Dataset1/D1T4SS
From Jsarmi
Contents |
Group Trajectory
Jason, X and X come to all sessions.
Session I
Late start. Big group (5 + facilitator). Relatively active facilitator mostly coordinating process but also some prompting. The team produces quickly the following set of X questions with almost everyone contributing one questions (all recorded in a textbox on the whiteboard labeled "Answer/Question Box"):
(C/W) What is the shortest route to take from A to B? (ss/fo?) (C/W) What is the difference between the shortest distance you are able to travel and the shortest distance "as the crow flies." (js) (C/W) How many possible routes are there from point A to B? (ss) (C/W) What is the area between the two shortest routes? (ih) (C/W) How many different routes can you take that are under 20 moves? (sg) (C/W) What is/are the longest route(s) you can take [without overlapping]? (js/ih) (C/W) If AB is a diameter, what is the area of the circle that it creates? (fo) (C/W) If AB is the diagonal of a rectangle, what is the area of the rectangle it creates? (js) (C/W) Suppose you can only travel down and to the right. What is the max. distance that can be traveled? Are all the possibilities 10? (fo) (C ) how about an obstacle on three points closest to A around B? (ih) (C ) What if your 'circle' has to stay on the grid lines, too? (facilitator)
A lot of movement of textboxes probably because more than one person wants to be recorder. Recorders: sg/ih Fo posts a question in the chat ("what is the shortest distance between the two points if one can only travel on they grey lines?") that, perhaps because it is taken as a repetitive question, is not transfered to a textbox, nor any discussion about it is generated. At the end, fo steers the group to work on his question about the area of the circle by making a drawing and asking them questions about it. They get an answer (Jason: 13(pi) would be the area of the circle with diameter AB / ImHere: bout 40.8) but then the facilitator intervenes so that they think more in terms of the "pretend world". Some questions are marked as "SOLVED" which the facilitator challenges.
Close to the end, they are about to engage in the grid-circle but time runs out and the moderator engages them in the end-of-session interview. Fo remarks that one thing she noticed was "That no matter what kind of path you use, in the pretend world, the shortest is always 10 units". Some of them also remark that it was very interactive and that there was no "filter". Probably because they are used to another kind of chat (Art of Problem solving, probably) where a facilitator picks what is to be broadcasted in the chat versus this "free-form" chat.
Session II
Starts with a lot of whiteboard playing. People remember missing participants from session 1. Team tries to select a name with a lot of ideas but no concensus. Moderator presents the list of questions, asks for new ones. No new questions. Ih asks "where is a and b" since the grid presented this time does not contain the points. Jason remembers that the "slope was 4, 6." They try to recreate the points on the whiteboard with a lot of movements and edits. At some point Fo posts "im here, I hate you" to which Ih responds "???" and later "anyways" and they just move on. Perhaps they know each other and are just playing. Reference to prior work:
Jason: so 1) the shortest path is drawn in read Jason: red* FooFoo: let's think of questions Jason: ok FooFoo: yes, except there is another path of the same distance Jason: sure, there are several more Jason: as we discussed on Tuesday rweisbac joins the room rweisbac leaves the room (ImHere draws the straight distance between A and B) ImHere: How long is that line? ImHere: Line AB FooFoo: 10 Jason: i'd have to disagree with 10
Noticed how "as we discussed on Tuesday" does the job of mitigating Fo's disagreement. Sort of like saying "I know/I am aware of that" or "you are not the only one who knows that." They work out this difference between distance in "blockland" and straight distance. Then move into a new problem: the area between the staircase and the hipothenuse (nice episode of indexicality) which, in fact, combines both distances. Then they chat about languages they know for a bit. At some point it seems as if Jason knows ImHere and they are dominating the conversation while Fooand Weisbari (new) are mostly silent. Then Fo posts: ("if the right and left edges are connected from A to B can be only 8 units") which others take to be related to question 9 ("Suppose the right and left edges of the grid are connected. How does that change the distances between points?") but Fo draws on the whiteboard connecting the top and down edges. Jason deletes Fo's drawing but there isn't much discussion about this problem, then time runs out and the moderator engages the team in the end-of-session interview. Fo says "i think the room should be slightly more moderated."
