first formula though.
Quicksilver 5/16/06 8:05:33 PM EDT: i don't think we did
Aznx 5/16/06 8:06:37 PM EDT: (2n-1)^2=the # of squares in the big square
Aznx 5/16/06 8:06:46 PM EDT: Correct?
Quicksilver 5/16/06 8:06:57 PM EDT: Yes
Quicksilver 5/16/06 8:07:27 PM EDT: But that is not in theri equation
Aznx 5/16/06 8:07:29 PM EDT: So isn't that our first formula right there?
Aznx 5/16/06 8:07:36 PM EDT: Hold on.
Quicksilver 5/16/06 8:07:39 PM EDT: no....we want the sides
Aznx 5/16/06 8:08:14 PM EDT: Read above.
Aznx 5/16/06 8:08:24 PM EDT: bwang kind of explains it.
Aznx 5/16/06 8:08:31 PM EDT: I somehow get it, but can't explain it.
Quicksilver 5/16/06 8:08:59 PM EDT: then lets pick it up next time when bwang can explain it
Aznx 5/16/06 8:09:12 PM EDT: So leave for today?
Quicksilver 5/16/06 8:09:18 PM EDT: i suppose

==Bwang's message in between sessions III and IV==

bwang8 joins the room 5/16/06 8:42:43 PM EDT
p M M M M M M M M M M M M M M M M M
bwang8 5/17/06 12:18:23 AM EDT: Sorry i have to leave early
bwang8 5/17/06 12:18:56 AM EDT: i updated our wiki page to explain the equation from the last session
p M M M
bwang8 5/17/06 12:34:54 AM EDT: i also added some stuff, change anything you want
bwang8 5/17/06 12:39:55 AM EDT: i hope you can read this

==Feedback III==

We started doing the problems you were doing and got very interested in them.
We did not always arrive at the same answers and we weren't always able to decide if we were looking at it
in the same way that you were, but we liked working "with you" in this sense.

From our perspective, the goal has not been for you to answer “our” problems,
but for you to figure out math questions that interest you and to pursue them.
That is why we set the challenge for the iPod as having your group excel at collaboration,
not at finding some answers.

You seem to have pursued some interesting questions and are all contributing and also
making use of each other’s ideas. It is sometimes hard for us to tell what you are writing and thinking.
It seems that there are times when you say you are following each other,
but it is not clear that you are really in agreement or completely understand each other.
You might actually discover some more math if you state things in more detail –
to be completely sure you are in agreement.

For session four, you could revisit a problem you were working on before,
in order to state more clearly for other groups in the wiki: (a) a definition of your problem,
(b) a solution and (c) how you solved the problem. Or you could try a new variation of these pattern problems,
like a 3-D version of group C’s diamond pattern.

It is up to you to pursue whatever most interests you and what enables you to improve and enjoy your ability to work together.
As you know, one hour goes by pretty quickly, so it’s easy to run out of time for a complicated problem.
Be creative and enjoy the session.

==Session IV==

===Recovering their "plan"===

The three members had postponed the "flat sided pyramid" and two of them (Az and Qs) postponed explaining their work (or bwang's formula) on the diamond pattern. They recover the pyramid problem

Quicksilver 5/18/06 7:03:44 PM EDT: for this session, it says to revisit an old problem
p M M
Aznx 5/18/06 7:04:10 PM EDT: Hm.
Aznx 5/18/06 7:04:16 PM EDT: Let's make a new problem
p M
bwang8 5/18/06 7:04:18 PM EDT: the pryamid one that we didn't finish last time
Aznx 5/18/06 7:04:21 PM EDT: Not necessarily 3-D
Aznx 5/18/06 7:04:26 PM EDT: Yeah
Quicksilver 5/18/06 7:04:31 PM EDT: ok
Aznx 5/18/06 7:04:32 PM EDT: let's do the pyramid one
Quicksilver 5/18/06 7:04:35 PM EDT:

After this they start reading the feedback and later on the decision of what to do, resurfaces:

bwang8 5/18/06 7:14:38 PM EDT: let's just focus on diamond problem today
Aznx 5/18/06 7:14:44 PM EDT: So let's really focus on the pyramid.
bwang8 5/18/06 7:14:48 PM EDT: we almost got the solution last seesion
Quicksilver 5/18/06 7:14:49 PM EDT: lol
Aznx 5/18/06 7:14:49 PM EDT: Diamond or pyramid?
bwang8 5/18/06 7:14:55 PM EDT: diamond
Aznx 5/18/06 7:14:59 PM EDT: aditya?
bwang8 5/18/06 7:15:02 PM EDT: because we worked on it longer
Quicksilver 5/18/06 7:15:03 PM EDT: diamond
Aznx 5/18/06 7:15:08 PM EDT: agreed then
bwang8 5/18/06 7:15:11 PM EDT: ok
Quicksilver 5/18/06 7:15:13 PM EDT: we have a more thorough understanding of it
bwang8 5/18/06 7:15:18 PM EDT: yeah

...

Aznx 5/18/06 7:16:03 PM EDT: I'd say, we work on the pyramid problem, solve it thoroughly, and then state the solution as they suggested in the feedback. Then, if we have enough time, which probably will ,we'll sytart on the pyramid problem.
Quicksilver 5/18/06 7:16:21 PM EDT: u said two pyramid problems?
Quicksilver 5/18/06 7:16:27 PM EDT: read ur thing again
Aznx 5/18/06 7:16:27 PM EDT: OOps
Aznx 5/18/06 7:16:34 PM EDT: I meant in the first part
Aznx 5/18/06 7:16:37 PM EDT: the diamond problem
Aznx 5/18/06 7:16:41 PM EDT: not the pyramid
bwang8 5/18/06 7:16:41 PM EDT: lol

===As usual Routine===

Aznx 5/18/06 7:12:00 PM EDT: Let's first discuss about the feedback.
bwang8 5/18/06 7:12:06 PM EDT: ok
Aznx 5/18/06 7:12:06 PM EDT: As usual, what do you guys think?

===So where were we?===

Quicksilver 5/18/06 7:15:57 PM EDT: so where were we?
bwang8 5/18/06 7:16:00 PM EDT: so right now we know that we must calculate the number of squares on each level by making a big square and minus the 4 extra corners

Notice how they orient to process/steps:

Aznx 5/18/06 7:16:57 PM EDT: we pretty much solved it didnt we?
bwang8 5/18/06 7:17:09 PM EDT: yeah
Aznx 5/18/06 7:17:11 PM EDT: Well 50% of it I should say.
Quicksilver 5/18/06 7:17:15 PM EDT: lets just recap the process
Quicksilver 5/18/06 7:17:27 PM EDT: from the point of view who had never seen this problem
bwang8 5/18/06 7:17:32 PM EDT: we know how to calculate the big square in a level
Quicksilver 5/18/06 7:17:44 PM EDT: ok hold on
bwang8 5/18/06 7:17:50 PM EDT: as in this
bwang8 5/18/06 7:17:56 PM EDT: whole thing
Quicksilver 5/18/06 7:17:57 PM EDT: our objective is to find the amount of squares and sticks in each level righrt?
bwang8 5/18/06 7:18:03 PM EDT: yeo

===We had already figured that out/We can use the equation from Session 1===

Pointing to a textbox created in Session 1!!!

bwang8 5/18/06 7:20:48 PM EDT: what is the pattern
Aznx 5/18/06 7:20:56 PM EDT: Triagnular numbers.
Quicksilver 5/18/06 7:20:58 PM EDT: triangular numbers!
bwang8 5/18/06 7:21:00 PM EDT: yep
bwang8 5/18/06 7:21:00 PM EDT: yep
Aznx 5/18/06 7:21:03 PM EDT: We had already figured that out.
bwang8 5/18/06 7:21:10 PM EDT: we can use the equation from session 1
Quicksilver 5/18/06 7:21:11 PM EDT: yes
Aznx 5/18/06 7:21:20 PM EDT: Yup.
bwang8 5/18/06 7:21:36 PM EDT: n(n+1)/2
p M M M
bwang8 5/18/06 7:21:56 PM EDT: 4*n(n+1)/2= the four corners
Quicksilver 5/18/06 7:21:57 PM EDT: this right? ['''Points to a textbox from Session 1 with formula''']
bwang8 5/18/06 7:22:03 PM EDT: yes
Aznx 5/18/06 7:22:06 PM EDT: Yeah
bwang8 5/18/06 7:22:28 PM EDT: (2n-1)^2-2n(n-1)
bwang8 5/18/06 7:22:48 PM EDT: this is the equation for each level

'''Is it here that bwang8 does his subtle transformation of "ns" and changes the equations so that the n in thefour corners from (7:21:56 PM EDT: 4*n(n+1)/2) which is 2n(n+1) matches that in the central square: 2n(n-1)? And integrates it into the complete formula (7:22:28 PM EDT: (2n-1)^2-2n(n-1))

The final textbox and the Wiki report end up with different formulas:
big square: (2n-1)^2
4 corners: n(n+1)/2*4

(2n-1)^2-n(n+1)/2*4

Wiki: (2n+1)^2-n(n+1)/2*4

===But that is not what it ENDS UP TO BE===

Aznx 5/18/06 7:25:43 PM EDT: But that's not what it ends up to be.
Aznx 5/18/06 7:25:56 PM EDT: If you double check with our already-given formula
Quicksilver 5/18/06 7:26:00 PM EDT: why?
Aznx 5/18/06 7:26:07 PM EDT: It's this
Quicksilver 5/18/06 7:26:12 PM EDT: oh yeah
Quicksilver 5/18/06 7:26:14 PM EDT: it doesn't work
p M
Aznx 5/18/06 7:26:16 PM EDT: The first one [''Points to Team C's formula for sticks which is on the whiteboard'']

They clarify which formula is for squares and Aznx accepts that he was confused

===What is the actual solution===

Aznx 5/18/06 7:28:22 PM EDT: So is that all?
Quicksilver 5/18/06 7:28:37 PM EDT: what is the actual solution then? those equations?
Aznx 5/18/06 7:28:43 PM EDT: Yeah.
p M
Quicksilver 5/18/06 7:28:59 PM EDT: but when we put in the wiki how we did it....what will we write
Aznx 5/18/06 7:29:20 PM EDT: Um.

This is what makes it to the Wiki:

In session 4, we continued our progress on the diamond problem. We found that if we filled up the diamound
with more squares and get an easier square with 2n+1 as the dimension. So the number of squares
in the big square is (2n+1)^2. We then minus the squares that we added on which was at the 4 corners,
which grow in the same pattern as the triangle number in the first session. We used the formula for # of squares
from the first session and times it by 4 to calculate the 4 corners that we add on to make the big square.
The final formula for the # of squares in the diamond is (2n+1)^2-n(n+1)/2*4. We tested it several times to check if it works.

Microgenetic Studies Of Learning

Jsarmi — Mon, 12 Nov 2007 22:12:04 GMT

Jsarmi:

''"Microgerzetic Analyses of Learning"''By ROBERT S. SIEGLER
CHAPTER 11 In HANDBOOK OF CHILD PSYCHOLOGY, SIXTH EDITION, Volumc Two: Cognition Perception, and Language
Volume Editors: OEANNA RUHN and ROBERI SIEGLER; Editors in Chief: WlLLlAM DAMON and RICHARD M. LERNER
----

The following list summarizes a number of the most consistent and important phenomena that have emerged within microgenetic studies of children's learning:

:#Substantial within-child variability is present during all phases of learning and at every level of analysis: associations, concepts, rules, strategies and so on
:#Within-child variability tends to be greatest during of periods of rapid learning, though substantial variability is present in relatively stable periods ;is well
:#Within-child variability tends to be cyclical, with periods of lesser and greater variability alternating over the course of learning
:#Within-child variability is substantial at all ages from infancy to older adulthood
:#Initial within-child variability tends to be positively related lo subsequent learning
:#Learning reflects addition of new strategies, greater re1iance on relatively advanced strategies that are already being used, improved choices among strategies, and improved execution of strategies
:#Learning tends to progress through a regular sequence of knowledge states that parallel those that characterize untutored development
:#The path of learning is usually similar for learners of different ages and different intellectual levels
:#Learning often includes short-lived transitional approaches that play important roles in the acquisition of more enduring approaches
:#New approaches are generated following success as well as failure of existing approaches
:#For most types of learning, older and more knowledgeable children learn more quickly, and show greater appropriate generalization than younger children
:#Tile rate of change is of human scale: faster than connectionist models imply, but slower than most symbolic models imply
:#New approaches usually are used inconsistently, discovery of new approaches tends to be the beginning of learning rather than the end
:#Once new approaches have been generated, their rate of uptake is positively related lo the degree to which their accuracy is superior to that of existing approaches
:#The breadth of change also is of human scale, including everything from instantaneous lo extremely gradual generalization
:#The likelihood of choosing any given approach can be increased either by increasing the strength of that approach or by weakening the strength of competing approach
:#Causal understanding plays a crucial role in learning
:#Requests to explain observations often promote learning above and beyond the effects of feedback and practice
:#The mechanisms underlying the effects of explanatory activity include increased likelihood of learners generating any explanation, increased persistence of explanatory efforts, and diagnosis and repair of flaws in mental models
:#Learning often proceeds with little or no trial and error; conceptual understanding often allowing children to reject inappropriate strategies without ever trying them

Microgenetic studies document '''HOW''' people learn. They stand in contrast with Piagetian theory of ''HOW'' children think at different ages and work by researchers who adopt an information-processing perspective who advance intriguing hypotheses about transition processes in cognitive development (eg , Klahr & Wallace, 1976) but stir attention '''away from HOW children learn.'''

Industry Resume

Jsarmi — Wed, 07 Nov 2007 18:20:15 GMT

Jsarmi:

__NOTOC__
=Johann W. Sarmiento=
:2601 Pennsylvania Ave, #508 Philadelphia, PA 19130 Phone: 215 - 888 0603
:jsarmi at gmail dot com - jsarmi at drexel dot edu

=Summary of Qualifications=

Results-oriented User-Experience (UE) researcher and practitioner with significant experience in the design, development, and evaluation of information systems such as enterprise decision-support systems, online collaboration environments, and internet resources. Keen interest in combining quantitative and ethnographic methods to guide different stages of the design cycle and making the experience of users useful, efficient, and enjoyable. PhD candidate in the College of Information Science and Technology at Drexel University with emphasis on Human-Computer Interaction and Collaborative Knowledge Building.

=Education=

==Ph.D. in Information Science and Technology 2008 (expected)==
:Drexel University, Philadelphia, PA.
:*Concentration: Human-Computer Interaction and Collaborative Knowledge Building
:*Highlights: First Prize, Graduate Student Research, Drexel Research and Innovation Day 2007 & 2005.
::::Honorable Mention, Graduate Student Research, Drexel Research Day 2006
::::Finalist, Microsoft Research and Microsoft Live Labs Fellowship, 2006
::::Invited presenter at the 2nd Annual IBM TJ Watson HCI Symposium on Social Computing, 2005.
::::Topic: “Bridging Interaction Spaces to Support Distributed Problem-Solving Teams”

==Master of Science in Computer Science 1999==
:Maharishi International University. Fairfield, IA.
:Co-op Postion: Client-server Systems, Telegroup, Inc. Fairfield, IA

==Bachelor of Engineering - Systems Engineering 1996==
:Universidad Industrial de Santander, Bucaramanga - Colombia
:Minor: Linguistics and Language Studies
:Thesis Topic: Natural Language Processing Interfaces and Applications

=Recent Experience=

==The Math Forum at Drexel University, 2004-present==
Research Associate/Project Manager: Virtual Math Teams (VMT) Project

:*Coordinated and executed design experiments and naturalistic observations of local and remote user interactions which led to the redesign of the Virtual Math Teams online collaboration environment
:*Conducted qualitative and quantitative analyses of data from recorded user interactions for exploratory and evaluative purposes of a chat and shared whiteboard environment
:*Coordinated interaction design teams and the actual implementation of design proposals with an external team at Fraunhofer IPSI-Germany

==Mid-Atlantic Regional Technology in Education Consortium, 2000-2004==
Research Associate/ Digital Portal Team Leader

:*Led the design and implementation of a digital portal for educational technology used by more than 65 thousand unique users during a 4 year period.
:*Performed formative and summative evaluation of the online portal via relevant stakeholders. Methods used included longitudinal focus groups, online surveys and log analysis.
:*Led the design of ReflectionConnection, a web-based collaborative tool for innovative professional development and knowledge management
:*Conducted two longitudinal field studies of ReflectionConnection using statistical analysis of usage patterns, discourse analysis, and usability interviews leading to successful redesigns.

==Advanced Technologies for Learning Lab at Temple University, 1999-2004==
Senior Research Associate/Principal Investigator.

:*Created and implemented a program of applied research and field services on innovative technologies for learning as part of the Center for Research in Human Development and Education ($20M, 5yrs)
:*Led the development and formative evaluation of new web applications serving K-12 education
:*Conducted exploratory research on innovative learning technologies. Methods included new technology evaluations, in-depth case studies, and statistical analysis of survey data.
:*Produced research reports and delivered presentations on topics such as collaborative knowledge-building tools in the classroom and the use of eLearning and data-driven decision support systems in K-12 contexts.

==Other Relevant Experience==
:*Software developer and Quality Assurance team member at the Client-Server group, Telegroup Inc. (Fairfield, IA)
:*Project lead in educational technology research and development at Nexus/Apple – Colombia
:*Owner and lead researcher of Maieutics, a Learning Technologies Consultants – Colombia
:*Research associate in technology and cognitive development, ASED Consultants – Colombia
:*Research Assistant, Natural Language Processing Research Group at the UIS (Colombia )

=Relevant Technical Skills=

:*Research Tools: SPSS, NVIVO, Camtasia Studio, Transana
:*QA Tools : QuickTest/LoadRunner automated testing tools
:*UX Skills : Rapid Prototyping, Cognitive walkthrough, Heuristic evaluation, SSM stakeholder analysis, Scenario-based Interaction Design, Ethnomethodology and Critical Ethnography
:*Web Technologies: HTML /XML, Web Services/Ajax
:*Programming: Java/JSP, Javascript, ASP

=Professional Affiliations=

:*Association for Computer Machinery (ACM), Special Interest Group: HCI
:*Philadelphia Human-Computer Interaction (Philly-CHI) group
:*Association for the Advancement of Computer in Education, SIG Interactive Learning Research
:*American Education Research Association (AERA), SIG of Advanced Technologies for Learning
:*Society of Hispanic Professional Engineers

=Other Activities=

:*Community Service: Art of Living Foundation, Greater Philadelphia Cares, Habitat-for-Humanity-Philadelphia
:*Languages: Fully fluent in Spanish and English; basic knowledge of French and German

Group Development

Jsarmi — Tue, 16 Oct 2007 18:00:51 GMT

Jsarmi: /* Tuckman's stages of group development: Forming, Storming, Norming, Performing and Adjourning */

The goal of most research on group development is to learn why and how small groups change over time. To do this, researchers examine patterns of change and continuity in groups over time. Aspects of a group that might be studied include the quality of the output produced by a group, the type and frequency of its activities, its cohesiveness, the existance of conflict, etc.

A number of theoretical models have been developed to explain how certain groups change over time. Listed below are some of the most common models. In some cases, the type of group being considered influenced the model of group development proposed as in the case of therapy groups. In general, some of these models view group change as regular movement through a series of "stages," while others view them as "phases" that groups may or may not go through and which might occur at different points of a group's history. Attention to group development over time has been one of the differentiating factors between the study of ad hoc groups and the study of teams such as those commonly used in the workplace, the military forces, sports or many other contexts.

= Theories and Models =

In the early seventies, Hill and Grunner reported that more than 100 theories of group development existed. Since then, other theories have emerged as well as attempts at contrast and synthesize them. A number of typologies of change theories have been proposed. A typology advanced by George Smith (2001) based on the work of Mennecke and his colleages (1992) classifies theories based on whether they perceive change to occur in a linear fashion, through cycles of activities, or trough processes that combine both paths of change or which are completely non-phasic. In a second typology proposed by Holly Arrow (1997), theories are grouped based on whether the primary forces promoting change and stability in a group are internal or external to the group. A third framework advanced by Marshall Scott Poole and his collaborator Andrew van de Ven, differentiates theories based on four distinct "motors" for generating change (e.g. Poole et al., 2000).

In the typology offered by Van den Den and Poole, the following four types of models are proposed:

:*'''Life cycle models''' describe the process of change as the unfolding of a prescribed sequence of stages following a proram that is prefigured at the beginning of the cycle (within the group or imposed on it).

:*'''Teleological models''' describe change as a purposeful movement toward one or more goals, with adjustments based on feedback from the environment.

:*'''Dialectical models''' see change as emerging from conflilct between opposing entities and eventual synthesis leading to the next cycle of conflict

:*'''Evolutionary models''' depict change as emerging from a repeated cycle of variation, selection and retention and generally apply to change in a population rather than change within an entity over time.

Some theories allow for combinations and interactions among these four motors. For example, Poole (see below) found empirically that seemingly complex patterns of behavior in group decision making result from the interplay of life-cycle and
teleological motors.

In his most recent work, Poole has turned his attention to organizational development and organizational change. At this levesl, models of change are even more complex and, as he argues, need to concentrate specially in understanding processes of change and explaining how changes unfold over time. To support this claim, Poole et. al. provide the following three advantages of process-oriented theories:

:*# They provide a deep understanding of how change comes about by describing the generative mechanism that drives the process;
:*# They can account for path dependence and the role of critical events in change and innovation; and
:*# They can incorporate the role of human agency in change without reducing it to causal terms.

Below we describe the central elements of some of the most common models of group development.

==Kurt Lewin's Individual Change Process==

The origins of the systematic study of group development have been linked as far back as the work of [[Kurt Lewin]], who introduced the term ''group dynamics'' (Arrow et al., 2005). His ideas about mutual, cross-level influence and quasi-stationary equilibria, although not very common in the traditional empirical research on group development, have resurged recently. His early model of individual change, which has served as the basis of many models of group development, described change as a three-stage process: unfreezing, change, and freezing.

{| class="wikitable"
|-
| '''Unfreezing:'''
| This phase involves overcoming inertia and dismantling the existing "mind set". Defense mechanisms have to be bypassed.
|-
| '''Change'''
| In the second stage change occurs. This is typically a period of confusion and transition. One is aware that the old ways are being challenged but does not have a clear picture to replace them with yet.
|-
|'''Freezing'''
| In the third stage the new mindset is crystallizing and one's comfort level is returning to previous levels. This is often misquoted as "refreezing" (see Lewin, 1947).
|}

==Robert Bales' Interaction Process Analysis==

Studies pioneered by Bales since the early 50s (Bales, 1950, 1953, Bales and Strodtbeck, 1951) focused on discovering the sequences of activities through which groups empirically reach solutions (ideally or in practice) and have used various systems of categories to analyze results. By abstracting the rhetorical form of group members' talk from its content and recording percentages of statements made in categories like "agree" and "gives orientation," this type of research has created models of the structure of group discussion over time. The classic model proposed by Bales and Strodtbeck (1951) describes a unitary sequence of three phases in groups' movement toward goals: orientation, evaluation, and control.

{| class="wikitable"
|-
| '''Orientation:'''
| Leaderless laboratory groups begin by placing major emphasis in activities such as asking for and providing orientation. This
orientation serves to define the boundaries of the task (i.e., what is to be done) and the approach that is to be used in dealing with the task (i.e., how it is to be accomplished).
|-
| '''Evaluation'''
| The orientation phase is followed by a period in which major emphasis is placed on problems of evaluation, for example asking for members opinions or giving one's opinion about the task to be accomplished by the group.
|-
| '''Control'''
| In the third and final phase the group is primarily concerned with problems of control, reflected in activities such as asking and providing suggestions for solutions to the task based on information gathered and evaluated in previous developmental periods.
|}

==Tuckman's stages of group development: Forming, Storming, Norming, Performing and Adjourning==

Bruce Tuckman reviewed about 50 group development studies (including Bales') in the early sixties and synthesized their commonalities in one of the most frequently cited models of group development. The model describes four to five linear phases that a group will go through in its ''unitary sequence' of decision making:

{| class='wikitable'
|-
|* '''Forming:'''
|Group members learn about each other and the task at hand. Indicators of this stage might include: Unclear objectives, Uninvolvement, Uncommitted members, Confusion, Low morale, Hidden feelings, Poor listening, etc.

|-
|* '''Storming:'''
|As group members become more comfortable with each other, they will engage each other in arguments and vie for status in the group. These activities mark the storming phase: Lack of cohesion, Subjectivity, Hidden agendas, Conflicts, Confrontation, Volatility, Resentment, anger, Inconsistency, Failure.

|-
|* '''Norming:'''
|Group members establish implicit or explicit rules about how they will achieve their goal. They address the types of communication that will or will not help with the task. Indicators include: Questioning performance, Reviewing/clarify objective, Changing/confirming roles, Opening risky issues, Assertiveness, Listening, Testing new ground, Identifying strengths and weaknesses.

|-
|* '''Performing:'''
|Groups reach a conclusion and implement the conclusion. Indicators include: Creativity, Initiative, Flexibility, Open relationships, Pride, Concern for people, Learning, Confidence, High morale, Success, etc.

|-
|* '''Adjourning:'''
|As the group project ends, the group disbands in the adjournment phase. This phase was added when Tuckman and Jensen's updated their original review of the literature in 1977.
|}

Each of the stages proposed by Tuckman involves two aspects: interpersonal relationships and task behaviors. Such a distinction is similar to Bales' (1950) equilibrium model which states that a group continuously divides its attention between instrumental (task-related) needs and expressive (socioemotional). To maintain balance between these two concerns a group engages in three distinct progressive phases: orientation (exploration), evaluation (seeking opinions), and control (norms that guide actions).

Some models offered subsequently have followed similar sequential patterns. Examples of similar sequences include: define the situation, develop new skills, develop appropriate roles, carry out the work (Hare, 1976); orientation,
dissatisfaction, resolution, production, termination (LaCoursiere, 1980); and generate plans, ideas, and goals; choose&agree on alternatives, goals, and policies; resolve conflicts and develop norms; perform action tasks and maintain cohesion (McGrath, 1984).

It has also been suggested, most notably by Timothy Biggs, that an additional stage be added of ''Norming'' after forming and renaming the traditional ''Norming'' stage ''Re-Norming''. This addition is designed to reflect that there is a period after Forming where the performance of a team gradually improves and the interference of a leader content with that level of performance will prevent a team progressing through the Storming stage to true performance. Other authors have also suggested an additional stage labeled ''Transforming'' since a team that lasts beyond an issue or task may transcend into a new task thanks to a transforming phase. Transformational management can produce major changes in performance through synergy and is considered to be more far-reaching than transactional management.

Tuckman's stages of group development are also similar to those developed by M. Scott Peck for larger-scale groups. Peck describes the stages of a community as: Pseudo-community, Chaos, Emptiness, True Community. In his view, communities may be distinguished from other types of groups by the need for members to eliminate barriers to communication in order to be able to form true community. Examples of common barriers are: expectations and preconceptions; prejudices; ideology, counterproductive norms, theology and solutions; the need to heal, convert, fix or solve and the need to control. A community is born when its members reach a stage of "emptiness" or peace.

==Tubbs' Systems Model of Group Development==

Stewart Tubbs "systems" approach to studying small group interaction led him to the creation of a four-phase model of group development:

{| class="wikitable"
|-
| '''Orientation:'''
| In this stage, group members get to know each other, they start to talk about the problem, and they examine the limitations and opportunities of the project.
|-
| '''Conflict:'''
| Conflict is a necessary part of a group's development. Conflict allows the group to evaluate ideas and it helps the group avoid conformity and groupthink
|-
| '''Consensus:'''
| Conflict ends in the consensus stage, when group members compromise, select ideas, and agree on alternatives.
|-
| '''Closure'''
| In this stage, the final result is announced and group members reaffirm their support of the decision.
|}

==Fisher's theory of decision emergence in groups ==

Fisher outlines four phases through which task groups tend to proceed when engaged in decision making. By observing
the distribution of act-response pairs (a.k.a. "interacts") across different moments of the group process, Fisher noted how the interaction changed as the group decision was formulated and solidified. His method pays special attention to the "content" dimmension of interactions by classifying statements in terms of how they respond to a decision proposal (e.g. agreement, disagreement, etc.

{| class='wikitable'
|-
| '''Orientation:'''
|During the orientation phase, group members get to know each other and they experience a primary tension: the awkward feeling people have before communication rules and expectations are established. Groups should take time to learn about each other and feel comfortable communicating around new people.
|-
| '''Conflict:'''
|The conflict phase is marked by secondary tension, or tension surrounding the task at hand. Group members will disagree with each other and debate ideas. Here conflict is viewed as positive, because it helps the group achieve positive results.
|-
| '''Emergence:'''
|In the emergence phase, the outcome of the group's task and its social structure become apparent. Group members soften their positions and undergo and attitudinal change that makes them less tenacious in defending their individual viewpoint.
|-
| '''Reinforcement:'''
|In this stage, group members bolster their final decision by using supportive verbal and nonverbal communication.
|}

Based on this categorization, Fisher created his "Decision Proposal Coding System" that identifies act-response pairs associated with each decision-making phase. Interestingly, Fisher observed that the group decision making process tended to be more cyclical and, in some cases, almost erratic. He hypothesized that the interpersonal demands of discusion require "breaks" from task work. In particular, Fisher observed that there are a number of contingencies that might explain some of the decision paths taken by some groups. For instance, in modifying proposals, groups tend to follow one of two patterns. If conflict is low, the group will reintroduce proposals in less abstract, more specific language. When conflict is higher, the group might not attempt to make a proposal more specific but, instead, because disagreement lies on the basic idea, the group introduces substitute prooposal of the same level of abstraction as the original.

==Poole's multiple-sequences model==

Marshall Scott Poole’s model suggests that different groups employ different sequences in making decisions. In contrast to unitary sequence models , the multiple sequences model addresses decision making as a function of several contingency variables: task structure, group composition, and conflict management strategies. Poole developed a descriptive system for studying multiple sequences, beyond the abstract action descriptions of previous studies. From Bales’ Interaction Process Analysis System and Fisher’s Decision Proposal Coding System, Poole proposes 36 clusters of group activities for coding group interactions and 4 cluster-sets: proposal development, socioemotional concerns, conflict, and expressions of ambiguity. However, in his latter work, Poole rejected phasic models of group development and proposed a model of continuously-developing threads of activity. In essence, discussions are not characterized by blocks of phases, one after another, but by intertwining tracks of activity and interaction.

Poole suggests three activity tracks: task progress, relational, and topical focus. Interspersed with these are breakpoints, marking changes in the development of strands and links between them. Normal breakpoints pace the discussion with topic shifts and adjournments. Delays, another breakpoint, are holding patterns of recycling through information. Finally, disruptions break the discussion threads with conflict or task failure.

{| class='wikitable'
|-
|'''Task track:'''
| The task track concerns the process by which the group accomplishes its goals, such as dealing doing problem analysis, designing solutions, etc.
|-
| '''Relation track:'''
|The relation track deals with the interpersonal relationships between the group members. At times, the group may stop its work on the task and work instead on its relationships, share personal information or engage in joking.
|-
|'''Topic track:'''
|The topic track includes a series of issues or concerns the group have over time

|-
| '''Breakpoints:'''
|Breakpoints occur when a group switches from one track to another. Shifts in the conversation, adjournment, or postponement are examples of breakpoints.
|}

==McGrath's Four Modes of Activity==
Work in the field of small group research (SGR) has theorized a number of possible patterns of changes for groups over time. In particular, research that concentrates on the concept of roles states that the organization of a group may vary over time for at least three reasons: "One is that, in a newly formed group, it may take several periods of conflict before an informal “pecking order” can be established. A second reason is that newmembers may join the group or old members drop out, requiring a newdistribution of roles.Athird reason is that the activities required in each phase of the development of a group may call for a different constellation of roles and a different group structure." (Hare, 2003, p. 129)

To carry out a group task, McGrath (1991, pp. 152-153) identified four modes of activity,
REPEAT?
McGrath's (1991) work emphasized the notion that different teams might follow different developmental paths to reach the same outcome. He also suggested that teams engage in four modes of group activity: ''goal choice, means choice, policy choice, and goal attainment'' (Hare uses the terms meaning, resources, integration, and goal attainment for these four modes). Groups addopt this modes with respect to each of three team functions: production, well-being, and member support. He further suggested that all team projects begin with Mode I (goal choice) and end with Mode IV (goal attainment) but that Modes 2 and 3 may or may not be needed depending on the task and the history of the group’s activities. McGrath contended that for each identified function, groups can follow a variety of alternative "time-activity paths" in order to move from the initiation to the completion of a given function.

{| class='wikitable'
|-
|'''Mode 1:'''
| Inception and acceptance of a project (goal choice) [meaning];
|-
|'''Mode 2:'''
| Solution of technical issues (means choice) [resources];
|-
|'''Mode 3:'''
| Resolution of conflict, that is, of political issues (policy choice) [integration];
|-
|'''Mode 4:'''
| Execution of the performance requirements of the project (goal attainment) [goal attainment].
|}

Other theories of group development add a fifth phase that includes evaluation (Tschan, 1995) as group members, either as actors or audience, reassess their understanding of “the meaning of all this.” The fifth phase is sometimes called termination (Keyton, 1993) or adjournment (Maples, 1988). I suggest that the fifth phase is actually a return to the same processes found in Phase 1, as group members redefine the situation to consider its implications for them as individuals if they are to take their separate ways or to begin a new task if the group is to remain together.

Not everyone agrees. Some observers of groups over time do not identify phases but evolution and maturation as group members learn to perform assigned tasks and to enhance the quality of their interpersonal interactions (Crouch & Yetton, 1988; Krayer, 1988; Morgan, Salas, & Glickman, 1993; Wekselberg, Goggin, & Collings, 1997). Others conclude that face-to-face groups reach a pattern of equilibrium, balancing task and social-emotional concerns, which is occasionally “punctuated” by a deadline (Seers & Woodruff, 1997)—including an awareness that the group is not immortal (Sokol, 1992)— or some other environmental cue (Arrow, 1997). However, I still go with the phase hypothesis originally suggested by Andrew Effrat, assuming that sequences of phases could be identified if one were to take a closer look at the data provided by those who describe continuous maturation or punctuating deadlines.

==Gersick's Punctuated Equilibrium Model==

Gersick study of naturally-occurring groups departs from the traditionally linear models of group development. Her punctuated equilibrium model suggests that groups develop through the sudden formation, maintenance, and sudden revision of
a "framework for performance". This model describes the processes through which such frameworks are formed and revised and predicts both the timing of progress and when and how in their development groups are likely, or unlikely, to be influenced by their environments. The specific issues and activities that dominate groups' work are left unspecified in the model, since groups' historical paths are expected to vary.Her proposed model works in the following way.

{| class='wikitable'
|-
|'''Phase I''':
| According to the model, a framework of behavioral patterns and assumptions through which a group approaches its project emerges in its first meeting, and the group stays with that framework through the first half of its life. Teams may show little visible progress during this time because members may be unable to perceive a use for the information they are generating until they revise the initial framework.
|-
|'''Midpoint:'''
|At their calendar midpoints, groups experience transitions-paradigmatic shifts in their approaches to their work-enabling them to capitalize on the gradual learning they have done and make significant advances. The transition is a powerful opportunity for a group to alter the course of its life midstream. But the transition must be used well, for once it is past a team is unlikely to
alter its basic plans again.
|-
|'''Phase 2'''
| A second period of inertial movement, takes its direction from plans crystallized during the transition. At completion,
when a team makes a final effort to satisfy outside expectations, it experiences the positive and negative consequences of past choices.
|}

==Morgan, Salas & Glickman's Team Evolution and Maturation (TEAM) model==

Combining multiple theories and the development models of Tuckman and Gersick, Morgan, Salas and Glickman created the TEAM model to describe a series of nine developmental stages through which newly formed, task-oriented teams are hypothesized to evolve. The periods of development are labeled "stages" and conceived to be "relatively informal, indistinct, and overlapping", because "sharp demarcations are not often characteristic of the dynamic situations in which operational teams work and develop". According to this model, teams might begin a given period of development at different stages and spend different amounts of time in the various stages. Teams are not always expected to progress in a linear fashion through all of the stages. A team's beginning point and pattern of progression through the stages depend on factors such as the characteristics of the team and team members, their past histories and experience, the nature of their tasks,
and the environmental demands and constraints (cf. McGrath, 1991).

The TEAM model identities a total of nine stages, seven central ones supplemented by two additional ones. The seven central stages of begin with the formation of the team during its first meeting (forming) and moves through the members' initial, and sometimes unstable, exploration of the situation (storming), initial efforts toward accommodation and the formation and acceptance of roles
(norming), performance leading toward occasional inefficient patterns of performance (performing-I), reevaluation and transition (reforming), refocusing of efforts to produce effective performance (performing-11), and completion of team assignments (conforming). The development of a team might be recycled from any of the final stages to an earlier stage if necessitated by a failure to achieve
satisfactory performance or if adjustments to environmental demands are required or if problematic team interactions develop.

The core stages of the model are preceded by a pre-forming stage that recognizes the forces from the environment (environmental demands and constraints) that call for, and contribute to, the establishment of the team; that is, forces external
to the team (before it comes into existence) that cause the team to be formed. The last stage indicates that after the team has served its purpose, it will eventually be disbanded or de-formed. Here. individuals exit from the group (separately or
simultaneously) and the team loses its identity and ceases to exist.

The TEAM model also postulates the existence of two distinguishable activity tracks that pass through the stages of the model. The first of these track involves activities that are tied to the specific task(s) being performed. These activities include interactions of the team members with tools and machines, the technical aspects of the job (e.g., procedures, policies, etc.), and other task-related activities. The other track of activities is devoted to enhancing the quality of the interactions, interdependencies, relationships, affects, cooperation, and coordination of teams.

The proponents of the model did not test its components or sequence of stages empirically but did confirm that the perceptions of team members concerning the performance processes of the team are perceived to include both team-centered and task-centered activities and that these perceptions seem to change over time as a result of team training.

==REVIEW GenPlore, Creation/Evaluation Divergent/Convergent==
Scheidel and Crowell [39] identify
two cognitive patterns which are central to various phase models of
group decision-making. These are:

i) the divergent phase, which is described as an activity for
searching and generating ideas where ideas are developed,
explored, perspectives are enlarged. As the divergent phase
proceeds individual opinions as they form diverge farther and
farther apart. The purpose of this phase is to promote diversity
in opinions so as to maximize the possibility that the best
solution emerges. Exemplar activities that support divergent
group processes are brainstorming [35], Delphi Method [29],
and the Nominal Group Technique [6].

ii) the convergent phase, which is described as an “arena of
conflict” [39]. In this mode the problem of conflict of individual
interests and viewpoints are resolved. The focus is on obtaining
a closure. The exemplar activity that reveals convergent thought
processes is the evaluation, preening, merging, and selecting an
element of a list of group alternative actions.

T. Scheidel and L. Crowell, Discussion and Deciding. New York:
Macmillan, 1979.

==Group Negotiatoin Models ==
Less abstract and more experimental phase models have been
furnished in the context of group negotiation [8]. In these models
different phases entail sequence of actions directed to different cluster
of goals. Stephenson, Kniveton, and Morley [42] confirm a threestage
model through interaction analysis, and Carlisle and Leary [2]
set forth a five-phase model. These phase models attempt to capture
the dynamic orientation of interaction by casting goals and objectives
as changing during different phases with clear breakpoints at the
end and beginning of each phase. In particular, Douglas [9] claims
that in the initial stages participants define issues and settle on the
agenda, while in the later stages final agreements are obtained through
exchange of proposals which include offers and concessions.
C. Process of Coordination
Following Douglas [9], we hypothesize that the process of coordination
cycles through four distinct though overlapping phases (as
depicted in Fig. 1). We now briefly describe each of the four phases
in the coordination cycle.
The Dejnitional Phase: During this phase conflicting sources of
information and inconsistent belief systems among participants are
brought to focus. Inconsistencies in perspectives are an inevitable
result of different experiential background of individuals and their
bounded views of the world. A high degree of commonality and
consistency about the problem definition is brought about in this
phase by changes enacted in the individual belief systems of the
participants as a result of exchange of messages.
The computer based support for the process of “assumptionsurfacing”
in group decision support systems (GDSS) is thus an
attempt to aid groups through this definitional phase. Similarly, the
gIBIS system developed by MCC [5], helps define the differing
perspectives of individuals on the problem in terms of their individual
positions and thus aids the group in arriving at a common definition
of the problem at hand.
The Conflict Resolution Phase: In the first phase participants arrive
at a common definition of the problem, whereas in this phase a
common course of action is decided upon for the group. But since
participants are autonomous their goals conflict. Different solutions to
the common problem affect participants differently. The focus in this
phase is on the conflict of goals among individuals and the attempt
to arrive at a consensus solution.
In the context of game theory [12] in the first phase the definition
of the game is settled upon, whereas in this phase the equilibrium
solution is worked out. This conflict resolution phase is dominated
by exchange of proposals, where a proposal from a member denotes
what each member of the group has to do in order that the group
problem is satisfactorily resolved.
The above two phases are similar to the concept of “due process”
[19], [20] which are described as:
“the activity of humans and computers for generating sound,
relevant, and reliable information as a basis for decisions.
. . .due process is inherently reflective in that beliefs, goals,
plans, requests, commitments, etc., exist as objects that can be
explicitly mentioned and manipulated as an object.”
Conflict
Consensus
Action
Fig. 1. Four phases of a coordination cycle.
We differ from Hewitt [20] in that we differentiate between getting
agreement as to what the problem is about and getting an agreement
as to what the common solution to that problem should be.
Following Douglas’ [9] model of negotiation, we can call the first
and second phases in each coordination cycle the negotiation stage
of coordination process.
The Consensus Action Phase: During this phase the commonly
agreed upon decision is enacted. The consensus action is viewed
as a transformation process, i.e., transformation of inputs to outputs.
In an office environment this is primarily informational in nature.
Information of some type and sources is transformed to another and
is communicated across time and space. In the context of a software
customer support context, action would imply preparing the revised
software (as agreed upon in the first two phases) from an existing
version and communicating the same to the customer.
The Adaptation Phase: This is the final phase in the cycle. During
this phase the participants observe (or receive messages about) the
outcome of their joint actions and draw their own conclusions. Many
of the management audit systems, cost control, and variance reporting
systems are part of the informational feedback mechanisms instituted
within organizations so that individuals and the group can adapt
through experience.

A. Douglas, Industrial Peace-Keeping. New York: Columbia University
Press, 1962.

J. Carlisle and M. Leary, “Negotiation groups,” in Groups at Work, R.
Payne and C. L. Cooper, Eds. New York: Wiley, 1981, pp. 165-188.

==References==
* Fisher, B. Aubrey. (1970). Decision emergence: Phases in group decision making. Speech Monographs, 37, 53-66.
* Hare, P. (2003). Roles, relationships, and groups in organizations: Some conclusions and recommendations. Small Group Research, 34 (2), 123-154.
* Lewin, K. (1947). Frontiers in group dynamics: Concept, method and reality in social science; social equilibria and social change. Human Relations, 1 (1), 5-41.
* McGrath, J. E. (1991). Time, interaction, and performance (tip): A theory of groups. Small Group Research, 22 (2), 147-174.
* Poole, Marshall Scott. (1981). Decision development in small groupsI: A comparison of two models. Communication Monographs, 48, 1-24;
* Poole, M. S. (1983). Decision development in small groups II: A study of mutiple sequences in decision making. Communication Monographs, 50, 206-232
* Poole, M. S. (1983). Decision development in small groups III: A multiple sequence model of group decision development. Communication Monographs, 50, 321-341
* Poole, M. S., & Roth, Jonelle. (1989). Decision development in small groups V: Test of a contigency model. Human Communication Research, 15, 549-589.
* Poole, M. S., & Holmes, M. E. (1995) Decision development in computer-assisted group decision making. Human Communication Research; 22(1) p. 90 -127
* Tubbs, Stewart. (1995). A systems approach to small group interaction. New York: McGraw-Hill, 1995.
* Tuckman, Bruce. (1965). Developmental sequence in small groups. Psychological Bulletin, 63, 384-399.

Portrait2

Jsarmi — Thu, 06 Sep 2007 14:43:55 GMT

Jsarmi:

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Portrait

Jsarmi — Thu, 06 Sep 2007 14:28:03 GMT

Jsarmi:

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Dissertation Proposal

Jsarmi — Tue, 14 Aug 2007 20:59:55 GMT

Jsarmi: /* Literature Review */

==Bridging mechanisms in team-based online problem solving: Continuity in collaborative knowledge building==

:Dissertation Proposal by Johann W. Sarmiento
:Doctoral Program in Information Science and Technology
:College of Information Science and Technology, Drexel University

:Dissertation Proposal Committee:
:{| border="0" cellpadding="4"
|-
|Gerry Stahl (Chair)
| College of Information Science and Technology, Drexel University
|-
|Susan Gasson
| College of Information Science and Technology, Drexel University
|-
|Robert B. Allen
| College of Information Science and Technology, Drexel University
|-
|Wesley Shumar
| Department of Culture and Communication at Drexel University
|-
|Steve Weimar
|The Math Forum - Drexel University School of Education
|}

----

==Overview==
Emergent theories and designs for collaborative knowledge building in fields such as social computing and information science and technology in general, continue to point to the pressing need to better understand how the power of virtual distributed teams and online communities can be harnessed. This kind of research and design work aims to realize the potential of such new forms of interaction to generate and advance learning and knowledge in organizations, communities of interest, academic disciplines, societies, and many other types of collectivity.

One particular aspect of the interdisciplinary study of computer-supported collaboration which is not well understood yet, is how interactions which are dispersed over time (e.g., long-term projects, multi-session problem solving engagements, etc.) and which cut across different collectivities (e.g., sub-teams, teams, communities, etc.) can more successfully be interlinked or "bridged" so that they lead to more constructive and sustained collaborative knowledge building. In fact, the study of this type of interactional bridging activity may provide a unique viewpoint into the interrelationship between the local small-group unit of analysis and other more wide-ranging groups (e.g., online communities, multi-team collectivities, etc.) as well as between the individual and the small-group. In addition to the need to understand the interactional nature of bridging, there is also a crucial need to learn more about which aspects of the computer tools provided to support collaborative knowledge building attend to these types of activities, and how such designs might be enacted in particular contexts.

This dissertation will investigate, from an interactional perspective, the ways in which bridging mechanisms contribute to sustaining continuity in the collaborative knowledge building of small groups in online learning communities. More specifically, it will pursue the following three goals by analyzing bridging phenomena within a particular online learning community appropriately structured for design-based research:

::*'''(a) Defining how three different aspects of the online interactions of virtual collaborative learning teams are bridged: episodes, collectivities, and perspectives.'''

::*'''(b) Exploring the effect of such bridging activity on the sustained knowledge work of virtual teams.'''

::*'''(c) Investigating how bridging activity can be supported by designed artifacts.'''

==Problem Statement==

The Math Forum at Drexel University, an online community active since 1992, promotes interactions among teachers of mathematics, students, mathematicians, hobbyists, staff members and other interested parties interested in learning, teaching, and doing mathematics. As the Math Forum continues to evolve, support for synchronous interactions becomes increasingly essential for sustaining and enriching the mechanisms of community participation available. A step in this direction, the Virtual Math Teams (VMT) project investigates the innovative use of online collaborative environments to support effective secondary mathematics learning at the Math Forum. The research proposed here is aimed at understanding how teams of participants in VMT online community "bridge" the apparent discontinuity of their interactions (e.g., multiple collaborative sessions, teams and tasks) and exploring the role that such bridging activity plays in their knowledge building over time. In addition, this research aims at informing the design of appropriate computational supports for long-term collaborative knowledge building.

In order to motivate our proposed research, this section presents some pilot data from the VMT project and raises a series of questions about several bridging phenomena that can be identified in these data.

''Recommencing problem solving work and managing participation''

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|It is the second time that this virtual team of students meets online to work on figuring out the mathematics of a "grid-world," a world where one could only move along the lines of a rectangular grid. In their previous session, a few days ago, ''Drago'' and ''Estrickm'' worked on exploring the grid-world and attempted to create a formula for the shortest distance between two points A and B in this world. This time, they are joined by two new team members; ''Gdo'' who had worked on this problem with another team once before and ''Mathwiz'' who is new to the task and to the team.||align = "center"| 
[[Image:JsarmiDissProposalv10_01.png|framed|none]]

 Your group has gotten together to figure out the math of this place. For example, what is a math question you might ask that involves these two points? ''Figure 2.1.Grid-world task''

|}

After the initial greetings and a discussion on what to do in this session, the following exchange takes place via the chat interface available in the virtual meeting environment:

{|border="2" cellspacing="0" cellpadding="4" width="94%" align="center"
|align = "right"|302||gdo<ref>The names presented in all transcripts used in this proposal correspond to anonymous chat handles as per the procedures approved for the VMT project by Drexel’s Internal Review Board.</ref>: now lets work on our prob (Points'' to Whiteboard'')

|-
|align = "right"|'''303'''||'''drago: last time, me and estrickm came up'''

|-
|align = "right"|'''304'''||'''drago: that '''

|-
|align = "right"|305||gdo: …………

|-
|align = "right"|'''306'''||'''drago: you always have to move a certain amount to the left/right and a certain amount to the up/down '''

|-
|align = "right"|307||gdo: what?

|-
|align = "right"|308||drago: for the shortest path

|-
|align = "right"|309||drago: see

|-
|align = "right"|310||drago: since the problem last time

|-
|align = "right"|311||drago: stated that you couldn<nowiki>’</nowiki>t move diagonally or through squares

|-
|align = "right"|312||drago: and that you had to stay on the grid

|-
|align = "right"|313||''gdo leaves the room''

|-
|align = "right"|314||mathwiz: would you want to keep as close to the hypotenuse as possible? or does it actually work against you in this case?

|-
|align = "right"|315||drago: any way you go from point a to b ''(Points to line 314)''

|-
|align = "right"|316||''gdo joins the room''

|-
|align = "right"|317||drago: is the same length as long as you take short routes

|-
|align = "right"|318||gdo: opps

|-
|align = "right"|319||gdo: internet problem

|-
|align = "right"|320||gdo: internet problem

|-
|align = "right"|321||drago: you always have to go the same ammount right, and the same ammount down ''(Points to line 317)''

|-
|align = "right"|322||gdo: ok ''(Points to line 314)''

|} 

This excerpt illustrates how the participants of this interaction chose to start a current collaborative task. Elements of their collaborative discourse signal to us that they are also engaged in using prior interactions as relevant resources in initiating their current work. Understandably, when teams sustain their collaborative work over multiple individual sessions, this task of recommencing knowledge-building activity becomes an issue that participants have to address. Furthermore, what participants do to "bridge" the discontinuity of their interactional episodes might have an impact on the ways collectivities evolve and the methods used to advance the development of group ideas. A close examination of this passage—by attending to the ways that the participants demonstrably orient to the interaction moment-by-moment—can help us construct ideas about how some aspects of such "bridiging" activity get done and guide us in the process of articulating relevant questions about collaborative knowledge building.

One way in which we can approach our analysis of this sequence of postings is to consider the characteristic question of ethnomethodology-oriented studies: "''why this now?''" In other words, what purpose do these particular textual postings serve at this point of the interaction of this virtual team? How is it that the ways in which ''Drago'' designed and presented his postings (e.g., the way they were segmented in the multiple postings, the way they were positioned after line 302, etc.) indicate their interactional role and their effects? We can see that ''Drago<nowiki>’</nowiki>s'' posting in line 303 ("''last time, me and estrickm came up''") stands as an uptake of the proposal for collective action put forward by ''Gdo'' in line 302 ("''now lets work on our prob''"). Furthermore, the distinctive juxtaposition between these two postings indicates to us the beginnings of the group<nowiki>’</nowiki>s orientation to the problem solving task. By contrasting "''last time''" with ''Gdo<nowiki>’</nowiki>s ''"''now''", ''Drago'' attempts to establish a particular kind of episodic continuity or "relevant history" of the team, categorizes ''Gdo'' and ''Mathwiz ''as newcomers and orients to them as such. Continuing our inquiry as this interactional sequence unfolds, we could pursue these observations and investigate how ''Drago'' and the rest of the small group of co-participants orient toward this reported history and the "spokesperson-addressees" framework and how this orientation evolves. In addition, we might be able to inquire about how these and other elements of their interaction influence and are influenced by the way the collaborative knowledge-building task is being approached by this team.

Turning now to the unfolding of the sequence which begins with ''Drago<nowiki>’</nowiki>s'' posting in line 306 ("''you always have to move a certain amount to the left/right and a certain amount to the up/down''") we can explore further the dynamics of bridging work. This posting in particularly seems central to our understanding how the bridging work that is currently being attempted is unfolding. The reply posted in line 307 by ''Gdo'' ("''what?''") and the subsequent elaboration attempted by ''Drago ''suggest that the posting in 306 was taken as a problematical response to the proposal to initiate the problem solving work. Perhaps additional work was necessary for line 306 to be fully sensible for the team; in other words, for ''Drago'' to successfully bridge prior work into the present. In the subsequent lines we can see the beginnings of an instance of the kind of interactional work that seems to be necessary for the team to engage with the reported past that ''Drago'' is presenting. Even without a thorough understanding of the mathematical task at stake, one can see that ''Drago'' elaborates on his initial posting by providing additional problem information (308, ''"for the shortest path''") and adding further references to elements of the past problem solving activity (310-312, "''since the problem last time stated that you couldn<nowiki>’</nowiki>t…''"). In this way, ''Drago ''continues to use past resources to organize a potential present for the problem solving task of the team and in doing so, attempts to project that past history on the current team members. We will come back to further inquire about the nature of posting in line 306 after exploring in more detail its uptake.

''How does knowledge building advance across collectivities?''

M''athwiz'' posting in line 314 ("''would you want to keep as close to the hypotenuse as possible? or does it actually work against you in this case?'') engages with the bridging activity opened up by ''drago'' in a particular way. ''Mathwiz'' seems to suggest a particular way of clarifying ''Drago<nowiki>’</nowiki>s'' presentation of how the grid-world works while at the same time doing the interesting work of positioning ''drago'' as the one who is to assess this suggestion (i.e. testing whether this case "''works against you''"). In this way, ''Mathwiz''<nowiki>’</nowiki> posting seems to actively situate ''Drago<nowiki>’</nowiki>s'' narrative of the past by ratifying its relevance for their current problem solving and assessing its practical comprehensibility. This short sequence signals only the beginnings of the type of interactional work necessary to fully bridge prior knowledge-work into present joint-activity and yet it is sufficient to provide us with significant evidence of the nuanced aspects of this type of activity.

One further aspect of this interactional sequence is worth exploring. The sequence below follows the excerpt presented initially from session two, and allows us to observe how this collectivity dealt with some of the challenges in the uptake of ''Drago<nowiki>’</nowiki>s'' presentation of the past finding about short distances in the grid-world.

{|border="2" cellspacing="0" cellpadding="4" width="94%" align="center"
|323||drago: ok....

|-
|324||drago: so

|-
|325||gdo: square root of 45

|-
|326||mathwiz: but you have to move on the grid lines, right?

|-
|327||gdo: 3<nowiki>^</nowiki>2<nowiki>+</nowiki>6<nowiki>^</nowiki>2=c<nowiki>^</nowiki>2 right?

|-
|328||drago: no

|-
|329||drago: you can<nowiki>’</nowiki>t go diagonal

|-
|330||gdo: ok

|-
|'''331'''||'''drago: the problem before said so, but you weren<nowiki>’</nowiki>t here'''

|-
|332||gdo: so the hypotenuse is not square root of 45?

|-
|333||gdo: i was on team 2

|-
|334||drago: I mean

|-
|335||drago: it is

|-
|336||gdo: but moved to team 5

|-
|337||gdo: since u guys didn<nowiki>’</nowiki>t have enough people

|-
|338||drago: but, we can<nowiki>’</nowiki>t move diagonally since that would be cutting through the grid

|-
|'''339'''||'''mathwiz: the hypotenuse is fine, but for the problem, you have to go on the grid lines'''

|-
|340||gdo: ok

|-
|341||drago: so

|-
|'''342'''||'''mathwiz: it<nowiki>’</nowiki>s like, you can<nowiki>’</nowiki>t walk in water, and the lines are dry lines'''

|-
|323||drago: ok....

|} 

Despite the fact that ''Drago'' is orientating to the recommencement of the prior work performed by him and ''Estrickm ''(and to a narrator-explainer framework of participation), ''Gdo'' departs partially from that orientation in line 325. ''Gdo'' does this by making a solution proposal ("''square root of 45''") for the shortest path between the points that they are currently examining. Consequently, the sequence of postings from 325 to 330 seems to indicate a local engagement with the problem as the present matter and no longer as a bridging move to re-use prior findings. However, in the sequence starting at line 331 ''Drago'' uses, once again, elements of prior interactions ("the problem before said so but you weren<nowiki>’</nowiki>t here") to address what appears to be a problem in ''Gdo<nowiki>’</nowiki>s'' understanding (i.e. that you can<nowiki>’</nowiki>t go on the diagonal). This alternation between present and bridged resources for problem solving indicates a dynamic engagement by the group with its distributed history and its current problem solving activity.

Also particularly interesting in this sequence are ''Mathwiz<nowiki>’</nowiki>'' postings in lines 339 and 342: "''the hypotenuse is fine, but for the problem, you have to go on the grid lines…it<nowiki>’</nowiki>s like, you can<nowiki>’</nowiki>t walk in water, and the lines are dry lines.''" These postings seem to do the interesting work of ratifying ''Gdo<nowiki>’</nowiki>s'' use of the hypotenuse —as well as his participation in the task— while at the same time offering him a new "rule" to manipulate the grid. It seems to us that this interactional move bears resemblance with the types of activities we have analyzed before and deserves the label of bridging work. By offering this new perspective on how to imagine and manipulate the grid ''Mathwiz ''identifies a boundary between different perspectives or understandings (using diagonals or not) and goes beyond simply refuting it to offer a link between the two. This bridging of perspectives can naturally occur between different problem solving episodes or collectivities but here we see it happening within the flow of a team<nowiki>’</nowiki>s interactions. With the dynamic changes in team membership that characterizes naturalistic environments and the diversity of points of view among individuals and teams typical of online communities, sustained problem solving work seem to require that co-participants also engage in this type of bridging of perspectives. Here we may ask what kinds of resources are produced by individuals and groups to overcome the boundaries that emerge as relevant during their interactions and which might aid with challenges of continuity, coordination or affiliation. It is possible that the methods and processes of doing this kind of boundary work could characterize effective collaborative learning interactions, but this remains a notion to be investigated further.

So far, we have explored a few instances of bridging activity in the trajectory of a particular virtual math team. In doing so, we have offered a preliminary analysis on how the collective engagement with past work is constituted across different interactions or episodes, how changes in participation signal various aspects of the sustained knowledge-work of the teams, and how problem solving perspectives are subject to bridging as well. This preliminary analysis demonstrates that, in interactional contexts where there are continual sequences of discrete problem solving episodes and where the membership of a team might change over time, sustaining continuity of the team<nowiki>’</nowiki>s knowledge work becomes a particular challenge for which teams need to develop particular interactional strategies. Furthermore, our analysis seems to suggest that these attempts to establish continuity in collaborative problem solving involve the recognition and use of discontinuities or boundaries as resources for interaction (e.g., temporal or episodic discontinuity), changes in the participants<nowiki>’</nowiki> relative alignment toward each other as a collectivity (e.g., narrators and interactive audience), and also the use of particular orientations towards specific knowledge resources (e.g., the problem statement, prior findings, what someone professes to know or remember, etc). Whether these are the central structural elements that characterize the establishment continuity in collaborative knowledge building and how such elements are used to sustain it, are questions that require further analysis. In fact, the analysis of other instances of this type of activity could lead us to uncover a range of bridging mechanisms used as part of this online learning community while at the same time helping us strengthen the methods utilized to conceptualize and analyze these phenomena.

''How does knowledge building develop over time in small groups?''

In addition to following the sequential unfolding of the particular instance of a team<nowiki>’</nowiki>s recommencement that we have pursued, we could also investigate retrospectively ''Drago<nowiki>’</nowiki>s'' "bridging" posting in line 306 ("''you always have to move a certain amount to the left/right and a certain amount to the up/down''"). We could do this by analyzing his prior work with ''Estrickm ''a few days back and trace the genesis of the reported finding. This approach would allow us to stretch the scope of our analysis not only from one problem solving episode into another but also from one particular collectivity (''Drago- Estrickm-Gdo''-''Mathwiz'')'' ''into a different one (the dyad ''Drago''-''Estrickm''). In brief, let us just say that line 306 in session two appears as a re-statement of something that ''Drago ''and ''Estrickm ''discovered in the first session that they held as a team. The following excerpt illustrates how this idea was articulated then:

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|168||estrickm:well, judging by my calculations, any root that does not go along a diagonal is the same length

|-
|169||drago: it should be (Points to line 168)

|-
|170||drago: except if you go some extra long way for no reason

|-
|171||estrickm:haha, precisely

|-
|172||drago: but why are they the same? I remember that I proved this once but I forgot...

|-
|'''173'''||'''estrickm:because you will alsways have to go down and to the right the same amount of times '''

|-
|174||drago: oh, seems reasonable (Points to line 173)

|-
|175||drago: so...any more questions you can think of?

|-
|176||estrickm:but i am not sure of the correct proof

|-
|177||drago: well...I guess its because whatever path you take, you will make tiriangles (Points to line176)

|}

The relationship between line 173 in this excerpt of session one and line 306 of session two appears significant. On the one hand, the use of the adverb "''always" ''in both postings seems to suggest a rule-like statement (or a conjecture) aimed at capturing a constructed understanding about the way the grid-world has been perceived to work. The fact that the creator of this text changes from ''Estrickm ''in session one to ''Drago'' in session two could be taken as an indicator that this rule is a collaborative understanding achieved by the dyad which is, later on, projected into a new collectivity and a "bridged" problem solving context. Based on this observation, we could construe the re-statement of prior findings and the change in authorship as indicators of sustainability in the co-construction of knowledge as the history of multiple teams in an online community evolves. Although not entirely conclusive, these two conditions certainly seem to point in that direction despite the fact that in small-group interactions the notion of authorship needs to be analyzed critically. For instance, if line173 is a response to line 172 and proceeds from the flow of the interaction, isn<nowiki>’</nowiki>t it really the dyad who should be credited with having produced the original rule about the grid-world? It is possible that we need to redefine certain notions such as authorship and construction of knowledge as we navigate individuals, small-groups and larger collectivities.

Beyond the changes in author, it is interesting to note how ''Drago<nowiki>’</nowiki>''''s'' text in line 306 of session two is different than the original posting from session one. In ''Estrickm''<nowiki>’</nowiki>s original posting there was only mention of moving "''down and to the right''" but in ''Drago<nowiki>’</nowiki>''''s'' restatement one has to move a certain amount "''to the ''''left/right ''''and a certain amount to the ''''up/down.''" Why has ''Drago ''modified the original rule by adding the "''/up''" and "''left''/" elements? In order to investigate this question, we should point out that the environment

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|in which these teams are interacting is much more complex than what is captured by the transcripts we have presented so far. In addition to the chat interface, a shared whiteboard is available to the participants. At the moment in session two when the exchanges that we have presented take place, the whiteboard in this team<nowiki>’</nowiki>s meeting room contains the picture presented in Figure 2.2. We can see in this snapshot of their shared whiteboard the points that they selected to explore the grid-world and also some elements of how they have graphically presented their reasoning about it. Interestingly, a very similar diagram was used by'' Estrickm ''and ''Drago ''in session one but, in that case, it ||align = "center"|
[[Image:JsarmiDissProposalv10_02.png|framed|none]]

 ''Figure 2.2 Snapshot of Team 5<nowiki>’</nowiki>s whiteboard, Session 2.''

|}

only included two points arranged in a similar way to the points A and B included in the diagram from session two. The arrangement of points used in session one matches ''Estrickm''<nowiki>’</nowiki>s original rule that "''you will always have to go down and to the right.''" As can be seen on Figure 2.2, there are two arrangement of points being considered in session two: The one including points A and B where the shortest path would be achieved by going down and to the right and another in which the movement would be up and to the right (linking the points labeled with circles). As a result, one can read ''Drago<nowiki>’</nowiki>s'' modification to the original rule as indication that he has adapted it to make it applicable to the two arrangements of points being considered by the team in session two. It is possible that ''Drago ''realized this generalization via further individual work in between team sessions, or that the position on the grid of the points that the team has selected in session two provided the need for the generalization to happen. Whatever the actual motive, ''Drago'' is presenting in session two a modified version of the finding constructed in session one suited to the current circumstances. Beyond simply citing prior findings, ''Drago'' has in fact bridged two problem solving contexts in an attempt to construct continuity. To further qualify this observation, we can contrast ''Drago<nowiki>’</nowiki>s'' tentative reasoning for why the rule works presented in line177 of session one (''well...I guess its because whatever path you take, you will make tiriangles'') with the sense of confidence that his presentation conveys in session two. This subtle change could illustrate a change in the strength of his understanding of the grid-world. Observations like these, although requiring further verification through triangulation and further analyses, start to point to critical interactional aspects of how knowledge work is sustained over time and hint towards longitudinal aspects of collaborative learning interactions. Furthermore, they reveal the need to understand how bridging interactions span across the individual and the different collectivities involved in an online community.

''How do designed artifacts support bridging work?''

Finally, we would like to consider a few questions regarding the collaboration supports used by the participants while engaged in the activities that we have presented. For example, it is reasonable to think that ''Drago'' is relying on his memory to produce, in session two, the account of the prior findings since the transcripts of prior chats were not publicly available. The arrangement of points and the graphical reasoning that we have presented in the snapshot captured in Figure 2.2. bear great resemblance with the work that ''Drago'' and ''Estrickm ''conducted in session one, but there was not a mechanisms available for them to reuse them once a session was over. The virtual room that the team was using was not available either to other teams who were working on the same problem despite the potential usefulness of these cross-team interactions. This motivates us to wonder about the forms in which records of prior interactions could be made accessible to virtual teams and how they would be used in cases where sustained problem solving is being conducted. Would access to such records aid teams in sustaining the processes of collaborative learning and problem solving? If, as in our current case, multiple teams are working on the same collaborative learning tasks, would access to other teams<nowiki>’</nowiki> ideas promote a sense of community? Questions like these point towards the necessary translation between our understanding of sustained collaborative work and the design principles that underlie the support environments made available to participants.

''In Summary''

As we indicated earlier, the excerpts presented here originated from a pilot study of small-group collaborative learning conducted as part of the Virtual Math Teams (VMT) project of the Math Forum. Numerous relevant questions can be pursued about the data presented here and about other excerpts in this dataset. Our intent, however, has not been to present a full analysis of these data but to uncover some of the complexities that need to be investigated about these kinds of interactions and begin to outline elements of the analytical methods needed to investigate the processes related to the establishment of continuity and discontinuity of this type of collaborative knowledge work.

In summary, sustained collaborative learning in small virtual groups and online communities requires that co-participants "bridge" multiple elements of their interactions continuously as they interact over time— a non trivial and possibly very consequential undertaking. One way in which we can cluster the kinds of questions that we have been asking about the data presented could be to take "bridging" as the central target of our inquiry. In the sense we have used it, the term "bridging" defines interactional phenomena that cross over the boundaries of time, activities, collectivities, or perspectives and defines a set of methods through which participants deal with the discontinuities relevant to their joint activity. Bridging thereby might tie events at the local small-group unit of analysis to interactions at larger units of analysis (e.g., online communities, multi-team collectivities, etc.) as well as between the individual and small-group levels. Studying bridging may reveal linkages among group meaning-making efforts across collectivities or interactional episodes over time.

Taking "bridging" as the central interactional phenomena of interest of this research, our central aim is to characterize the ways in which bridging contributes to the establishment of continuity and discontinuity in the knowledge-building experience of online collaborative learning teams in the VMT online community.

In particular, we are interested in pursuing '''three specific goals:'''

''' (a) Defining how the bridging of episodes, collectivities, and perspectives in the online interactions of virtual collaborative learning teams is achieved;'''

'''(b) Exploring the effect of such bridging on the sustained activity of these virtual teams and the online community in which they are situated; and'''

'''(c) Investigating how this bridging activity can be supported by designed artifacts.'''

In addition, by synthesizing the observations that we have posed based on the data presented in this section, we define the following '''three central''' '''research questions''' which guide our proposed research:

{|border="0" cellspacing="2" width="100%"
|'''Q1.||What are the bridging mechanisms that can be identified in the VMT online learning community? How can we effectively conceptualize these phenomena and analyze their effects?'''

|}

{|border="0" cellspacing="2" width="100%"
|'''Q2.||What is the structural analysis of these phenomena? How do they span the individual, small group and community levels of activity? How do they span across individuals, across teams and across time spans?'''

|}

{|border="0" cellspacing="2" width="100%"
|'''Q3. ||How should online environments and associated activity systems (tasks, resources, scaffolding, etc.) be designed to promote bridging and take advantage of it?'''

|}

Before presenting the details of the proposed methods and the experimental design selected to answer these three central questions, we first review the current state of the relevant literature in order to better ground our choice of problem in the larger research context, explore to what extent similar phenomena have been investigated in relevant research fields, and identify potential contributions of our work.

==Literature Review==

Given our choice of research problem and the context in which we propose to carry on our investigation, we find our work to be highly situated in the multidisciplinary field of Computer-supported Collaborative Learning (CSCL). CSCL has been defined as being concerned with understanding "the practices of meaning making in the context of joint activity, and the ways in which these practices are mediated through designed artifacts" (Koschmann, 2002). CSCL has also taken up the research program outlined by the sociohistorical psychologist Lev Vygotsky and his formulation of the "genetic law of cultural development" in which higher psychological functions in humans are demonstrated to originate at the social level (between people), and only later, through a "long series of developmental events", these functions are internalized by the individual. (Vygotsky, 1930/1978). As a branch of the learning sciences, CSCL is particularly concerned with the practices of meaning making that help us understand "how people can learn together with the help of computers" (Stahl et al., 2006). In its first ten years, CSCL studies have uncovered some of the unique ways in which groups create, represent and use knowledge (Roschelle, 1996; Schwartz, 1995), the particularities of how technology affordances support group collaboration (Schwartz, 1995; Stahl, 2004a; Suthers & Hundhausen, 2003), and the fact that, in many instances, the collaborative process needs to be explicitly supported or "scaffolded" for it to succeed (Jermann et al., 2004; Pea, 2004; Rummel & Spada, 2005). As illustrated in Firgure 2.1, CSCL encompasses fields as diverse as educational psychology, small-group research, groupware design, and other research areas that inform CSCL with theoretical models, analytical methods or contexts of applications.

[[Image:JsarmiDissProposalv10_06_1024.png|framed|Figure 2.1. Composition of the multidisciplinary field of Computer-supported Collaborative Learning|none]]

Significant progress has been made within CSCL in advancing our understanding of the nature of learning in small-groups and how to support it with designed artifacts (Koschmann et al., 2002; Koschmann et al., 2005; Stahl, 2002; Wasson et al., 2003)  but much remains to be discovered, especially about the longitudinal patterns of meaning-making in naturalistic small-groups and larger collectivities (e.g., online communities). Next, we review some of the theoretical frameworks and areas of research relevant to the proposed research questions.

''What interactional mechanisms explain collaborative learning over time?''

Successful collaborative learning in small groups is, in fact, a complex phenomenon that involves numerous factors (e.g., nature of the task, number of participants, time, pooled expertise, communication patterns, etc.). These contextual factors interact in non trivial ways (Dillenbourg et al., 1995) to shape the dynamics and outcomes of collaboration. Given such complexity, current research attempts to understand the interactional mechanisms that underlie different collaborative interactions and the ways that they could explain particular collaborative outcomes. A number of these interactional mechanisms have been studied in the CSCL literature and also in related fields. For instance, researchers have argued that collaborative knowledge-building advances thanks to the power of peer explanations and the sharing of knowledge among peers (Dansereau, 1988; Webb, 1985, 1991, 1992) or through argumentation derived from cognitive conflict (M. J. Baker, 1991). An attempt to characterize the dynamics of bridging activity, as presented in the previous section, as peer knowledge sharing or peer explanations seems to miss important parts of the dynamics of such interactions.

For example, some of the limitations of the "peer sharing" perspective are made evident when we revisit the data we have analyzed before in our trace of the interactions of team 5. Even in the brief excerpts we have analyzed, we clearly see how explanations are not simply furnished directly from an "explainer" to a "tutee", nor are summaries of prior activity necessarily presented only by a "recaller" to a "listener." The type of activity that we have identified as "bridging" clearly goes beyond simple peer-explanations or "recalling" of findings, primarily, because of the active and multi-dimensional engagement that characterizes what team participants seem to orient to. In addition, the boundaries imposed by multiple interactional episodes and changing collectivities seem to inflict significant constraints on how the traditional interactional mechanisms, discovered mostly from studying single-episode dyadic interactions, are enacted. Furthermore, recent research on dyadic explanation and argumentation has recognized that these interactional mechanisms, when successful, are co-constructed jointly by both peers through collaborative interactions (Hausmann et al., 2004) Co-construction, however is seen as synchronous and local phenomena and theorized to work through continuous, moment-by-moment engagement in attending and monitoring shared issues of understanding (Chi et al., 2004), exploring and transforming the joint problem-space (Roschelle, 1996), and engaging with each other<nowiki>’</nowiki>s proposals (Stahl, 2006c). Our challenge is to investigate how the apparent discontinuity of the interactions affect these processes when virtual teams collaborate over time as part of an online community, and what new processes of co-construction emerge in these contexts.

''Does the "contribution model of grounding" from communication theory explain bridging activity?''

One of the communication theories most commonly used in CSCL, CSCW, and other fields to understand the process of co-constructing shared understanding in small-group collaboration, is Clark and Schaefer<nowiki>’</nowiki>s "''contribution model of grounding''" (Clark & Brennan, 1991; Clark & Schaefer, 1989). In this theory, rational parties in a conversation not only produce and receive messages but also monitor their mutual understanding by seeking and providing feedback that the message has been understood or by "specifying some content and grounding it" (Ibid, p. 124). The mechanics of this process, the structure of presentation and acceptance phases, and the underlying concept of "common ground", outlines how conversational parties are seen to reach identical or closely aligned mental contents. Several CSCL and CSCW studies have used grounding as a central theoretical concept to explain interactional aspects of how knowledge is established through conversation (M. Baker et al., 1999; McCarthy et al., 1991). Recently, significant criticism has been expressed about the limitations and inadequacies of this model to truly capture the interactional aspect of collaborative meaning-making and its applicability in the design of collaboration support systems (Koschmann & LeBaron, 2003; Stahl, 2006b). On the one hand, it is not clear how the systematics of the model scale up to interactions that span larger collectivities and time scales from the short dyadic exchanges studied by Clark and Brennan. In addition, the concept of common ground as a psycholinguistic object might not be sufficient to explain how complex shared understandings, routines, and community norms, are created and maintained in sustained collaborative interactions. In fact, in the data excerpts presented in Section II, we can already see that the notion of common ground can only explain a small portion of how we see these sequences of interactions unfolding. Contributions to the process of constructing shared meaning in the groups<nowiki>’</nowiki> discourse can bee seen to come from multiple sources and be more contingent than what the theory of common ground may suggest. We can see that bridging implies contributions from the individuals<nowiki>’</nowiki> knowledge of the task, their resources, skills, memories, etc., but equally important in this process is the role of the teams<nowiki>’</nowiki> distributed knowledge of their local history (e.g., what the team has accomplished up to a point in time), the cultural knowledge of the community in which bridging is localized.

''Is bridging the same as "transactive memory" as described by the social-psychological study of teams:?''

The construct of "''transactive memory''" recently adapted from the study of interpersonal relationships to research in team and organizational learning (Moreland et al., 1996) appears also as highly relevant to the study of longitudinal, knowledge-building interactions. Transactive memory is theorized as a distributed memory system through which a collectivity stores and recalls information and is used as the basis to explain how a team becomes a "knowledge-acquiring, knowledge holding, and knowledge-using system" (Wegner et al., 1985, p. 256). The theory argues that a collectivity composed of individuals develops a memory system by constantly updating a "directory" of expertise (knowing who knows what), communicating to allocate information, and communicating to retrieve information. These processes are highly dependent on the establishment of a shared conception of the topics that the individual members know, something that the theory of transactive memory predicts is achieved through the grounding processes described by Clark and Brennan and discussed before. The interdependence developed in this way, is theorized to create a holistic system of people, knowledge, and tasks responsible for the performance benefits usually attributed to teams. In this sense, the value of teams is related to an enhanced memory system that supports unique distributed operations.

Experimental research in social psychology and the recently emerging area of ''"team cognition"'' appears to have confirmed the existence of the transactive memory construct (Hollingshead, 1998a, 1998b) and quantified its positive impact on team performance when, for instance, promoted through collective training programs (Moreland, 1999; Moreland & Myaskovsky, 2000). Interestingly, some of this research has documented that group performance decreases with the turnover in group membership but that giving newcomers access to information about the knowledge of other group members (and vice versa) has positive effects.

Research on transactive memory extends the concept of common ground in ways that seem to address some of our observed limitations but, at the same time, does not seem to provide a completely adequate perspective to investigate "how" teams develop and advance their knowledge building over time. On the one hand, its use of grounding as the central mechanism through which transactive memory is established seems to limit its applicability to our context for the reasons discussed before. Furthermore, the interactional mechanisms through which the distributed system of knowledge and memory is achieved as theorized by this line of research are highly underspecified as "communication" processes. In this respect, our goal is to extend our preliminary analyses of data from virtual teams engaged in sustained problem solving to review the adequacy of constructs such as common ground and transactive memory to explain the mechanisms by which joint understanding is achieved in our longitudinal contexts.

:In fact, in the interdisciplinary field of small group research, lead researchers have recently pointed out that new theoretical frameworks are necessary to truly address and understand the complexity of small group interactions (Arrow et al., 2000). Key group processes such as those related to group formation, development, and adaptation have only been superficially understood by the laboratory experiments that had dominated this field. Furthermore, researchers have expressed their concern that the topic of group development has faded away as a result of the preference for laboratory experiments with ad hoc groups that have "no past and no anticipated future" (Arrow et al., 2005). This has resulted in the recent resurgence of studies that pay more attention to temporal analyses and to what Arrow and colleagues call "groups<nowiki>’</nowiki> traces, trajectories and timings." Some of this work which views of groups as complex systems has attracted particular attention in the field of CSCW (Fitzpatrick, 2003; McGrath & Arrow, 1995) and other areas of socio-technical research concerned with the dynamics of knowledge management and organizational learning. We will review more of the relevant work from the field of CSCW later in this section especially as it relates to groupware supports for continuity and knowledge management.

''Progressive problem solving and the theory of knowledge building''

In general, even in CSCL only a handful of studies treat the small group as the unit of analysis while instead treating the collectivity as a context in which individuals interact. Our proposed focus on bridging and its relationship to collaborative learning over time, attempts to contribute to the emergent preoccupation for treating collectivities as holistic units. One unique line of research in CSCL contrasts with the shortage of studies examining the continuous nature of meaning-making mechanisms underlying longitudinal sequences of small-group interactions: the theory of knowledge building. In this theory developed by Carl Bereiter and Marlene Scardamalia (Scardamalia & Bereiter, 1996) (as well as in the computer supports designed to support it), it is argued that successful collective learning results from the intentional engagement in a progressive process of idea refinement and communal discourse as part of a shared enterprise. Progressive problem solving is seen as the identifying characteristic of both individuals becoming experts and also experts working "at the edges of their competence" both strongly situated in a sociocultural setting. Ten years of research in this theory has documented the viability of decentralized, open knowledge building and the development of collective knowledge as well as the necessary pedagogy and technological supports for it to flourish (Scardamalia & Bereiter, 2006). A series of principles have been advanced to characterize successful knowledge building including ''idea diversity, collective responsibility, epistemic agency, ''and ''symmetric knowledge advancement'' (Scardamalia, 2002). Many of these principles operate at the macro or community level and their interactional achievement at the small-group and individual levels is still a matter of research. We see our proposed research as expanding this line of inquiry by illuminating the interactional aspects of how progressive knowledge building is actually achieved by small-groups situated in an online community and, specifically, how bridging of interactional episodes, collectivities, and perspectives contributes to the sustainability of knowledge building.

Research about virtual communities, a field closely related to CSCL, has also advocated a more encompassing approach to investigation of how knowledge is built over time in large online interaction spaces. Unfortunately, most of the online communities investigated are typically based on asynchronous mechanisms of participation (e.g., online forums and discussion boards) and offer views highly anchored by this factor. Despite this limitation, the foundation established by this research is highly relevant to our research interests. For example, Renninger and Shumar (Renninger & Shumar, 2002) in their introduction to the first collection of research on how learning and change can be fostered by online communities, argued that "the connection (that participants develop in) virtual communities is supported by affordances that invoke imagination about and identification with a site, such as autonomy, time, space, choice, opportunity, support, and depth of content. Furthermore, the learning that is undertaken as participants work with a site has an agency and opportunity for changed understanding of self" (Ibid, p. 7). It is our goal to examine through our analysis of virtual teams the similarities with these observations. The authors also state that "the availability of stored resources and information, coupled with the flexibility in the time and space of usage, may well account for the attributions of utopian possibilities for community via the Internet" (Ibid, p. 11). Our interest in the longitudinal interactions of virtual teams and in the ways that designed artifacts can support them is aligned with this observation and will potentially expand it<nowiki>’</nowiki>s applicability to other forms of interaction. Other authors (Stahl, 2004b) also argue that small groups represent the central mediating force between individual learning and community learning, and that "community participation takes place primarily within small group activities. The proposed plan of research offers an opportunity to test this conjecture empirically.

:Another framework commonly used in researching large-scale collaborative learning environments originates form the study of social networks and the theory of social capital. Robert Putnam in particular, distinguishes two type of social capital: ''bonding'' and ''bridging''. Bonding social capital is produced through social networks between homogeneous groups of people, while bridging emerges thanks to the linkages between socially heterogeneous groups (Putnam, 2002). Bridging social capital is theorized to produce the highest benefit for communities, societies, and individuals. The dynamics of "bridging," the type of social capital responsible for ties across dissimilar groups, however, remain vaguely understood. What is that "bridgers" do that generates the theorized benefits for the collectivities? In the particular context of knowledge-building communities, what processes characterize bridging? These unanswered questions require that the mechanisms through which bridging is achieved and their role in the continuity of knowledge-building collectivities be investigated.

''Continuity and Computer-supported Cooperative Work (CSCW) research''

:Research in the field of CSCW has dedicated a significant amount of attention to issues of continuity of collaborative work and the designed environments aimed at supporting it. In fact, CSCW researchers have led the integration of design and investigation goals in their attempts to, both, understand collective action and support it through design artifacts. For instance, in their call to "take CSCW seriously" Schmidt and Bannon (Schmidt & Bannon, 1992) proposed "articulation work" —the coordination of work among team members — to be the central concern of studies of joint work and argued that CSCW needed to go beyond socio-technical studies of work in order to implement design research that is better suited to support group work. In general, the problem of coordination of work has been central to CSCW (Malone & Crowston, 1990; Montoya-Weiss et al., 2001). Coordination can also be seen as the interactional work necessary to overcome the "gaps" that characterize collective activity and which, in some cases, become magnified in computer-based environments(Ishii et al., 1993). Coordination work includes temporal continuity, coordination across team members and also across organizations. As we will see in the next paragraphs, coordination and bridging activity share a lot in common.

Initially, a great deal of CSCW research revolved around decision-support systems and electronic meeting environments (e.g., Nunamaker et al., 1991). Within these environments, it became evident that supporting continuity of interactions was both an opportunity (given the digital recordings available) but also a significant challenge. Diverse approaches to meeting synthesis and summarization emerged, some which attempted to build intermediate semantic representations of the structure and content of the artifacts available as guides for the creation of summaries. Few of these approaches have evolved into mature summarization systems given the complexity of such approach. However, it is interesting to note that these line of research has concluded that providing users with appropriate interfaces for them to manage their own issues of continuity might be a more effective strategy than attempting to create perfect summaries of interactions (Farrell et al., 2001; Waibel et al., 2001). More recently, Greenber and Roseman have argued that using designs based on the room metaphor is an effective way to overcome the numerous "gaps" identified in computer-based joint activity by almost 20 years of CSCW research (2003). In particular, the authors explore how room-based designs with persistent records can ameliorate four different types of gaps: the gap between individual and team work, the gap between synchronous and asynchronous interaction, the social awareness gap, and the gap that needs to be overcome in order to foster a sense of community among teams. Unfortunately, no experimental data is provided to validate these claims. In our case, we expect to provide and empirical analysis of how these boundaries or gaps are actually bridged and how the proposed designs are enacted in naturalistic interactions.

The last ten years of research in CSCW has led to the development of the area of "social computing" or "social systems," largely as a result of a commitment to better understand the realities of social interaction, one of the critical failures of initial CSCW research pointed out by Grudin (1990) and others. A crucial goal of this area of work lies in realization that mutual awareness of the histories and interrelationships among participant in a collectivity is critical to the collective outcome. To support this kind of activity, some researchers have proposed the use of "social proxies" (Erickson et al., 1999) and other strategies aimed at creating "socially translucent" environments. In addition, the design and use of systems that support "persistent conversations" (Erickson & Kellogg, 2001; Smith, 2002) has also emerged as a need to understand these new forms of interaction and their role in organizations and general culture. Persistent records of interactions, an apparent solution to problems of continuity, do not come without consequences and, as several researchers have pointed out, system designs have to go beyond "recording and reporting" (Bodker & Christiansen, 2006) and avoid the naïve view that "everywhere and forever" is always the best alternative (Grudin, 2002). Even in contexts where knowledge work is sustained over time, it is in the analysis of the practices that participants engage in that CSCW has been able to make progress in the understanding of processes such as "knowledge distillation" (M. Ackerman et al., 2003), "organizational memory" or the use of boundary objects (M. S. Ackerman & Halverson., 1999). In general, work in this area is the result of sustained design experimentation and analysis of users<nowiki>’</nowiki> interactions and serves as the basis for the claim that CSCW, and human-computer interaction in general, need to dedicate more attention to understanding the "collaborative user experience." Our proposed work to study bridging in the context of virtual problem solving teams extends this orientation by considering the close relationship between collaboration and knowledge work.

:Similarly, CSCW research has also evolved beyond single-team collaboration systems to consider larger arrangements of collective activity such as those in multiple team configurations, and those supporting larger organizational knowledge management. In fact, the issue of group-to-group collaboration in distributed settings has become extremely important recently. Some researchers, for instance, argue that a "new class of interaction problems" emerge when collective activity is analyzed in these contexts (e.g.,Mark et al., 2003p. 101). This interaction problems all stem from the need to overcome different terminology, perspectives, and work procedures across individual, sub-teams, teams and larger collectivites very much as we have described in our problem formulation. At the moment, it is clear that support mechanisms provided at the ''data level'' (e.g., offering access to records of interactions) or at the ''process level'' (e.g., controlling workflow) might be insufficient or too rigid (Miao & Haake, 1998) unless we understand how bridging activity works. Interestingly, research on group-to-group collaboration has highlighted the importance of studying the "space between" collectivities and understanding the connections, interdependencies and gaps across groups and organizations (Weick & Sutcliffe, 2005), a goal shared with research in organizational science and knowledge management.

Research in knowledge management has also made significant recent contributions to the understanding of the dynamics of sense-making (Carlile, 2002; Thomas et al., 2001; Weick, 1996). For example, the field has recently increased its attention towards studying the development of expertise in organizational contexts and to interdisciplinary teams, boundary objects, and boundary-spanning work (Gasson, 2005; Star, 1989). The unit of analysis that is suggested by the concept of "boundary objects" is of particular interest to our approach. The concept, proposed by Star based on historical case studies of scientific work involving both professional scientists and amateurs (Star, 1989), suggests that the participants: "(1) cooperate without having good models of each other<nowiki>’</nowiki>s work; (2) successfully work together while employing different units of analysis, methods of aggregating data, and different abstractions of data; and (3) cooperate while having different goals, time horizons, and audiences to satisfy." (p. 46). Star suggested that in the activity observed, it was the boundary objects that made cooperation possible. Boundary objects are "objects that are both plastic enough to adapt to local needs and constraints of the several parties employing them, yet robust enough to maintain a common identity across sites while sitting "in the middle of a group of actors with divergent viewpoints." Recent research has highlighted the intrinsically cross-functional nature of boundary objects (Carlile, 2002). From our preliminary analysis of trajectories of knowledge building in Virtual Math Teams, the cross-functional aspect of these interactions does not appear as salient as in other contexts and, yet, we have identified bridging artifacts co-developed within the interaction and used as a part of activity geared towards mediating or bridging contexts. For example, in the last excerpt presented in section II, we noticed how Mathwiz<nowiki>’</nowiki> postin in line 342 ("''it<nowiki>’</nowiki>s like, you can<nowiki>’</nowiki>t walk in water, and the lines are dry lines''") seem to be a resource created to bridge a boundary of viewpoints and understandings and wondered whether the methods and processes of doing this kind of boundary work could characterize effective collaborative interactions. We expect to expand this analysis and pursue the investigation of the processes involved in the creation and use of these types of "bridging" objects in the Virtual Math Teams community. This type of analysis may provide a starting point to answer the question that Star has recently posed about the concept of boundary objects: "How are boundary objects established and maintained? Does the concept scale up? What is the role of the technical infrastructure?" (Bowker & Star, 2002)

Bridging as we have tried to define it can also be seen as related to the longitudinal process of expertise development. Recent research in expertise development states that continued improvements in achievement are not automatic consequences of more experience but that, instead, successful "aspiring" experts seek out particular kinds of experience. This special experiences are characterized as "deliberate" practice and characterized by they types of activities designed, typically by another expert or a mentor, for the sole purpose of effectively improving specific aspects of an individual<nowiki>’</nowiki>s performance (Ericsson et al., 1993). Only these types of activity provide optimal opportunities for performance improvement through cycles of feedback and re-construction of knowledge and skills. The careful study of bridging as an interactional phenomenon may provide an entry into the nature of these cyclical processes at the small-group level. Interestingly, in a recent review of the literature on problem solving, Pertz, Napes and Stenberg (2003) urge researchers to devote more attention to the early phases of the problem solving cycle related to problem formulation. Although considerable empirical research has been conducted on the latter stages of problem solving, the authors point to the little that is known about "what makes a person more likely to engage him or herself in seeking out ill-defined problems and experimenting with various ways of representing them" (p. 27). Interestingly, there is a clear opportunity in investigating these phenomena in group-interactions going beyond theories of individual problem solving and exploring new constructs such as group and team cognition (Salas & Fiore, 2004; Stahl, 2005, 2006a). By studying open-ended tasks in collaborative contexts and attending to the moment-by-moment unfolding of the interaction we hope to inform precisely these areas of problem exploration, problem finding, and problem definition.

''Methodological perspectives in the study of interaction''

Our review of the literature provides not only theoretical guidance and validation for the significance of our research questions but also informs our choice of research method. We will discuss in depth our selected research method in the next section and will restrict our discusion here of a few alternative methods emerging from several different perspectives in the literature. For instance, the methodological framework originated from the field of Computer-mediated discourse (CMD) studies is certainly one that is closely related to the proposed research questions. CMD studies evolved from research in Computer-mediated communication and as such investigate a diverse array of interpersonal communication carried out on the Internet via e-mail, instant messaging systems, mailing lists, newsgroups, web discussion boards, and chat rooms (Herring, 2001). However, although CMD research often encompasses perspectives from the pragmatic, discourse-analytic, and sociolinguistic points of view, it still centers on the study of linguistic artifacts more than language-mediated interactions. In CMD studies the concentration is usually in the collection of linguistic artifacts, the analysis of their representativeness or typicality within a genre, and the processing of such artifacts to derive conclusions about discourse practices (Herring, 2004). In some cases, CSCL studies adopt a methodological orientation similar to that used in CMD studies. Different coding schemes have been developed and used in CSCL in order quantify aspects of observed collaborative processes (e.g., the DISCOUNT coding scheme of Kneser & Ploetzner, 2001; Pilkington & Parker-Jones, 1996). In these schemes, roles (e.g., information seeker, explainer, task performer and reflector), "moves" (e.g., statement, couter-proposal, elaboration, etc.), episodes (e.g., negotiation, explanation, etc.), and other theorized elements are labeled and their quantitative patterns analyzed as a way to understand, and sometimes assess, processes such as externalization of knowledge, elicitation of knowledge, or consensus building. In such cases, regardless of whether the methods are used in CMD or CSCL studies, the linguistic artifacts are seen as representing a message or meaning to be uncover by the analyst, a position which contrasts with the tenants of ethnomethodology (EM) which "is not in the business of interpreting signs. EM is not an interpretive enterprise. Enacted local practices are not texts which symbolize "meanings" or events. They are in detail identical with themselves. The witnessably recurrent details of ordinary everyday practices constitute their own reality. They are studied in their unmediated details not as signed enterprises." (Garfinkel, 2002). Only in a few cases, CMD studies do explore how individuals use linguistic resources to participate in every-day activities mediated by computer networks and adopt an interactional perspective that make them strongly aligned with our methodological choices.

Furthermore, our approach differs significantly from the traditional method of interaction analysis in which a system of codes and categories (e.g., giving information, questioning, harmonizing, dominating, etc.) are used to label and analyze quantitatively the different ways in which teams engage in joint activity (Bales, 1951; Jordan & Henderson, 1995). On the one hand, these categories are centered on what an observer (i.e. the analyst) perceives while we strive to uncover the perspective of the participants and how they orient to the moment-by-moment interaction. In addition, classical interaction and other coding approaches take the linguistic unit as their unit or analysis when assigning a code to a sentence or posting. In our case, our unit of analysis requires that we define activities and networks of activities that can span from a few seconds to a series of interactional episodes.

In summary, diverse research literatures have approached, directly or indirectly, the problem of sustaining continuity in collective knowledge building. However, the constructs and theories explored do not account for the entire range of phenomena that we have characterized as "bridging" and which we have illustrated through he preliminary data analysis provided in section II. Next we elaborate on how some of these concepts will be used to construct our choice of theoretical framework and present the details of our proposed method proposed to investigate the three three research questions outlined.

==Plan of Inquiry==

Having explored the relationship between our research questions and the current state of relevant knowledge, we outline now the particular process of inquiry devised to investigate the phenomena of "bridging" in a particular computer-supported collaborative learning context. Considering that our central aim is to ''characterize the ways in which bridging contributes to the establishment of continuity in the knowledge-building experience of virtual teams in online learning communities'', our means of inquiry are fundamentally descriptive and grounded on naturalistic data resources collected longitudinally. In the following subsections we describe the theoretical framework guiding this plan and the research method selected, including the strategies and time estimates devised for data collection and analysis.

===Conceptual framework:===
We define "bridging" as the interactional work performed by co-participants to establish continuity in a context in which virtual teams collaborate in learning tasks across multiple sessions and where multiple teams might form an online community. One of the central conjectures of our proposed research is that bridging is highly consequential for the nature of the overall knowledge-building experience. We seek to understand how bridging is achieved in interaction and to explore its role for the collaborative learning activities conducted by the teams we propose to study. In an attempt to identify the relationship between bridging and collaborative learning and specify a conceptual framework, we start by characterizing these interactions as strongly determined by the particulars of the participants, the activities that they orient to, and the resources at their disposal; all contextual factors which are made relevant in and through interaction. This foundational position emerges from our preliminary analysis of virtual teams and is also supported by the stance of situated cognition (Engestrom & Middleton, 1998; Suchman, 1987; Winograd & Flores, 1986) , also known as the "''situative''" perspective (Greeno, 2006).

The situative perspective argues that the organization of action is an emergent property of moment-by-moment interactions between actors, and between actors and the environments of their action. Furthermore, it argues that learning and knowledge are distributed across people and artifacts, and because of this, focuses on understanding activity and changes in the activity systems in which knowledge is co-constructed and used jointly. As Greeno has recently argued (2006) the situative approach encompasses other perspectives such as those underlying sociocultural psychology (Rogoff, 1995; Wertsch, 1991), activity theory (Engeström et al., 1999), and distributed cognition (Hutchins, 1995) given their fundamental commitment to analyze performance and transformations of ''activity systems. ''This can also be extended to apply to the recently proposed theory of ''group cognition'' (Stahl, 2006a) in which collaborative group discourse is examined as the central force behind the emergence of group knowledge, as we discussed in section III.

The initial conceptual model of bridging (which we expect to refine through the research proposed), theorizes bridging interactions as mediators of effective, sustained collaborative learning. We expect bridging activity to be closely related to the productive knowledge-building experience of teams. As indicated in Figure 4.1, bridging might occur at many social and temporal levels with the arrows indicating bridging across interactions among individuals, teams and communities and across time .

[[Image:JsarmiDissProposalv10_03.png|framed|none]]

''Figure 4.1 Conceptual model of timelines and trajectories of sustained collaboration''

As individual teams engage in their episodes of knowledge building and collaborative-learning they generate ideas and co-construct resources that can be – and are designed by the participants to be – taken up by the same team, later on, or by other teams as part of a larger collectivity (e.g., an online community). In fact, in these particular contexts where longitudinal work is pervasive, the retrospective and projective relationship of moment-by-moment interactions is expected to signal active engagement with the knowledge work of the team itself and, possibly, its larger context. This process of uptake, the establishment of continuity and relevance that attempts to span across interactional boundaries, is expected to play a significant role in the sustainability of knowledge-building work across individual episodes and across multiple collectivities or teams. The particular dynamics of this bridging activities constitute the object of study of our proposed research and is expected to reveal how past episodes are made relevant as constitutive resources (e.g., contrasting, confirming, expanding present work) which co-participants use in particular ways. In addition, instances of bridging are expected to signal the interdependency between the local small-group unit of analysis and higher units of analysis (e.g., online communities, multi-team collectivities, etc.) as well as between the individual and small-group levels. It is important to note that we restrict our goals to the characterization of bridging and its role in online collaborative learning in settings like VMT.

An important contribution of this dissertation will be the development of a set of theoretical constructs for characterizing the dynamics of bridging and for analyzing bridging mechanisms. This framework builds on core concepts of situated theory, activity theory, distributed cognition and group cognition, but goes beyond them based on detailed analyses of examples in our data. Some phenomena and terms that we anticipate explicating and refining are: ''bridging'', ''bridging artifact'', ''projective bridging'', ''bridging interaction'', ''bridging methods'' and ''interactional continuity''. Central to our conceptual framework is the view that, to understand bridging and its functions, the interactional perspective is essential. In addition to the elements of our conceptual model of bridging, the commitment to bridging as interactional phenomena is central to our theoretical framework. This commitment also guides our choice of naturalistic data and the use of micro-level methodologies as we will explore in subsequent sections.

===Method===

In the following sections we present our choice of research framework and the corresponding data analysis techniques proposed. In addition, we define our proposed unit of analysis and other central elements of these research plan.

====Research Framework: Design-based Research====

As discussed in section III, the research proposed here is situated in the context of the field of Computer-supported Collaborative Learning (CSCL) and, more generally, within the emerging field of the Learning Sciences. Research in the learning sciences attempts to "better understand the cognitive and social processes that result in the most effective learning, and to use this knowledge to redesign classrooms and other learning environments so that people learn more deeply and more effectively" (Sawyer, 2006) . Our research goal is highly rooted in this orientation for we strive to understand "bridging" as interactional phenomena related to knowledge building in online collaborative learning teams, and use our findings to advance the design of interaction supports for the Virtual Math Teams (VMT) online community. Consequently, we have adopted the framework of "design-based research" proposed within the Learning Sciences as the guiding structure of our method and of inquiry.

The concept of Design-Based Research (DBR) was introduced in the early nineties, in writings by learning scientists Ann Brown (Brown, 1992) and Allan Collins (Collins, 1992) who proposed the use of "design experiments" as a strategy to cope with the complexities of investigating how designed artifacts (e.g., curricula, computational tools, etc.) contributed to learning in real-life settings . Design experiments were conceived as a way to extend laboratory experiments, ethnographies, and large-scale studies by providing a framework for formative research which combines incremental design and the progressive development of theory (Cobb et al., 2003; diSessa, 1991). The typical design experiment is defined by Cobb et al. (2003) as "both ''engineering'' particular forms of learning and systematically studying those forms of learning within the context defined by the means of supporting them" (p.9). This iterative combination of applied design and systematic theoretical development is the central characterizing element of design experiments and the motivation behind its current widespread use (Barab & Kirshner, 2001; Design-based Research Collective, 2003; Edelson, 2001). It is precisely because of this iterative synergy between incremental design and systematic theory building that we propose to adopt the framework of design-based research. In our case, we aim to incrementally expand our understanding of specific interactional aspects of learning in online teams and virtual communities and utilize this knowledge to inform the design of computational supports'''.'''

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For our particular purposes, we propose to use '''three cycles of design experimentation.''' These cycles are conceived as a way to iteratively refine our understanding of bridging in the context of the VMT online community but also as a strategy to test the utility of this research framework. Each cycle is comprised of a design experiment in which a particular aspect of the theory in development will be explored in close relation to a design instance of the interaction environment provided. Initially, we proposed a design experiment aimed at characterizing the dynamics of bridging in virtual teams interacting with basic computational supports. Following the results of the first design experiment, we expect to explore the effects of bridging activity and the role of designed artifacts in supporting bridging, through two subsequent experiments. These three design-research cycles, with their theory and design components, are presented in figure 4.2. Next, we outline how to define the data sources and observables that will be studied in each cycle, the units of analysis to be considered, and the actual data analysis methods selected.

[[Image:JsarmiDissProposalv10_07.png|framed|none]]

Figure 4.2. ''Three cycles of design experimentation proposed''

====Participants, Data Sources, and Procedures====

The Virtual Math Teams (VMT) project is structured as an experimental platform and – at the same time – as a real-world application. As part of a funded research project, VMT provides an ideal environment for design-based research. Virtual teams participated in VMT by interacting online and solving mathematical problems in multiple sessions over time. Because all interactions during sessions take place online, logs of these interactions are readily available for analysis. We have access to re-play software that allows us to view and re-view at different speeds any part of the sessions, including all the information that was shared and available to the student participants.

For each one of our three proposed design experiments, teams of students at the middle and high school level who participate in the VMT online community will be the subjects of the proposed research. These students will be recruited through announcements posted on the Math Forum website and will undergo a process of registration in which demographic information will be collected (e.g., age, grade level, attitudes towards mathematics, etc.). The data collected from the online interactions of the teams recruited will always be treated anonymously using only online handles. Data collection procedures are approved by the Drexel<nowiki>’</nowiki>s Institutional Review Board (IRB) under the normal operation of the Math Forum. The analyses conducted as part of this dissertation will be treated as secondary analysis of existing data derived from existing educational services.

{|border="0" cellspacing="2" width="100%"
|Each of the cycles of design experimentation will be defined by the following three elements: The particular'' theoretical focus'' for investigation, ''goals and elements of the design ''being studied, and the ''task settings ''where observations will be collected. Below, we describe each one of these elements for each cycle.|| 

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'''Design Study I: ''''''''Characterizing Bridging'''''

In this initial design experiment, we will investigate the basic characteristics of bridging work by observing participating teams sustain their collaboration in a sequence of problem solving interactions using an online environment with no explicit computational supports for

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|bridging. ''''' '''''Teams will use a new chat room for each one of their interactions and will be given no access to records of their prior work together. The data used for this cycle will represent no less than 3 teams interacting in a sequence no shorter than 4 collaborative sessions. This study will use data from sessions conducted in May 2005 (such as the pilot data in section II). We estimate the analysis of the data collected in this phase to be completed in 3 months. Towards the end of the analysis phase, re-designs for the environment will be proposed which are expected to be implemented in a basic way to allow experimentation in subsequent phases.|| ''Theory Goal:'' The dynamics of bridging in sustained problem solving. ''Participants:'' 3 online teams of 3-5 students ''Duration:'' 4 1-hour online sessions ''Task: ''Open-ended mathematical task with problem formulation and problem solving prompts. ''Environment: ''Basic chat and shared whiteboard virtual room 

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'''Design Study II: ''''''''Defining Interactional Effects of Bridging'''''

The second design experiment will be focused on expanding the characterizations made in phase I in order to further investigate the structure of bridging interactions and explore the interactional effects of the bridging activity observed. The particular theoretical

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|focus will be further defined after the first cycle has been completed but we expect it to be closely related to the establishment of the relationship between bridging activity and the nature of collaborative knowledge building over time. In addition, this cycle will also investigate specific design features of a new collaborative environment which will offer basic supports for explicit aspect of bridging work such as continuity of group composition, persistence of rooms across sessions, feedback between sessions stressing continuity and other supports. Participating teams will use this redesigned online environment to engage in a similar sequence of collaborative episodes as in the first cycle. This study will use data from session conducted in May 2006. || ''Theory Goal:'' The effects of bridging in knowledge building over time. ''Participants:'' 3 online teams of 3-5 students ''Duration:'' 4 1-hour online sessions ''Task: ''Open-ended mathematical task with problem formulation and problem solving prompts. ''Environment: ''Persistent chat and shared whiteboard virtual room with basic supports for cross-team bridging (e.g. Wiki environment) 

|}

'''Design Study III: ''''''''Scaling Up Bridging Supports'''''

The final design experiment will be focused on exploring the relationship between computational supports for bridging and sustained collaborative learning. In addition, we expect this phase to serve as a test of the robustness and scalability of concepts produced in

{|border="2" cellspacing="0" cellpadding="4" width="100%"
|the two previous experimentation phases. Participating teams will use a final redesign of the online collaboration environment implementing explicit supports for continuity based on the findings from the first two studies. Similar teams to those used in the previous two studies will engage in a comparable task spread over a longer sequence of collaborative episodes. We expect this final cycle of experimentation to produce the necessary data to integrate all findings from the two previous cycles into a final characterization of the relationship between bridging activity, knowledge building over time, and the role of computer supports.|| ''Theory Goal:'' The relationship between computational supports and bridging activity. ''Participants:'' 3 online teams of 3-5 students ''Duration:'' 4-6 1-hour online sessions ''Task: ''Open-ended mathematical task with problem formulation and problem solving prompts. ''Environment: ''Persistent chat and shared whiteboard virtual room with explicit bridging supports

|}

[[Image:JsarmiDissProposalv10_05_1024.png|framed|none]]

Figure 4.3. Anticipated ''Participation Structures in each Experimentation Cycle''

In summary, we will select records of teams who have engaged in a sequence of online collaborative sessions related to a particular problem solving task using a version of the online environment to be tested in each one of the three cycles of experimentation outlined in the previous section. A minimum of three teams will be selected for each cycle which will have a total duration no shorter than 4 online sessions (see Figure 4.3). Each cycle will require teams to engage in small-group, synchronous math problem solving sessions as well as in asynchronous community activities when deemed necessary for the purpose of the study. The researcher will adjust the parameters of the online environment, determine the task for each session, assign individuals to teams, and adjust the duration of the sessions as necessary. Time-stamped transcripts and recordings of the synchronous sessions, traces of any asynchronous participation, demographic and attitudinal data as well as general system usage data will be collected over time and used as part of the data sources to approach the investigation proposed. '''A total of 36 data sessions''' (9 team sequences with an average duration of 4 sessions) will be analyzed for this study. Next we describe our unit of analysis and how particular elements of these data sources will be identified as relevant for the research questions proposed.

====Units of Analysis and Observable Phenomena====

The framework of design-based research (DBR) is strongly rooted in the theoretical framework outlined before; especially as it relates to the perspective that learning, cognition, knowing, tools, media and context are irreducibly co-constituted and cannot be treated as isolated entities or processes (Greeno, 2006; Stahl, 2006a). For this reason, we attempt to analyze the performance and transformations over time of '''''activity systems''' ''consisting of situated arrangements of co-participants interacting with a variety of technological artifacts. Rather than concentrating on the individuals, their characteristics, abilities and thoughts, we look at situated teams, their resources, interactions (within the team and between teams) and continuities. We will focus on an activity system as the '''''unit of analysis'''.'' Given the complexity characteristic of activity systems, it is necessary that we define more precisely the elements of an activity system that would be observed and investigated, articulate the ways in which we expect them to be related to the phenomena of bridging, and outline the mechanisms that can be used to detect and define changes in activity systems that might be relevant to bridging.

The data excerpts that were used to frame our choice of problem and research questions in section II can also assist us in defining our orientation towards observing bridging in the data that will be collected. These excerpts were extracted from recordings of the chat interactions of virtual teams participating in a pilot program of the VMT online community. In our presentation, we acknowledged that the textual transcripts offered did not fully capture the situated dynamics of the team working on the math task and using the chat and shared whiteboard available. However, they provided us an entry point into the activity system by making available the moment-by-moment discourse of the group. Based on these resources, we are able to identify verbal and interactional "markers" that signal the presence of relevant bridging work. Furthermore, based on the fact that the experimental situation was structured as a sequence of four collaborative learning sessions in which virtual teams attempted to sustain their problem solving work, we also identified the gaps in between sessions as potential "triggers" for bridging work. Changes in the membership of the team also provided for displays of bridging activity. These situational elements, the moment-by-moment interaction of the participants and the larger institutional framework that surrounds them, are key elements of the activity system being observed by virtue of their ability to trigger the phenomena of our interest. In summary, we identify the relevant elements of the activity system being observed based on their observable influence in the local interaction being studied.

In order to identify and select '''instances of bridging''' activity, we will use the structural elements defined from the first cycle of experimentation (as presented in the pilot analysis in section II). At the moment, three defining elements have been identified as regularities when bridging appears in the interactions observed: First, the presence of "boundary" markers that identify discontinuities (e.g., those generated by the suspension and recommencement of activity, by interactions across multiple collectivities, etc.); second, visible changes in the participants<nowiki>’</nowiki> orientation toward each other (e.g., alignment towards participation frameworks such as narrator-audience or un-ratified vs. ratified listener, etc.); and finally, changes in epistemological orientation (i.e. the display of what can be claimed as known or as suitable to be known by an individual or a collectivity). These characteristics of bridging, although based on the preliminary analysis of pilot data and subject to possible revision, will be used in the first phase of analysis to identify instances of bridging and characterize them.

For instance, in the case of the first excerpt presented in section II, the presence of a temporal deictic terms such as "''now" ''and "''last time"'' triggered our initial recognition of this segment as an attempt to establish continuity from previous problem solving work. From this marker on, we followed the unfolding of the interaction with its different actors and their participation as a holistic unit. We also traced some of our observations back to prior interactions as a way to investigate how they were being reconstituted in the present. At times, we used additional contextual information such as the number of chat sessions that some team members had attended in the past in order to guide our analysis. In addition to the chat transcript we used snapshots from the shared whiteboard to trace the origin and uptake of certain graphical artifacts used by the team as knowledge resources. These resources and interactions are material evidence of the methods, strategies and routines that the participants used to accomplish the tasks that they were orienting to, that is of the situated activity system. Based on this evidence, we propose to both, iterative construct a descriptive theory of bridging in online collaborative learning contexts as well as advance candidate design patterns for supporting bridging. As we will elaborate in the next section, our characterization of what counts as observables is closely related to our choice of method of analysis. Rather than defining bridging as an analytical concept, we will ground its characterization in the demonstrable instances recorded in the data that will be collected and investigate how participants do the types of activities that we have characterized under the concept of bridging work.

====Data Analysis Method: Chat Interaction Analysis====
The activity system is a flexible unit of analysis, which allows us to focus our attention simultaneously in different directions and apply different lenses when pursuing our questions of interest. When investigating the role of bridging in sustained collaborative learning we will pay special attention to the members<nowiki>’</nowiki> methods and the ''appropriation'' of tools and practices of the collectivities (Wertsch, 1998). To do so, we will investigate patterns of interaction in three trajectories of interaction: The situated interaction of the team members, the emergent properties that might come into view at the group and community levels and the ways that the individuals participating in the team might use to re-construct such outcomes (Greeno, 2006). The particular method that will be used to analyze the data collected is derived from interaction and conversation analysis and strongly rooted in the ethnomethodological tradition (Garfinkel, 1967; Heritage, 1984; Livingston, 1986). Ethnomethodology is a phenomenological approach to qualitative sociology which attempts to describe the methods that members of a culture use to accomplish what they do, such as carrying on conversations(Sacks et al., 1974), using information systems (Button, 1993; Button & Dourish, 1996; Suchman, 1987) or doing mathematics (Livingston, 1986). As part of the phenomenological perspective, ethnomethodology is based on naturalistic inquiry to "inductively and holistically understand human experience in context-specific settings" (Patton, 1990). As a result, ethnomethodolog encourages the study of phenomena within its natural setting, insisting that "the research interaction should take place with the entity-in-context for fullest understanding" (Lincoln & Guba, 1985). It also promotes an inductive approach to data analysis as a way to iteratively build characterizations of interactions and explicate the realities and experiences of the participants.

In ethnomethodology, particular attention is given to the ways that the participants demonstrably orient to the interaction moment-by-moment. At each moment of the interaction we, as analysts and competent members of the culture of the participants being observed, attempt to answer the question: "''why this now here?''" We inquire about how the textual postings and other actions in the online environment demonstrate to the participants the methods used to accomplish the tasks being carried out. Members<nowiki>’</nowiki> methods are seen as the ways that people produce social order and make sense of their shared world. For instance, conversation analysis, a particular branch of ethnomethodology, has shown that there are well-defined procedures that people use to take turns at talk (Sacks et al., 1974), to conduct telephone conversations (Schegloff, 1979) and to recommence meetings (Atkinson et al., 1978). Applying the approach of ethnomethodology to the analysis of our team interactions means that we need to define procedures to analyze the textual messages and other actions observable in the online environment when teams are engaged bridging work and explore the relationship of such activities with their overall collaborative learning work. Using this approach, we will identify through the data the relevancy of the types of phenomena that we have labeled as "bridging work," validate the proposed structural elements related to bridging, and investigate the members<nowiki>’</nowiki> methods utilized to deal with instances of bridging as well as their interactional effects.

Considering that we have chosen the activity system as our unit of analysis, it seems necessary to comment on how our method relates to the field of Cultural-Historical Activity Theory (CHAT). We argue that ethnomethodology and Activity Theory are highly compatible frameworks but that the enthonmethodological orientation provides a more concrete set of guidelines for how to explore the data captured from observing specific activity systems. Activity theory does not preclude other approaches and does not reject the usefulness of other conceptual schemes since no conceptual tool, no matter how powerful it is, can serve all needs and help solve all problems<nowiki>’</nowiki> (Kaptelinin, 1996). To conduct these investigations we propose to use ''data sessions'' (Jordan & Henderson, 1995) as a way to iterative refine our analysis of the interactional data collected. Data sessions assemble a number of researchers who review and discuss excerpts from the data available and collaboratively discuss, as competent members of the culture, possible interpretations of the activity being studies. Researchers try to make sense of the data as participants, since they have access to the same resources as the participants did and can understand them in similar ways. By encouraging analysts to work collaboratively, data sessions can minimize the idiosyncratic analyses. These data sessions will be conducted as part of the regular research activities of the Virtual Math Teams project at the Math Forum. Once instances of bridging work have been identified and their structural characteristics have been analyzed, further comparative work will be conducted as a way to expand the components of a theory of the role of bridging in online collaborative learning. This method of analysis complements the iterative framework provided by design-based research by providing an analytical focus to the overall project of theory building and system design.

An additional advantage of ethnomethodology-oriented approaches lies on its strong compatibility with the process of interaction design and research of the users<nowiki>’</nowiki> experience. Norman and many other HCI researchers have argued that the skills necessary to effectively observe potential users in their normal settings and determine real user needs is most likely to come from anthropology and sociology, "where the skills of careful, systematic observation are taught" (Norman, 1998). Coincidentally, ethnomethodology advocates "an intense, and at the same time respectful, intellectual interest in the details of the actual practices of people in interaction" (ten Have, 1999) as a way to produce characterizations of actions, and propose methods for those actions as well as describe the sequential and interactional features of those methods (Pomerantz & Fehr, 1991). These characterizations are extremely valuable as guidelines for design and have been effectively used in the design of information systems (Crabtree et al., 2000; Woodruff et al., 2002). We expect that using a method of analysis that is closely related to the actual practices of participants both aspects of our research goals, theoretical development and design, will be supported.

Although design-based research is a powerful tool for investigating learning in real-life settings, serious challenges arise from the intrinsic complexity of such settings. One commonly acknowledged weakness of the method is that large amounts of data emerging from the investigation pose a serious management and analytical demand on researchers (Barab, 2006). In our case, we have purposively tried to delimit the object of our investigation in a way that will allow the researcher to manage this risk. Although large amounts of data will emerge from the three design studies, by selecting the recordings of the interactions as the primary data source and concentrating on the activity system as a unit, we expect to generate a manageable set of instances of bridging which will be sufficient to advance the corresponding theory. We will select a relatively small set of examples that illustrate important bridging phenomena. We will select these excerpts or sequences of excerpts to detailed analysis in order to understand what takes place in them and to help us characterize specific cases of bridging phenomena as they actually occurred in the VMT real-world application.

Another challenge related to design-based research that applies to our study is related to the difficulties in establishing comparisons and generalizing across contexts. In our case, we will be comparing different teams using the same set of tools and performing similar activities within each design study, and possibly, comparing such results with different subjects, tools, and tasks in subsequent studies. However, underlying all of these contexts, we will always have the common structure of online, mathematical collaborative-learning interactions. We are confident that this overarching setting will provide enough of a unifying structure for all cases to be comparable within reasonable measures. We will not claim to extend generalizations to other contexts, for instance virtual teams in organizations or general online communities of interest. This dissertation is not intended to produce replicable quantitative findings or statistical models, but to explore and refine concepts of bridging in settings like the VMT service. It is a descriptive and analytic study.

===Research Timeline===

To finalize our research plan, we present an estimated duration of each phase of design experimentation described earlier. As stated, the sequence of experimentation cycles has been structured with an experimental phase followed by an analysis phase aimed are refining the characterization of bridging and its effects while also informing aspects of the designed environment to be used in each subsequent cycle. Design study I will use data from sessions conducted in May 2005 (such as the pilot data presented in section II). We estimate the analysis of the data collected in this phase to be completed in 3 months. Design study will use data from sessions conducted in May 2006. The analysis of these data is scheduled to be of similar length as in study I (a total of 3 to 4 months). The experimental phase of design study III is expected to last between 4 and 5 weeks and will be conducted during the spring of 2007. The final summative analysis which includes the results from this final phase as well as the lessons learned from the three cycles of design experiments is estimated to take between 4 and 5 months.

The following table summarizes the structure of these three design-based research cycles, their goals and time estimates:

[[Image:JsarmiDissProposalv10_04_1024.png|framed|none]]

Table 4.1 ''Proposed design experiments and timeline''

==Significance==

Based on our review of the literature and the preliminary analysis of our pilot data we propose that bridging —the purposeful crossing of interactional boundaries— is a consequential and often unsupported aspect of the collaborative user experience of virtual teams and online communities. The ultimate goal of the research plan presented in the preceding sections is that of increasing our understanding of how virtual teams establish and sustain continuity of their knowledge-building work. By doing so, we also intend to advance the knowledge necessary for the design of effective online collaboration environments. The completion of the research plan presented here will generate critical foundational knowledge for the understanding of bridging as an interactional phenomenon and will ascertain its role in the establishment of continuity of collaborative knowledge building.

Given the fact that our proposed work is highly localized within the context of the Virtual Math Teams project at the Math Forum online community, this endeavor has great significance for the participants and members of this innovative online entity. The products of the research work outlined in this proposal will empower the Math Forum to continue to provide richer mechanisms for community participation to its members and to support the complex and diverse knowledge-building work that has characterized it since its inception. In addition, the further development and evaluation of the analytical methods proposed for the study of bridging in team-based online problem solving will be a very valuable outcome to other researchers interested in similar contexts and research questions. In particular, the use of the design-based research framework in combination with the method of chat/interaction analysis will test the theoretical and practical value for studies such as those conducted in areas such as computer-supported collaborative learning, social informatics, information science, and the study of learning and social practices in online environments.

Because continuity in itself is important to the success of many collectivities involved with knowledge work and in particular those related to distributed virtual teams and online communities, the knowledge developed through this research will significantly contribute to emergent theories and designs for collaborative knowledge building in fields such as social computing, computer-supported collaborative learning, and information science and technology in general. By understanding the structural significance of "bridging," researchers in these fields will be better able to understand how members of online collectivities recognize, constitute, and use the boundaries emerging from their interactions (e.g., those related to multiple online sessions, sub-collectivities, and knowledge-perspectives). In addition, designers of online environments will be in a better position to support bridging activities through particular "bridging supports" and to produce environments that take into account this very consequential phenomenon. In this way, collaboration environments will be in a better position to realize the potential of new forms of collective interaction to generate and advance learning and knowledge in organizations, communities of interest, academic disciplines, societies, and many other types of collectivity.

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----

<references/>

Dataset1/D1T5S2n

Jsarmi — Tue, 14 Aug 2007 18:36:49 GMT

Jsarmi:

=We just came up with some questions / about the points - what are the points?=

188 ModeratorJ: The questiosn on the Whiteboard were generated by different teams on Tuesday
189 gdog: k
190 ModeratorJ: Did you participate on tuesday, gdog?
191 gdog: no
192 gdog: just started today
193 ModeratorJ: o.k. dragon and estrckmcnizzle can fill you in
194 dragon: ok
195 dragon: so
196 dragon: basically, we worked on a problem
197 gdog: ok
198 dragon: where we were given two points, A and B
199 dragon: and
200 gdog: k
201 ModeratorJ: Oops... be careful with the whiteboard... this is a shared whiteboar so all you did affect everyone
202 dragon: you could not go diagonally on the grid, but only on the grid
203 dragon: such as
204 dragon: up or down, left or right
205 dragon: and
206 dragon: then we just came up with some questions
207 dragon: about the points
208 gdog: what are the points?
209 dragon: I don't remember
210 mathwhiz344: so if this were point a
211 gdog: k
212 dragon: but they were pretty random
213 gdog: ok
214 mathwhiz344: anyway, nvermind, i got it
215 dragon: ok
216 gdog: so what questions are you guys on?
217 dragon: dunno
218 ModeratorJ: So, now you can identify questions that interest you from, for example some of the ideas
from that list of questions generated by all the teams, or you can create new questions.
Then you can go on to answer the ones that you are most interested in. (To 216)
219 gdog: ok
220 dragon: do you know hwere the points are locatied? (To 218)
221 mathwhiz344: i can't think of any, but numb er 6 looks interesting
222 dragon: number 7
223 mathwhiz344: so which one should we do?

=Too complicated/difficult, drop it=

223 mathwhiz344: so which one should we do?
224 dragon: I don't know, anything that interests us I guess
225 gdog: #6 is interesting to me
226 dragon: problem is
227 dragon: there really isn't an answer to number 6 though
228 weisbari: joins the room
229 mathwhiz344: yeha
230 gdog: that's why it's interesting
231 dragon: it depends who is giving the problem
232 mathwhiz344: the grid probably extends for ever,
233 mathwhiz344: but if it's a curved space, it might meet
234 gdog: assuming if it doesn't..........
235 dragon: that would make things too complicated
236 dragon: I guess
237 gdog: y?
238 dragon: but it could work maybe
239 mathwhiz344: what if we asssumed the grid is a universe...
240 mathwhiz344: i guess your right
241 gdog: ok
242 gdog: i understand
243 dragon: well, first of all, the paper would crumple (if it were real) to form a sphere [To 237]
244 mathwhiz344: why a sphere?
245 gdog: ?
246 dragon: I mean, if it were "curved" as you said before [To 244]
247 dragon: like
248 mathwhiz344: oh
249 dragon: it would curve to itself
250 mathwhiz344: yeah
251 dragon: and then it would have to get smaller in some areas to fit
252 dragon: nvm
253 dragon:
254 estrickmcnizzle: im drinking 7 up
255 dragon: this is getting way too complicated, xp
256 gdog: dragons right [To 249]
257 gdog: we should probably solve another problem
258 dragon: so, do you guys think any other questions would be good to answer?
259 mathwhiz344: yeah:0
260 gdog: and drop that question
261 dragon: I like 7
262 mathwhiz344: 7's good
263 gdog: ok, we can try 7
264 estrickmcnizzle: so is 7 up
265 dragon: alright
266 dragon: lol
267 gdog: lol
268 mathwhiz344: :)
269 dragon: so anyway, lets create some imaginary points or something

Dataset1/D1Mods

Jsarmi — Mon, 13 Aug 2007 20:13:28 GMT

Jsarmi: /* Session I */

Moderators role.

=Session I=
Presented the basic "task situation" to the team, encourage them to generate questions and explore the ones that interested them. Framing postings included:

Moderator: After each session we can share your ideas with other groups and you can learn from them and compare if you want.
But it's not a contest. Each group will be different. For now we are calling you group #, but at some point,
if you want, you can pick a name for your group.

Moderator: So, to get started with the math, we will describe a situation to you and you will then explore it,
make up questions about it, discuss them as a group and try to answer the ones that you find
the most interesting. o.k.?

=Session II=
Presented a set of questions on the whiteboard, introduced to the teams with these messages:

ModeratorX: As we said before, after each session we can share your ideas with other groups
and you can learn from them and compare if you want. But it's not a contest. Each group is different.
ModeratorX: So, last Tuesday, all groups generated a number of questions about the world that we had
and we collected some of them for you to consider today. I am going to paste then on the whiteboard
for you to look at

Questions:
1. What is the shortest path along the grid between the two points?
2. How many possible routes are there from point A to point B?
3. What is the maximum distance from point A to B if you can only travel on each POINT once?
4. How many ways are there to get from A to B in rectangle ABCD?
5. Make a right triangle with AB as the hypotenuse. What is the area of the circumscribed circle?
6. Can you go off the edge and come back somewhere else?

Questions that your work made the moderators think of:
7. What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)?
8. How many shortest paths are there from A to B and how does this vary with changes in the positioning of A relative to B?
9. Suppose the right and left edges of the grid are connected. How does that change the distances between points?

=Session III=

Via chat:

Today, we will share some questions and observations from other mathematicians who have been looking
at the questions and solutions you have been inventing and pursuing.

During the first two sessions of this program the groups have at times explored a math where points
only exist at the intersections of a grid (this one is 12 lines by 12 lines), evenly spaced one unit
apart as in the image on the whiteboard. There are no "diagonal" lines, at least not in the way
we usually think of them.

Distance between any two points in this grid world is defined as the length of the shortest path
along the grid lines connecting the points. Several groups showed there may be several shortest paths,
but the distance is well-defined. This is a system of math that you are inventing,
just as the Greeks invented geometry.

Did anyone think of any other questions after the last session?

...

Here are some questions that come up when looking at your work. You don't need to pay any attention to these
if you don't want to. Again, your goal is to identify or invent new math questions that are interesting to you
and pursue them.

On the whiteboard:

1. What is a mathematical formula for the distance between any two points on the grid?
Call the points “A” at some grid coordinate (x1, y1) and “B” at (x2, y2).

2. How many shortest paths are there along the grid between pairs of points?
Is a general formula?

3. Suppose that the left and right edges of the grid are connected, so there is 0 distance between them.
For instance, the distance between (0, 5) and (11, 5) = 0. (One could say that those two sets of coordinates
are two different names for the same point.) Now what is the distance along the grid between points?
How many shortest paths are there?

4. Suppose that all the edges of the grid are connected, so there is 0 distance between them.
For instance, the distance between (1, 5) and (7, 10) = 2. (One could say that all the edge coordinates
are different names for a single point.) Now what is the distance along the connected grid between points?
How many shortest paths are there?

=Session IV=

Group Creativity

Jsarmi — Mon, 30 Jul 2007 20:46:49 GMT

Jsarmi: /* Reference */

==Chapter 9. Newcomer Innovation in Work Teams==

Collaborative work is an increasingly important aspect of organizational life. Many
organizations now assign their most critical tasks to small groups, particularly work
teams (Hackman, 1990; Sundstrom, 1999). This is not surprising, because there
are several reasons to believe that teams should be more effective than individual
workers. Not only do most teams possess more task-relevant skills and knowledge
than do individuals, but team members can also share these resources, redistribute
responsibilities to meet new task demands, and motivate one another
to work hard. Unfortunately, however, there is evidence that teams do not always
provide the benefits they promise. Research in laboratory settings shows that teams
often fail to realize their potential productivity because of coordination and motivation
problems (Steiner, 1972). And research in organizational settings suggests
that team effectiveness is often reduced by such managerial mistakes as using
teams for tasks that are better done by individuals, assuming team members possess
all the skills they need to work together, and failing to provide adequate organizational
support for team activities (Hackman, 1998).

===Personnel Turnover===
One of the most daunting challenges for teams is personnel turnover, defined as the entry of new members and/ or the exit of old members.

Research on turnover has been done in both organizations and small
groups. In reviewing the organizational literature, Argote (1993, 1999) concluded
that the effects of turnover are mixed and depend on such factors as
the organization?s coordination requirements, the level of organizational structure,
and the individual?s skill level. Research on turnover in small groups
indicates that turnover typically disrupts group performance but is more deleterious
under some conditions than others. For example, group performance
does not vary with the mean rate of turnover but declines when turnover is
greater than usual (Trow, 1960). In addition, turnover causes fewer problems
when group members work independently rather than interactively (Naylor
& Briggs, 1965), and when the group has high rather than low structure (Devadas
& Argote, 1995).
Although these and other studies (e. g., Hollenbeck et al., 1995) provide
useful information about the impact of turnover, they only scratch the surface
of a very complex phenomenon. In particular, they pay little attention to the
possibility that turnover can have positive rather than negative consequences
for group performance. Turnover can improve group performance through two
mechanisms: the exit of oldtimers who lack the skills or motivation to help the
group attain its goals, and the entry of newcomers who possess such skills or
motivation. In this chapter, we focus on the latter mechanism.

==Reference==
Paulus, Paul B.(Editor). Group Creativity : Innovation through Collaboration.
Cary, NC, USA: Oxford University Press, Incorporated, 2003. p 203.
http://site.ebrary.com/lib/drexel/Doc?id=10085239&ppg=218

Copyright © 2003. Oxford University Press, Incorporated. All rights reserved.

LitReview

Jsarmi — Mon, 30 Jul 2007 20:45:41 GMT

Jsarmi:

: Paulus, Paul B.(Editor). [[Group_Creativity]] : Innovation through Collaboration. Cary, NC, USA: Oxford University Press, Incorporated, 2003. p 202. http://site.ebrary.com/lib/drexel/Doc?id=10085239&ppg=217 Copyright © 2003. Oxford University Press, Incorporated. All rights reserved.

Publications

Jsarmi — Thu, 26 Jul 2007 20:47:03 GMT

Jsarmi:

:EARLI paper at simposium
:Paper presented at the VMT Workshop, CSCL 2007
:Paper presented at Doctoral Consortium, CSCL 2007
:Creativity and Cognition 2007
:Paper presented at the Graduate Sympossium, CC2007
:Stefan's publications
:CP chapter (in press)
:HICSS workshop on Persistent Conversation

Reviews for
:ijCSCL
:HICCs, Persistent Conversation minitrack, Knowledge Management and Dcog
:Brazilian Journal
:CHI

CSCL07 Doctoral Consortium

Jsarmi — Tue, 17 Jul 2007 13:50:09 GMT

Jsarmi: /* Effects of Knowledge Awareness (Sukji Kwon) */

==Panel 1: Awareness Tools for Collaborative Learning: Three Design Studies==

===Knowledge Mirroring (Jessica Dehler vgk.de)===
:Representation of one's own knowledge and that of your partners
:Self-assessment: QUALITY of your understanding (did I understand X correctly)
:Knowledge Awareness -> Helps a peer tutor assess "usefulness" (what to ask, what to explain)
:IS "REPRESENTATION OF HIS KNOWLEDGE" TOO STRONG A TERM?
:BUT WHAT IS THE NATURE of an ASSESSMENT? IS it obscured with a rating? e.g failure of learners models on mistakes!

===Effects of Knowledge Awareness (Sukji Kwon)===
:Awareness in CSCW: an understanding of the activities of others (Dourish & Bellotti, 1992)
:Knowledge Structure Awareness -> An understanding of the constituent part of key concept and relations between parts OF OTHERS

===Effects of Awareness of Group Memebers' Rationales (Lu Xiao)===
:Dewey: Reflective thought as "active, persistent, and careful consideration of any belief or supposed form of knowledge... it is a consciouls and voluntary effort to establish belief upon a firm basis of reasos" (1970)
:Van Manen: Technical, Practical and Critical reflection

Dataset1/D1T5S4n

Jsarmi — Tue, 29 May 2007 15:25:00 GMT

Jsarmi:

== Collective Remembering ==
This instance is fully analyzed [[Dataset1/Collective_Remembering |here]].

== I suggested this yesterday ==

218 estrick, 20:50: we arent getting anything done
219 meets, 20:50: any suggestion?
220 estrick, 20:51: i dont know, maybe just a more simple problem
221 estrick, 20:52: less time consuming
222 gdog, 20:52 (20.05): drop the questoin
223 drago, 20:51: I think I know the answer...
224 gdog, 20:52 (20.05): more simpel one that i can understnad plz :)
225 meets, 20:52: ask the mod to put up the questions
226 meets, 20:52: or we can do the summer one
227 meets, 20:52: wat is it @: Message 223: To whole message
228 drago, 20:52: not quite sure... @: Message 227: To whole message
229 MFmod, 20:52: what would you like?
230 gdog, 20:53 (20.05): lol
231 drago, 20:52: but it is a series of multiplication
232 gdog, 20:53 (20.05): i was watchin gu guys do the work
233 gdog, 20:53 (20.05): seems like u got smthign but not enough
234 drago, 20:52: like
235 drago, 20:52: from ADP
236 drago, 20:52: you go from a to d to p
237 drago, 20:52: and there is only one way
238 drago, 20:53: but from A to C
239 drago, 20:53: then you can go G
240 drago, 20:53: which has one way
241 drago, 20:53: or you can go k
242 meets, 20:53: permutation?
243 drago, 20:53: which has one way
244 drago, 20:53: or you can go op
245 drago, 20:53: yea...
246 meets, 20:53: i suggested that last time
247 drago, 20:53: but
248 drago, 20:53: I can't find the equation
249 drago, 20:53: let me work it out on paper
250 drago, 20:54: I'll be gone for a sec
251 meets, 20:54: okay @: Message 250: To whole message
252 meets, 20:54: meanwhilel.......
253 meets, 20:54: we do a different problem?

Dataset1/D1T1S5n

Jsarmi — Tue, 29 May 2007 15:13:37 GMT

Jsarmi:

Dataset1/Its a Permutation

Jsarmi — Tue, 29 May 2007 13:17:58 GMT

Jsarmi: /* Session 3 – Team 1 */

== Session 2 - Team 1 ==

284 rweis, 20:48 : so lets get to it
285 meets, 20:48 : okay
286 meets, 20:48 : so..
287 meets, 20:48 : without goign backwards right?
288 rweis, 20:49 : yes
289 meets, 20:49 : okay
290 meets, 20:49 : thats one
291 meets, 20:50 : plus the reflection where line AB is the reflectign line
292 meets, 20:50 : imma make the line AB a different color
293 rweis, 20:50 : It is not efficient to just sit there and count
294 meets, 20:50 : true
295 meets, 20:50 : well...
296 meets, 20:51 : we can try to find a patterN?
297 rweis, 20:51 : so do u have a formula
298 rweis, 20:51 : yes
299 meets, 20:51 : not distances
300 rweis, 20:51 : ok
301 meets, 20:51 : im not good at this stuff sorry
302 rweis, 20:51 : Nether am I
303 meets, 20:52 : i have an organized way of counting
304 meets, 20:52 : but that's not going ot get anywhre FAST
305 rweis, 20:52 : ok
306 meets, 20:52 : oh wait nevermind
307 meets, 20:52 : darn it
308 rweis, 20:52 : ok
309 meets, 20:52 : actually
310 meets, 20:52 : i do have anorganized way
311 meets, 20:52 : ignore the top half
312 rweis, 20:53 : great lets see it!!!
313 meets, 20:53 : cuz we're going to x2 our results on the bottom half
314 rweis, 20:53 : yes we will
315 meets, 20:53 : k so i drew the first line right?
316 rweis, 20:53 : right
317 meets, 20:53 : then, we can have 5 more paths of the same pattern
318 rweis, 20:53 : ok
319 meets, 20:53 : etc.
320 meets, 20:53 : and then...
321 meets, 20:54 : oh
322 rweis, 20:54 : what
323 meets, 20:54 : i have an algebraic way to od this
324 meets, 20:54 : i just thought of it right now
325 meets, 20:54 : each "step"
326 rweis, 20:54 : YAAAAY algebra
327 meets, 20:54 : has a max of 3 places to travel
328* meets, 20:54 : '''this is like a permutation'''
329 rweis, 20:55 : Were are just going over this in class
330 meets, 20:55 : lol
331 rweis, 20:55 : lol
332 meets, 20:55 : lemme delete these lines
333 rweis, 20:55 : ok
334 meets, 20:55 : okay
335 meets, 20:55 : so...
336 meets, 20:55 : lemme use green
337 rweis, 20:56 : ole
338 meets, 20:56 : there are 3 possibilites for the first step
339 rweis, 20:56 : yes
340 meets, 20:56 : now...
341 meets, 20:56 : i dunt really know how to do this
342 meets, 20:56 : but
343 meets, 20:56 : we either have 3 ways
344 meets, 20:56 : over here...
345 meets, 20:57 : or just 2
346 rweis, 20:57 : then there are three more ways to do that
347 rweis, 20:57 : no there are just there
348 meets, 20:57 : we can sorta branch it off
349 rweis, 20:57 : three
350 rweis, 20:57 : yup
351 meets, 20:57 : no
352 meets, 20:57 : because
353 meets, 20:57 : if you go UP
354 meets, 20:57 : then there's only 2 ways
355 meets, 20:57 : i think we can branch this off
356 meets, 20:58 : go to the rig ht of the grid
357 meets, 20:58 : under the questions
358 meets, 20:58 : we can both branch off together
359 meets, 20:58 : starting from
360 rweis, 20:58 : ok
361 meets, 20:58 : 3 represents
362 meets, 20:59 : 3 ways for the first move
363 meets, 20:59 : oh... this is gonna get really messy
364 rweis, 20:59 : right
365 meets, 20:59 : maybe not actually
366 rweis, 20:59 : it is it is @: Message 363: To whole message
367 meets, 20:59 : :-/
368 meets, 20:59 : hmm..
369 meets, 20:59 : got any other ideas?
370 rweis, 21:00 : nope
371 meets, 21:00 : im eating dinner soon
372 meets, 21:00 : when does this end?
373 rweis, 21:00 : right now

== Session 3 – Team 1 ==

122 Moderator_A, 20:12 : Today, we will share some questions and observations from other mathematicians
who have been looking at the questions and solutions you have been inventing and pursuing.
123 rweis, 20:12 : ok
124 Sheenav, 20:34 : 'kay
125 #1MATHWHIZ, 20:12 : k
126 mathman, 20:12 : k
127 mathpudding, 20:13 : k
128 Moderator_A, 20:13 : During the first two sessions of this program the groups have at times explored
a math where points only exist at the intersections of a grid (this one is 12 lines by 12 lines),
evenly spaced one unit apart as in the image on the whiteboard. There are no "diagonal" lines,
at least not in the way we usually think of them.
129 Rweisbac, 20:13 : so
130 Moderator_A, 20:13 : Distance between any two points in this grid world is defined as the length of the shortest path
along the grid lines connecting the points. Several groups showed there may be several shortest paths,
but the distance is well-defined. This is a system of math that you are inventing,
just as the Greeks invented geometry.
131 Moderator_A, 20:14 : Did anyone think of any other questions after the last session?
132* rweis, 20:13 : '''ITS A PERMUTATION!!!'''
133 Sheenav, 20:36 : it's what?
134 rweis, 20:14 : A permutation I'll explain later
135 Sheenav, 20:36 : okay
136 rweis, 20:14 : good
137 Moderator_A, 20:15 : Here are some questions that come up when looking at your work.
You don't need to pay any attention to these if you don't want to.
Again, your goal is to identify or invent new math questions that are interesting to you and pursue them.

Dataset1/NoEffect

Jsarmi — Tue, 29 May 2007 13:11:10 GMT

Jsarmi:

Instances where the group did not pick up on the report being presented:

==Session 3 – Team 4==

80 vmtguy, 20:16 (17.05): As you work, you may want to have other textboxes to keep track of new questions
or important results you have found. Feel free to use the Whiteboard in any way that you,
as a group, think is useful
81 Shuichi, 20:21 (17.05): that*
82 vmtguy, 20:16 (17.05): Go ahead...
83 EatUrSqRts, 20:16 (17.05): the picture, imean
84 EatUrSqRts, 20:17 (17.05): forget the last comment, my comp lagging
85 EatUrSqRts, 20:19 (17.05): so last week, we found out that if moving only right and down, it will always be 10 moves frm a to b
86 Shuichi, 20:24 (17.05): yea i got that
87 Shuichi, 20:24 (17.05): so wa do we do now???
88 EatUrSqRts, 20:19 (17.05): ask questions
89 EatUrSqRts, 20:20 (17.05): hey, vmtguy, do we still need a team name?
90 vmtguy, 20:21 (17.05): You can pick one if you want.
91 ssjnish, 20:20 (17.05): joins the room
92 EatUrSqRts, 20:21 (17.05): hi ssjnsh
93 ssjnish, 20:21 (17.05): hi all
94 Jason, 20:21 (17.05): hello
...

Dataset1/Collective Remembering

Jsarmi — Tue, 29 May 2007 13:07:35 GMT

Jsarmi: /* Where did you guys last leave off */

= Session 4 - Team 5: Collective Remembering =

This excerpt illustrates a case in which a team is collectively engaged in trying to reconstruct parts of their previous session in order to initiate their current problem solving activity. Remembering of past activity unfolds as a collective engagement in which different team members participate dynamically. Some of the current team members were not present in the previous session and yet, they are instrumental in the reconstruction of that past and in shaping its current relevance.

==Last Tuesday you worked on finding a formula ==
This was the fourth session of team five. Towards the beginning of the session, with only two participants present (Gdo and Meets), the moderator stated that he was a "new" moderator and asked them if they were part of the chat "last time." Gdo and Meets assented and added that they remembered other people being present. Ten minutes had passed since the start of the session when the facilitator stated that maybe Gdo and Meets were going to the "the team" for the night. A few minutes later, Gdo joined the room while the facilitator was explaining general aspects of how and why the chat sessions were offered. Later on, Extrick joined the room as well.

After this introductory period, the facilitator suggested (8:22:09 PM) that during the summer the team members could work with their friends on a new problem he posted: the "circle problem." Later, he added that they could "pursue the circle questions in this chat" if they wanted or "any other questions and worlds" that they thought of. The team seemed disoriented about what to do and after more than a minute of silence the following sequence took place:

111 8:25:38 PM meets: ert
112 8:25:42 PM meets: whoops
113 8:25:52 PM meets: we're doing the problem he juts gave us right?
114 8:26:05 PM Mod: Last Tuesday you worked on finding a formula for the number of shortest paths
between any two points A and B on the grid. You explored multiple possibilities
and figured out that x+y and x^2+y^2 work (where x and y correspond to the # of units
you need to travel along x and y axis to get from A to B) but only for some points, not all.
You may want to continue exploring more cases and see if you can find a general formula.
115 8:26:31 PM Mod: or you can work on the problem i posted earlier
116 8:26:50 PM drago: ok
117 8:27:04 PM Mod: I can also post all the original questions if you would like to see them
118 8:27:17 PM gdo: post the original
119 8:27:42 PM drago: ok

(Followed by whiteboard activity by the facilitator and by Gdo, from 8:27:35 PM to 8:29:18 PM to post and arrange a textbox
with “all the original questions”)

This sequence involves a number of interesting features. In particular, the facilitator's posting on 114 employs a set of resources which seem specially relevant for our analysis of continuity. First, the posting uses the temporal marker "last Tuesday" to index a prior event which is then described using declarative assertions constructed with past-tense verbs (e.g. you worked on finding a formula, you explored multiple possibilities, you figured out that x+y and x^2+y^2 work, etc.). These assertions, in addition to weaving together an ambiguous subject "you" and a number of actions being reported, index a set of artifacts that are presented as descriptors of prior achievements: a formulas for shortest paths, points A and B, the grid, etc. All of these resources, as presented, are positioned in different ways with relation to the facilitator and the rest of the participants and, as such, can be consider to constitute the developing interactional "deictic field" (Hanks, 2005). Hanks describes the ''deictic field'' as composed of:

::#The positions of communicative agents relative to the participant frameworks they occupy (that is, who occupies the positions of speaker [Spr], addressee [Adr], and others as defined by the language and the communicative practices of its speakers)
::#The positions occupied by objects of reference, and
::#The multiple dimensions whereby the former have access to the latter (p. 193)

Based on this description, Hanks defined "act of deictic reference" as one which takes up a "position in the deictic field" (p.193). In our case, the diectic field is being constituted by the participants to include ''objects of reference'' and ''communicative agents'' associated with a prior encounter. Line 114 attempts to position past participants and prior doings as relevant objects of reference for the current interaction. Towards the end, the posting switches from past-tense descriptions to a series of future-oriented suggestions: ''you may want to continue exploring more cases and see if you can find a general formula'' (...) ''or you can work on the problem I posted earlier.'' These combination of features in the design of the posting alert the recipients to its "bridging" construction in the sense that relevant prior activity performed by an unspecified group of participants ("you") is used to produce a set of task proposals for the current participants. The participation framework that seems to be enacted after postings 115 and 117, the facilitator setting up a set of possible tasks for the team to take on, calls for the current participants to decide for themselves on what problem to pick and, in doing so, they might need to take a stake on the positioning put forward by line 114.

==Where did you guys last leave off==

The uptake of the tasks proposals made by the facilitator involve a series of interesting interactional maneuvers which involve the constitution of the current situation or deictic field and its corresponding positioning. In the excerpt reproduced below, line 120 is preceded by lack of chat conversation that lasts more than two minutes. The group is not taking action on deciding on its task or might be oriented to reading the textbox on the whiteboard with the original questions. Gdog's requests a description of where the group "last" left off in line 120 and uses the terms "u guys" to address his request in a similar all-inclusive way as the original facilitator posting in 114. By using the expression "last leave off", Gdog seem to use a communicative method that allows parties in conversation to segment or index specific portions of experiences and relate them in ways that allows them to form sequences of participation and activity.

119 8:27:42 PM drago: ok
120 8:30:11 PM gdo: where did u guys last leave off (Points to Message 119)
121 8:31:20 PM MFmod: I think that the above section I wrote is where the group last was (Points to Message 114)
122 8:31:36 PM MFmod: yes?
123 8:31:42 PM drago: well
124 8:31:48 PM gdo: i dont remember that
125 8:31:51 PM drago: actually, my internet connection broke on Tuesday
126 8:31:56 PM drago: so I wasn't here
127 8:32:12 PM MFmod: so maybe that is not the best place to pick up
128 8:32:14 PM estric: i wasnt able to be here on tuesday either
129 8:32:50 PM gdo: how bout u meets
130 8:33:01 PM meets: uh...
131 8:33:11 PM meets: where'd we meet off....
132 8:33:16 PM meets: i remember
133 8:33:22 PM gdo: i was in ur group
134 8:33:24 PM meets: that we were trying to look for a pattern
135 8:33:27 PM gdo: but i didn't quite understand it
136 8:33:34 PM gdo: can u explain it to us again meets

It is possible that Gdo was present in the prior session but left early and, as a result, wants to know about the last portion of the session that he missed; or perhaps he wasn't there but is only interested in knowing what the group discovered at the end of the session to see if they can build on it now. In either case, Gdo is orienting the group back to "last Tuesday" although his participation in such episode of interaction is still left unspecified. In contrast, after the facilitator calls for an assessment in lines 121 and 122 of whether he had described where "the group last was" in message 114, Gdo states in line 124 that he does not remember "that." At this point Gdo has position himself in a different stance in relation to the object of reference "last Tuesday" and with the description produced by the facilitator in 114. Subsequently, Drago and Estric both decline responding to the assessment called for by the facilitator, also positioning themselves as not having participated in last Tuesday's session. Meets is the only participant whose position with regards to last Tuesday's session has not been addressed and Gdo calls for him to do so in line 129. In fact, in constructing his requests to Meets further, Gdog specifies in more detail that he remembers being in meet's group so effectively, we had an asymmetrical position with regards to last Tuesday's session where Drago and Estric cannot claim direct knowledge of what was done but Drago and Meets can. Interestingly, after Meet has started his tentative recollection, Gdo attempts to reformulate Meets recollection as an explanation by requesting it to be presented to the group ("us") that way (136).

137 meets: with the square, the 2by 2 square, and the 3by2 rectangle
138 meets: sure...
139 meets: so basically...
140 gdo: o yea
141 gdo: i sort of remember
142 meets: we want a formula for the distance between poitns A and B
143 drago: yes...
144 meets: ill amke the points
145 MFmod: since some folks don't remember and weren't here why don't you
pick up with this idea and work on it a bit
146 meets: okay
147 meets: so there are those poitns A and B
148 meets: (that's a 3by2 rectangle
149 meets: we first had a unit square
150 meets: and we know that there are only 2 possible paths......

One of the things that are remarkable about the way this interaction unfolds is the fact that although it might appear as if it is Meets who remembered what they were doing last time, the actual activity of remembering unfolds as a collective engagement in which different team members participate dynamically. In fact, later in this sequence there is a point where Meets remembers the fact that they had discovered that there are 6 different shortest paths between the corners of a 2-by-2 grid but he reports that he can only “see” four at the moment. Even though Drago did not participate in the original work leading to that finding, he was able to see the six paths when Meets presented the 2- by-2 grid on the whiteboard and proceeded to invent a method of labeling each point of the grid with a letter so that one can name each path and help others see it (e.g., “from B to D there is BAD, BCD …”). After this, Meets was able to see again why it is that there are six paths in that small grid and together with Drago, they proceeded to investigate, in parallel, the cases of a 3-by-3 and a 4-by-4 grid using the method just created. The result can be seen on the whiteboard:

[https://www.ischool.drexel.edu/upload/vmt/Data/ConcertChat2005Pilot/Session4/VMT0519G5_files/WhiteboardImage.jpg]

Despite the fact that this picture is a restrictively static representation of the team’s use of the whiteboard, it allows us to illustrate some unique aspects of this remarkable creative organization of their collective activity. First, we see again the crucial role of indexicals and referencing activity in the collective construction of the mathematical ideas of the team (e.g., through the use of labels, the witnessing of actions on the whiteboard, and the coordination of parallel activity).

The use of the whiteboard represents an interesting way of making visible the procedural reasoning behind a concept (e.g., shortest path). The fact that a newcomer can use the persistent history of the whiteboard to re-trace the team’s reasoning seems to suggest a possible strategy towards preserving complex results of problem-solving activities. However, the actual meaning of these artifacts is highly situated in the doings of the co-participants, a fact that challenges the ease of their reuse despite the availability of detailed records such as those provided by the whiteboard history.

Despite these technical limitations, we could view the artifacts created by this team as “bridging” objects which, in addition to being a representation of the teams’ moment-to-moment joint reasoning, could also serve for their own future work and for other members of the VMT online community. These particular objects are constructed in situ as a complex mix of resources that “bridge” different points in their own problem-solving and, potentially, those of others. As can be seen in Figure 4, the two team members combined the depiction of the cases being considered, the labeling and procedural reasoning involved in identifying each path, a summary of results for each case (i.e., the list of paths expressed with letter sequences) and a general summary table of the combined results of both cases. The structure of these artifacts represents the creative work of the team but also documents the procedural aspects of such interactions in a way that can be read retrospectively to document the past, or “projectively” to open up new possible next activities.

==Endnotes==

[*] According to Hanks (2005): “My approach to deictic practice relies centrally on the field concept, which in turn derives from three overlapping sources. The first of these is the standard linguistic sense of semantic field, which denotes any structured set of terms that jointly subdivide a coherent space of meaning. (…) The second usage of “field” was introduced by Buhler (1990[1934]), who defined speech context in terms of two interlocking fields: (I) The symbolfeld (symbolic field), made up of words, other signs, and the concepts they represent, and (2) the Zeigfeld (demonstrative field), the experiential present of utterance production, which he labeled “Here Now I.” (…) The third source is social practice theory in which the concept of field is both more abstract and more encompassing than either the semantic or phenomenological usages. According to Bordieau (1985, 1990, 1991a), a field is a space of positions and position takings in which agents (individual and collective) engage and through which various forms of value or “capital” circulate.

Dataset1/SandLines

Jsarmi — Tue, 29 May 2007 12:53:57 GMT

Jsarmi:

===Bridging problem-solving perspectives: “…it's like, you can't walk in water, and the lines are dry lines …”===

The further unfolding of the excerpt from team five in session one which we analized before provides some more evidence on how bridging activity affects a problem-solving interaction. Starting with mathwiz’s posting in line 314 (“would you want to keep as close to the hypotenuse as possible? or does it actually work against you in this case?) continues the bridging activity opened up by drago in a unique way. Mathwiz’s posting suggests an active way of orienting towards drago’s presentation of how the grid-world had been found to work, while at the same time ratifying drago's position as the one who is to respond to assessments of his report (i.e. testing whether this case “works against you”). In this way, mathwiz’ posting seems to actively situate drago’s narrative of the past by ratifying its relevance for their current problem solving and assessing its practical comprehensibility. The presentation of a “test case” by mathwiz follows gdo’s presentation of a general rule in a way that signals the sustainability of the team’s knowledge building. It is precisely because of this type of engagement that we do not see this interaction simply as a peer explanation nor do we label the relationship between prior members of the team and newcomers as an entirely asymmetrical one of explainer–audience. This short sequence signals only the beginnings of the type of interactional work necessary to fully bridge prior knowledge work into present joint activity, and yet it is sufficient to provide us with significant evidence of the nuanced aspects of this type of activity. Other researchers have pointed out that the management of attention and knowledge proposals as well as the roles of the co-participants in establishing join attention are consequential for the collective achievements of small groups (Barron, 2000) (Stahl, 2006b). Here we see how these interactional processes are especially important for the establishment of continuity of knowledge building over time.

One further aspect of the second session of team five is worth exploring. The excerpt below follows the one from session two presented earlier and it allows us to observe how this collectivity dealt with the uptake of drago’s presentation of the past finding about short distances in the grid-world.

323 drago: ok....
324 drago: so
325 gdo: square root of 45
326 mathwiz: but you have to move on the grid lines, right?
327 gdo: 3^2+6^2=c^2 right?
328 drago: no
329 drago: you can't go diagonal
330 gdo: ok
331 drago: the problem before said so, but you weren't here
332 gdo: so the hypotenuse is not square root of 45?
333 gdo: i was on team 2
334 drago: I mean
335 drago: it is
336 gdo: but moved to team 5
337 gdo: since u guys didn't have enough people
338 drago: but, we can't move diagonally since that would be cutting through the grid
339 mathwiz: the hypotenuse is fine, but for the problem, you have to go on the grid lines
340 gdo: ok
341 drago: so
342 mathwiz: it's like, you can't walk in water, and the lines are dry lines
323 drago: ok....

Despite drago’s orientation to the recommencement of the prior work that he and estrick did before (and to a narrator-explainer framework of participation), gdo departs partially from that orientation in line 325 by making a solution proposal for the shortest path between the points they are currently examining (“square root of 45”). Consequently, the sequence of postings from 325 to 330 seems to indicate a local engagement with the problem as the present matter and no longer as a bridging move to re-use prior findings. However, in the sequence starting at line 331 drago uses, once again, elements of prior interactions (“the problem before said so but you weren’t here”) to address what appears to be a problem in gdo’s understanding (i.e. that you can’t go on the diagonal). This alternation between present and bridged resources for problem solving indicates a dynamic engagement by the group with its distributed history and its current problem-solving activity.

Also particularly interesting in this sequence are mathwiz’s postings in lines 339 and 342: “the hypotenuse is fine, but for the problem, you have to go on the grid lines…it's like, you can't walk in water, and the lines are dry lines.” These postings seem to do the unique work of ratifying gdo’s use of the hypotenuse —as well as his participation in the task— while at the same time offering him a new “rule” or perspective to manipulate the grid. It seems to us that this interactional move bears resemblance with the types of activities we have analyzed before and deserves the label of bridging work. By offering this new perspective on how to imagine and manipulate the grid, mathwiz identifies a boundary between different perspectives or forms of understanding (i.e. being able to use diagonals or not in the grid world) and goes beyond simply refuting it by offering a link or bridge between the two. This bridging of perspectives can naturally occur between different problem-solving episodes or collectivities but here we see it happening within the flow of a team’s interactions. With the dynamic changes in team membership that characterize naturalistic environments and the diversity of points of view among individuals and teams that are typical of online communities, sustained problem-solving work seems to require that co-participants also engage in this type of bridging of perspectives. Additional research is necessary to explore the range of resources produced by individuals and groups to overcome these types of perspectival boundaries which emerge as relevant during their interactions and which relate to overcoming challenges of continuity, coordination or affiliation. It is possible that the methods and processes of doing this kind of boundary work could characterize effective collaborative learning interactions, but this remains a notion to be investigated.
So far, we have explored a few instances of bridging activity in the trajectory of a particular virtual math team in our experiment. In doing so, we have offered a preliminary analysis of how the collective engagement with past work is constituted across different interactions or episodes, how changes in the alignment of the participants signal various aspects of the sustained knowledge work of the teams, and how problem-solving perspectives are subject to bridging as well. Furthermore, our analysis seems to suggest that these attempts to establish continuity in collaborative problem solving involve the recognition and use of discontinuities or boundaries as resources for interaction (e.g. temporal or episodic discontinuity), changes in the participants’ relative positioning toward each other as a collectivity (e.g. narrators and interactive audience), and also the use of particular orientations towards specific knowledge resources (e.g., the problem statement, prior findings, what someone professes to know or remember, etc.). This initial analysis demonstrates that in interactional contexts where there are continual sequences of discrete problem-solving episodes and where the membership of a team might change over time, sustaining continuity of the team’s knowledge work becomes a particular challenge for which teams need to develop particular interactional strategies. In fact, the analysis of other instances of this type of activity could lead us to uncover a range of bridging mechanisms used as part of the teams’ engagement in this online learning community.

Dataset1/D1T5S1n

Jsarmi — Sun, 27 May 2007 21:28:24 GMT

Jsarmi:

===“I remember that I proved this once but I forgot...”===

In addition to following the prospective unfolding of the particular instance of a team’s recommencement, we can also investigate retrospectively drago’s “bridging post” in session two (line 306: “you always have to move a certain amount to the left/right and a certain amount to the up/down”). We could do this by analyzing his prior work with estrick a few days back and explore the genesis of the reported finding. This approach would allow us to stretch the scope of our analysis not only from one problem-solving episode into another but also from one particular collectivity (drago-estrick-gdo-mathwiz) into a different one (the dyad drago-estrick). In essence, line 306 in session two appears as a re-statement of something that drago and estrick discovered in the first session that they held as a team. The following excerpt illustrates how this idea was articulated then:

168 estrick: well, judging by my calculations, any root that does not go along a diagonal is the same length
169 drago: it should be (Points to line 168)
170 drago: except if you go some extra long way for no reason
171 estrick: haha, precisely
172 drago: but why are they the same? I remember that I proved this once but I forgot...
173 estrick: because you will alsways have to go down and to the right the same amount of times
174 drago: oh, seems reasonable (Points to line 173)
175 drago: so...any more questions you can think of?
176 estrick: but i am not sure of the correct proof
177 drago: well...I guess its because whatever path you take, you will make tiriangles (Points to line176

The relationship between line 173 in this excerpt of session one and line 306 of session two appears significant. On the one hand, the use of the adverb “always” in both postings seems to suggest a rule-like statement (or a conjecture) aimed at capturing a constructed understanding about the way the grid-world works (from the participants’ perscpective). The fact that the creator of this text changes from estrickm in session one to drago in session two could be taken as an indicator that this rule is a collaborative understanding achieved by the dyad which is, later on, projected into a new collectivity and a “bridged” problem-solving context. Based on this observation, we could construe the re-statement of prior findings and the change in authorship as indicators of sustainability in the co-construction of knowledge as the history of multiple teams in an online community evolves. Although not entirely conclusive, these two conditions certainly seem to point in that direction despite the fact that in small-group interactions the notion of authorship needs to be analyzed critically. For instance, if line173 is a response to line 172 and proceeds from the flow of the interaction, isn’t it really the dyad who should be credited with having produced the original rule about the grid-world? These kinds of interactions point to the need to carefully redefine the notion of authorship as we navigate individuals, small-groups and larger collectivities engaged in knowledge building.

Beyond the apparent changes in authorship, it is interesting to note how drago’s text in line 306 of session two, differs from estrickm’s original posting from session one. Originally, there was only mention of moving “down and to the right,” but in drago’s restatement, one has to move a certain amount “to the left/right and a certain amount to the up/down.” Why has drago modified the original rule by adding the “/up” and “left/” elements? At this point, we need to mention that the environment in which these teams are interacting is much more complex than what is captured by the transcripts we have presented. In addition to the chat interface, a shared whiteboard is available to the participants in the virtual room provided. At the moment in session two when the exchanges that we have presented took place, the whiteboard in this team’s meeting room contains the picture in Figure 2. We can see in this snapshot the points that they selected to explore the grid-world and also some elements of how they have graphically presented their reasoning about it. Interestingly, a very similar diagram was used by estrick and drago in session one, as can be seen in Figure 3. However, in that case the diagram only included two points similar in their arrangement to points A and B in the diagram from session two. The arrangement of points used in session one matches estrick’s original rule that “you will always have to go down and to the right.” On Figure 2, there are two arrangement of points being considered: The one involving points A and B where the shortest path would be achieved by going down and to the right and another in which the movement would be up and to the right (linking the points labeled with circles). One can then read drago’s modification to the original rule as indication that he has adapted it to make it applicable to all arrangements of points based on the cases used by the team in this session.

Figure 2. Snapshot of Team 5’s whiteboard, Session 2.

Figure 3. Snapshot of Team 5’s whiteboard, Session 1

It is possible that drago realized this generalization via further individual work in between team sessions, or that the position on the grid of the points that the team has selected in session two provided the need for the generalization to happen. Whatever the actual motive, drago is presenting in session two a modified version of the finding previously constructed suited to the current circumstances. Beyond simply citing prior findings, drago has in fact bridged two problem-solving contexts in an attempt to construct continuity To further qualify this observation, we can contrast drago’s tentative reasoning for why the rule works presented in line177 of session one (well...I guess its because whatever path you take, you will make tiriangles) with the sense of confidence that his presentation conveys in session two. This subtle change could illustrate a change in the strength of his understanding of the grid-world. Observations like these, although requiring further verification through triangulation and further analyses, start to point to critical interactional aspects of how knowledge work is sustained over time and hint towards longitudinal aspects of collaborative learning interactions. Furthermore, they reveal the need to understand how bridging interactions span across the individual and the different collectivities involved in an online community.

Dataset1/D1T3S4n

Jsarmi — Thu, 24 May 2007 20:00:18 GMT

Jsarmi:

dc and fg, who where together in session 1, but have not participated in sessions 2 or three, return and work as a dyad.

==Do you remember session 1's work?==

42 ModeratorJ, 20:23 (19.05): Did you guys remember exploring the formula of the distance in the grid-world?
43 fogsurrounds12, 20:26 (19.05): yes @: Message 41: e where tha
44 davidcyl, 20:26 (19.05): yes, but we didn't come up with a formula @: Message 42: o
45 eModerator, 20:25 (19.05): joins the room
46 eModerator, 20:25 (19.05): leaves the room
47 ModeratorJ, 20:24 (19.05): would you like to work on that right now?
48 davidcyl, 20:26 (19.05): ok
49 fogsurrounds12, 20:26 (19.05): sure
50 ModeratorJ, 20:25 (19.05): o.k. go ahead!
51 davidcyl, 20:27 (19.05): ok so we have A and B
52 ModeratorJ, 20:25 (19.05): I'll paste the question in a textbox for you
53 davidcyl, 20:28 (19.05): so given a distance as the crow flies?
54 ModeratorJ, 20:27 (19.05): you can creat labels with the textbox tool (next to the circle) or the freehand tool.
@: Message 51: To whole message
55 fogsurrounds12, 20:29 (19.05): the distance is the shortest distance between the two points not on the lines right?

Dataset1/D1T3S3n

Jsarmi — Thu, 24 May 2007 19:43:38 GMT

Jsarmi: /* Newcomer uses diagonal distance */

==Newcomer uses diagonal distance==

107 templar, 20:21 (17.05): the formula for distance is sqrt[(x1-x2)^2+(y1-y2)^2]

Templar's partner, mathwiz, drops from the system so Templar is moved to [[Dataset1/D1T1S3n|Team 1]] where he participates actively right away.

Dataset1/D1T2S4n

Jsarmi — Thu, 24 May 2007 19:02:02 GMT

Jsarmi:

==It's new for everyone==

Moderator_G 5/19/05 8:04:22 PM EDT: OK, We are ready to start. Today, you can finish the work that you have been doing
as a team in the previous three sessions. There are five teams in this project and they have all
explored very interesting questions about the “grid-world” that we started with.
Moderator_G 5/19/05 8:04:46 PM EDT: Before you begin doing math today, we wanted to see if you had any questions for us
about why we offered these chats or what we are trying to do or how we think it went?
Moderator_G 5/19/05 8:05:23 PM EDT: I posted a long explanation about how we think about this.
Moderator_G 5/19/05 8:05:45 PM EDT: What do you think? Any questions or comments?
mathisfun 5/19/05 8:06:02 PM EDT: This is very interesting class
mathisfun 5/19/05 8:06:21 PM EDT: It was very different from anything i've had before
Moderator_G 5/19/05 8:06:44 PM EDT: It's new for everyone

==The other two are not here yet==

Moderator_G 5/19/05 8:10:05 PM EDT: Well, I guess you want to get back to the math
bob123 5/19/05 8:11:49 PM EDT: the other 2 aren't here yet though
Moderator_G 5/19/05 8:12:18 PM EDT: Well, you can get started

==Moderator frames prior work==

Moderator_G 5/19/05 8:12:48 PM EDT: I thought you might want to work on the idea that someone suggested at the end last time
Moderator_G 5/19/05 8:13:13 PM EDT: So I put the problem in the text box and drew a new grid for you
mathisfun 5/19/05 8:13:25 PM EDT: thanks
mathisfun 5/19/05 8:13:36 PM EDT: So I guess we can get started...

on the whiteboard:

Last time you rolled up the grid so that the left edge met the right edge and formed a cylinder.
You worked on the distance between points by passing through the inside of the cylinder.
At the end of the session, someone suggested folding the paper to form a prism (solid triangle).
This might actually be easier to work with than a cylinder. Suppose you have a grid that is 12 unit squares
by 12 unit squares. Number the vertical lines from 0 to 12. fold the grid along line 4 and 8, and join the edges
at 0 and 12 to form a solid equilateral triangle. Now find the shortest distance between any two points along the grid
and through the prism. Is there any relationship between the two measures of distance?

==BRIDGING: You do the same you did with the circle (Bird's eye view)==

mathisfun 5/19/05 8:15:26 PM EDT: k letz get started
bob123 5/19/05 8:15:54 PM EDT: the way i see it, you do the same thing you did with the circle
mathisfun 5/19/05 8:16:05 PM EDT: alright
mathisfun 5/19/05 8:16:16 PM EDT: so letz draw the triangular prism
mathisfun 5/19/05 8:17:39 PM EDT: there
mathisfun 5/19/05 8:18:42 PM EDT: so should i make the bird's eye view?

==WHAT IS THIS? Long reference==

bob123 5/19/05 8:28:24 PM EDT: and how do you use the two sides and the degree to find the third side?
mathisfun 5/19/05 8:28:33 PM EDT: one moment
mathisfun 5/19/05 8:28:58 PM EDT: There is a fomula I think
bob123 5/19/05 8:29:13 PM EDT: i said use the law of cosines earlier
bob123 5/19/05 8:29:24 PM EDT: there
bob123 5/19/05 8:29:30 PM EDT: there ''(points to: bob123 5/19/05 8:23:41 PM EDT: using law of cosines)''

Dataset1/D1T2S3n

Jsarmi — Thu, 24 May 2007 18:34:59 GMT

Jsarmi:

==Moderator works on continuity==

Moderator_G 5/17/05 7:37:19 PM EDT: I was curious about your formula for the number of shortest paths
bob123 5/17/05 7:37:36 PM EDT: it's pascal's triangle
Moderator_G 5/17/05 7:37:53 PM EDT: Oh!
Moderator_G 5/17/05 7:38:22 PM EDT: why would that be the number of shortest paths?
Moderator_G 5/17/05 7:41:31 PM EDT: It did seem to work for the examples you tried
Moderator_G 5/17/05 7:41:48 PM EDT: But I did not understand how you thought it up
bob123 5/17/05 7:43:03 PM EDT: draw a rectangle
bob123 5/17/05 7:43:07 PM EDT: and label it with numbers
bob123 5/17/05 7:43:27 PM EDT: for the number of ways to get there
bob123 5/17/05 7:43:46 PM EDT: starting from the top right corner and ending at the lower left corner
bob123 5/17/05 7:43:49 PM EDT: the top right corner is 1
bob123 5/17/05 7:44:53 PM EDT: then the rest, you just add the numbers of the two vertices that are next to it
(the one on the right of it and the one on top of it)
Moderator_G 5/17/05 7:46:14 PM EDT: Whoa, Bob. You are going too fast for me. Let's wait for the others to show up.
bob123 5/17/05 7:47:09 PM EDT: ok
Moderator_G 5/17/05 7:52:10 PM EDT: Bob, Where did you learn about Pascal's triangle?
...
qwer 5/17/05 7:55:57 PM EDT: hi
bob123 5/17/05 7:56:13 PM EDT: hi
Moderator_G 5/17/05 7:56:42 PM EDT: Hi everyone
qwer 5/17/05 7:56:54 PM EDT: What's Pascal's triangle?
Moderator_G 5/17/05 7:57:30 PM EDT: Bob and I started talking about his formula last time.
Moderator_G 5/17/05 7:57:47 PM EDT: Can you see our messages?
qwer 5/17/05 7:57:54 PM EDT: Yes
...
qwer 5/17/05 8:03:54 PM EDT: I just found a description of the triangle at http://mathworld.wolfram.com/PascalsTriangle.html

==The problem is, I don't remember my formula==

bob123 5/17/05 8:04:07 PM EDT: the problem is
bob123 5/17/05 8:04:17 PM EDT: i'm not too sure what the formula i made up last week is
mathisfun 5/17/05 8:04:34 PM EDT: then how u get it?
bob123 5/17/05 8:04:51 PM EDT: i got it
bob123 5/17/05 8:04:55 PM EDT: but then i forgot it
bob123 5/17/05 8:05:00 PM EDT: give me 5 minutes to reget it
bob123 5/17/05 8:05:14 PM EDT: i have short term memory loss
bob123 5/17/05 8:06:09 PM EDT: ok
bob123 5/17/05 8:06:10 PM EDT: there
bob123 5/17/05 8:06:14 PM EDT: i remember how i got it now
bob123 5/17/05 8:06:43 PM EDT: or do i...
bob123 5/17/05 8:07:21 PM EDT: there we go

''on the whiteboard'':

In an n by m rectangle (n>m), the number of ways to get from the top left corner to the bottom right corner
without retracing steps or going backwards (where going backwards is defined as making a move
such that it would result in making the distance between the point and the top left corner shorter) is:

(m+n) choose (m) or (m+n) choose (n) or
(m+n)!/(m!n!)

== Where is the other guy?==

bob123 5/17/05 8:08:35 PM EDT: where's the other guy?
bob123 5/17/05 8:08:45 PM EDT: the SithLordVader or something guy

== Summarize to a newcommer==

Moderator_G 5/17/05 8:16:47 PM EDT: Can someone explain to theyypu234 what you found about the grid?
qwer 5/17/05 8:17:56 PM EDT: In the yellow box bellow the grid is a formula for how many shortest distances
there are from one point on a grid to another, staying on the lines of the grid.

==Moderator's questions... ==

Moderator_G 5/17/05 8:19:36 PM EDT: During the first two sessions of this program the groups have at times
explored a math where points only exist at the intersections of a grid (this one is 12 lines by 12
lines), evenly spaced one unit apart as in the image on the whiteboard. There are no "diagonal"
lines, at least not in the way we usually think of them.
Moderator_G 5/17/05 8:19:53 PM EDT: Distance between any two points in this grid world is defined as the length of the shortest path
along the grid lines connecting the points. Several groups showed there may be several shortest
paths, but the distance is well-defined. This is a system of math that you are inventing, just as
the Greeks invented geometry.
Moderator_G 5/17/05 8:20:09 PM EDT: Did anyone think of any other questions after the last session?
bob123 5/17/05 8:20:14 PM EDT: oh, i only got a 3 on my AIME, my index was like 25.7 (barely made B, :))
bob123 5/17/05 8:20:20 PM EDT: umm
mathisfun 5/17/05 8:20:32 PM EDT: still thinking about the last question...
qwer 5/17/05 8:20:35 PM EDT: Yes, but I forgot it.
mathisfun 5/17/05 8:20:54 PM EDT: the one about the cylinder or a flat surface one
bob123 5/17/05 8:20:58 PM EDT: oh
bob123 5/17/05 8:21:37 PM EDT: i think i get that one now
Moderator_G 5/17/05 8:21:53 PM EDT: I put some questionsin the yellow box that come up when looking at your work.
You don't need to pay any attention to these if you don't want to. Again, your goal is to identify
or invent new math questions that are interesting to you and pursue them.
mathisfun 5/17/05 8:21:55 PM EDT: so do u still think it is a cylinder?]

==There was a question last time, on Thursday==

mathisfun 5/17/05 8:21:55 PM EDT: so do u still think it is a cylinder?]
qwer 5/17/05 8:22:10 PM EDT: think what is?
bob123 5/17/05 8:22:21 PM EDT: i know it's a cylinder
mathisfun 5/17/05 8:22:30 PM EDT: there wsa a question last time on Thursday remember?
qwer 5/17/05 8:23:19 PM EDT: Which one?
mathisfun 5/17/05 8:23:41 PM EDT: the one where the paper wsa folded and then we find the distance
qwer 5/17/05 8:23:51 PM EDT: Yes.
bob123 5/17/05 8:23:54 PM EDT: yep, i get it now
mathisfun 5/17/05 8:23:57 PM EDT: (the paper was folded in half)
mathisfun 5/17/05 8:24:04 PM EDT: K i'll make a cylinder
bob123 5/17/05 8:24:07 PM EDT: think right triangles
bob123 5/17/05 8:24:15 PM EDT: and circumference of base circle
bob123 5/17/05 8:24:51 PM EDT: finding the distance would involve the law of cosines, but that's ok

==Plans and Reflections?==

Moderator_G 5/17/05 9:03:21 PM EDT: What did you conclude about the cylinder?
mathisfun 5/17/05 9:04:00 PM EDT: it was an interesting problem
mathisfun 5/17/05 9:04:17 PM EDT: thinking about it really helped
Moderator_G 5/17/05 9:04:40 PM EDT: did talking about it with others help?
mathisfun 5/17/05 9:04:53 PM EDT: yeah
qwer 5/17/05 9:04:58 PM EDT: yes
Moderator_G 5/17/05 9:05:22 PM EDT: what do you want to do next time?
qwer 5/17/05 9:05:53 PM EDT: mabey use points on another shape
mathisfun 5/17/05 9:06:18 PM EDT: fold the shape into thirds...
mathisfun 5/17/05 9:06:37 PM EDT: or we can work on the new problems given
Moderator_G 5/17/05 9:07:20 PM EDT: Anything else?
Moderator_G 5/17/05 9:07:44 PM EDT: Think about what you want to do between now and Thursday
mathisfun 5/17/05 9:07:52 PM EDT: alright

Dataset1/D1T2S2n

Jsarmi — Thu, 24 May 2007 18:18:49 GMT

Jsarmi:

==Remember what you were doing?==

Moderator_G 5/12/05 7:57:50 PM EDT: Remember what you were doing Tuesday?
mathisfun 5/12/05 7:57:56 PM EDT: sorta
qwer 5/12/05 7:57:57 PM EDT: Yes.
Moderator_G 5/12/05 7:58:04 PM EDT: What?
mathisfun 5/12/05 7:58:13 PM EDT: i'm pretty sure
qwer 5/12/05 7:58:55 PM EDT: There were two points on a grid in which one could only travel on the lines and
we made and answerd questions about it.
Moderator_G 5/12/05 7:59:56 PM EDT: Right. There were several groups like yours and they each came up
with several ideas about this grid world
Moderator_G 5/12/05 8:00:11 PM EDT: I listed some of their questions ...
Moderator_G 5/12/05 8:00:41 PM EDT: ... and also some questions that these group questions raised for the moderators
Moderator_G 5/12/05 8:01:04 PM EDT: What do you think of these questions?

On the whiteboard:

Pretend you live in a world where you can only travel on the lines of the grid.
You can't cut across a block on the diagonal, for instance. How does this change the math?

Questions from the groups:
1. What is the shortest path along the grid between the two points?
2. How many possible routes are there from point A to point B?
3. What is the maximum distance from point A to B if you can only travel on each POINT once?
4. How many ways are there to get from A to B in rectangle ABCD?
5. Make a right triangle with AB as the hypotenuse. What is the area of the circumscribed circle?
6. Can you go off the edge and come back somewhere else?

Questions these raised for the moderators:
7. What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)?
8. How many shortest paths are there from A to B and how does this vary with changes in the positioning of A relative to B?
9. Suppose the right and left edges of the grid are connected. How does that change the distances between points?

mathisfun 5/12/05 8:05:48 PM EDT: though we already discuss the 8th with number 4 we this one uses more thinker involved

==Newcomer goes for diagonal others correct her: WE are going along the lines==

Marisol 5/12/05 8:18:49 PM EDT: for 7, the shortest way is the square root of [(x2-x1)**2 + (y2-y1)**2]
bob123 5/12/05 8:19:27 PM EDT: but that wouldn't be along the grid
qwer 5/12/05 8:19:39 PM EDT: or absolute vale, instead of using squares.
mathisfun 5/12/05 8:19:51 PM EDT: We are going along the lines of the grid no diagonals allowed
Marisol 5/12/05 8:20:12 PM EDT: O.K

==Recorder role is "remembered" Original recorder is not present, somebody else takes over==

mathisfun 5/12/05 8:21:16 PM EDT: who want to write that down?
qwer 5/12/05 8:21:27 PM EDT: I will.
mathisfun 5/12/05 8:21:30 PM EDT: k

==We already did that yesterday, here it is (Formula reappears), try it, no need, I am not so sure==

bob123 5/12/05 8:22:36 PM EDT: we already did that yesterday
qwer 5/12/05 8:22:53 PM EDT: we did?
mathisfun 5/12/05 8:23:02 PM EDT: but we did it so that there was only right and down
bob123 5/12/05 8:23:07 PM EDT: i mean tuesday
mathisfun 5/12/05 8:23:35 PM EDT: i guess we will do it with left and up?
qwer 5/12/05 8:24:03 PM EDT: It would be almost the same.
bob123 5/12/05 8:24:05 PM EDT: it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1)
bob123 5/12/05 8:24:12 PM EDT: try it if you like
mathisfun 5/12/05 8:24:17 PM EDT: nah
mathisfun 5/12/05 8:24:25 PM EDT: if you are so sure...

bob123 5/12/05 8:25:36 PM EDT: i'm not
bob123 5/12/05 8:25:39 PM EDT: actually
bob123 5/12/05 8:25:45 PM EDT: take out the -2 and the -1
mathisfun 5/12/05 8:25:59 PM EDT: then letz check it
...

==Difficulties in Indexing common referent: right, down, down, or down, down, right, right, righ==

mathisfun 5/12/05 8:28:44 PM EDT: is the one by two going to be 4 ways?
qwer 5/12/05 8:29:26 PM EDT: Can't you go, from A, right, down, right down, right, or right, right,
right, down, down, or down, down, right, right, right...
mathisfun 5/12/05 8:29:48 PM EDT: for which one?
qwer 5/12/05 8:30:01 PM EDT: #8
mathisfun 5/12/05 8:30:12 PM EDT: which shape?
qwer 5/12/05 8:30:41 PM EDT: the two points labled A and B
mathisfun 5/12/05 8:30:51 PM EDT: its one by one
qwer 5/12/05 8:31:14 PM EDT: On my screen it looks like 2x3.
mathisfun 5/12/05 8:31:24 PM EDT: are u at 100%?
qwer 5/12/05 8:31:42 PM EDT: Never mind. It changed.
mathisfun 5/12/05 8:31:51 PM EDT: good

==Work on Qwer's past suggestion: reimman holes?==

mathisfun 5/12/05 8:38:24 PM EDT: so lets work on number nine
qwer 5/12/05 8:38:45 PM EDT: It makes the plane into a cylender.
mathisfun 5/12/05 8:39:45 PM EDT: wait it a cylinder or a flat plane that is down
mathisfun 5/12/05 8:39:56 PM EDT: (cut into half)?
qwer 5/12/05 8:40:37 PM EDT: I imagine both sides wrapping around and connecting in the back.

==Marison reapears later reinforcing the grid rule in a different context: 3D==

Marisol 5/12/05 8:49:16 PM EDT: but wouldn't you have to follow the curved surface

==I am bored==
bob123 5/12/05 8:52:00 PM EDT: i'm bored

==A plan for Next Tuesday==

Marisol 5/12/05 9:00:11 PM EDT: Moderator, what is your opinion on #9
Moderator_G 5/12/05 9:00:56 PM EDT: I will think more about it between now and Tuesday.
Marisol 5/12/05 9:01:30 PM EDT: k
Moderator_G 5/12/05 9:01:53 PM EDT: I also found your solution of 8 very creative. I do not understand how you got it or why it works
qwer 5/12/05 9:02:08 PM EDT: Neither do I.
mathisfun 5/12/05 9:02:43 PM EDT: I was something that bob found out
mathisfun 5/12/05 9:02:54 PM EDT: I guess we should ask him next time...
mathisfun 5/12/05 9:03:00 PM EDT: or unless he responds
Moderator_G 5/12/05 9:03:31 PM EDT: Maybe we can all think about it some more ... and make sure it really works
Moderator_G 5/12/05 9:04:09 PM EDT: See you on Tuesday!

Dataset1/D1T2S1n

Jsarmi — Thu, 24 May 2007 18:03:46 GMT

Jsarmi: /* What is that? */

==Naming a Recorder==

Moderator_G 5/10/05 8:21:17 PM EDT: Will one of you want to serve as recorder and type the questions in a textbox on the whiteboard?
SithLordVader91 5/10/05 8:21:33 PM EDT: i will

What does a recorder do? SithLordVader91 creates this textbox on the whiteboard:

Our Questions
What is the shortest way to get from A to B?
What is the longest way?
What is the straight distance between A and B?
What is the measure of angle B?
How many ways are there to get from A to B?

==What did you type?==

173 qwer: Who ment qwer?
174 mathisfun: me
175 mathisfun: its about your question
176 qwer: What did you type?
177 mathisfun: this one (REFERENCE TO 148 by qwer: What's the longest way, staying in the box?)
178 mathisfun: can u overlap?

==Overlap==

mathisfun 5/10/05 8:25:25 PM EDT: can u overlap?
qwer 5/10/05 8:26:15 PM EDT: If you can overlap, there is no longest way. You can keep going back and forth. I ment not overlapping.
SithLordVader91 5/10/05 8:26:19 PM EDT: if u can, it would be infinite
mathisfun 5/10/05 8:26:24 PM EDT: k
qwer 5/10/05 8:28:06 PM EDT: Aren't there a lot of shortest ways? You could go up 4 then left 6, or up 1, left 3, up 3, left3...
qwer 5/10/05 8:28:45 PM EDT: If you can only follow the grid it doesn't matter.
SithLordVader91 5/10/05 8:28:49 PM EDT: yeah there are... i meant the shortest # of lines
qwer 5/10/05 8:29:06 PM EDT: Then there are 2.

==Straight Distance==

what is the straight distance between A and B? (suppose each line is 1 unit
bob123 5/10/05 8:31:53 PM EDT: 2rt(13)

==Read This==

qwer 5/10/05 8:45:52 PM EDT: or infinite, if you don't have to follow the lines
mathisfun 5/10/05 8:46:07 PM EDT: read this
mathisfun 5/10/05 8:46:20 PM EDT: it say that there needs to follow lines
qwer 5/10/05 8:46:32 PM EDT: ok
qwer 5/10/05 8:46:56 PM EDT: Can you fold the plane?

==Asymmetry of Understanding: what does that mean?==

bob123 5/10/05 8:48:34 PM EDT: (4-1+6-1) choose (6-1) or (4-1)
bob123 5/10/05 8:48:41 PM EDT: is 56
bob123 5/10/05 8:48:43 PM EDT: that's the answer
bob123 5/10/05 8:48:50 PM EDT: assuming you can only go right and down
qwer 5/10/05 8:48:56 PM EDT: what does that mean?
bob123 5/10/05 8:49:13 PM EDT: the number of ways to choose 5 things from 8 things
bob123 5/10/05 8:49:15 PM EDT: it's a formula
qwer 5/10/05 8:49:25 PM EDT: ok
bob123 5/10/05 8:49:43 PM EDT: the formula to find the number of ways in an n by m rectangle like this is (n+m-2) choose (m-1)
mathisfun 5/10/05 8:51:02 PM EDT: anyone got any other questions?