Despite this team having a very stable core of members, this session feels a bit less productive than session 1. There were only three active participants versus four (or five) active participants in session 1. That being said, they did create/explore some new questions but only briefly.
Session III
ImHere welcomes vmtguy back. New participant Su. ImHere changes names to EatUrSqRts. Ih recreates the points A and B again with a distance of four (vertical) and 6 (horizontal). Facilitator posts list of questions. Failed bridging instance?:
EatUrSqRts: so last week, we found out that if moving only right and down, it will always be 10 moves frm a to b Shuichi: yea i got that Shuichi: so wa do we do now??? EatUrSqRts: ask questions EatUrSqRts: hey, vmtguy, do we still need a team name? ...
It is unclear if Ih was trying to start a new activity but Su took his comment as simply another piece of information (I got that). Later, howerver Sh posts: "id the hypotinus is a^2 +b^2=c^2 and there is no diagnoal lines then the shortest distance should be wa is marked." What is Sh doing with this post? Ss joins late but jumps right in. For a while they mix working on question 1 and finding new questions. Then they concentrate on question 2 (number of paths). (At this point the grid has been resized and the points are now at a horizontal distance of 5). Ss who missed session 1, takes the lead:
ssjnish: well the way i know how to find number of possibilities is through permutations and tree diagrams Jason: can you show us by drawing on the board? Shuichi: wait... aren't we not alloud to have dioganal lines??? Jason: that's just theoretically there ssjnish: no, these represent possibilities EatUrSqRts: i dunno bout the permutation EatUrSqRts: how do u use it to solve this Jason: i dun either ssjnish: the first choice starting at A is either traveling east or south EatUrSqRts: permutationis a limited factorial
This team then struggles with not having a clear method to label all paths and count them. They try drawing them and keeping a count but it becomes too difficult. As Su says "if we draw them thenb the rectangle thing will be so colorful.." But the act of drawing the paths gives Ih a sense of pattern: "EDT: k wait/ i think i found a formula / every row is 4 i think / and 4 lines / so 4*4=16 / 16*2=32 / any objections?" Jason proposes that they check the formula, Ih posts the formula in the chat and Jason puts it in a textbox on the whiteboard: " so formula is (# of columns minus 1)*(# of rows)*2= all ways to walk" They try different cases but the formula is found not to work, but right before the moderator initiates the end-of-session interview, Ih posts that "just find the amt of ways w/ one row, mult. by the # of rows, and then mult. by 2" Interesting sequence:
vmtguy: What could you do differently as a team to work better? ssjnish: define ourselves more accurately ssjnish: like in what we are saying ssjnish: its hard over the net ssjnish: its easier in person EatUrSqRts: dont just say yes to doubtful formulas ssjnish: yea EatUrSqRts: actually try it Shuichi: ok... Shuichi: sure... Jason: yeah
This time they agree on a team name not without a lot of discussion.
Session IV
An attempt to continuity?
Moderator_R: Have you been thinking about the Math you have been doing during the last three sessions? Jason: yes Moderator_R: How so? Jason: well we were basically just discussing more questions about the points A and B on the cartesian coordinate EatUrSqRts joins the room EatUrSqRts: Sorry im late, track finals FooFoo: how did you do? (points to Jason's) Moderator_R: Hi, EatUrSqRts! Welcome to our final session of Virtual Math Teams! EatUrSqRts: well, then lets make it worthwhile! Jason: umm we did well, basically discussing the shortest paths from A to B (points to Fo's posting)
When the moderator is about to start his framing of a task, Ih posts that he thought of a new question:
EatUrSqRts: So i thought of another question EatUrSqRts: does every kno wut an infinte series is? Moderator_R : Last Tuesday you work on finding a formula for the number of shortest paths between any two points A and B on the grid. At the end you had this formula as a possible solution but you weren’t so sure about it: (# of columns minus 1)*(# of rows)*2= all ways to walk. Have you thought more about it? Would you like to continue working on it? FooFoo: no FooFoo: to eat your square roots EatUrSqRts: ? EatUrSqRts: o EatUrSqRts: k, EatUrSqRts: so an infinite series is a fraction x EatUrSqRts: let x be 1/2 EatUrSqRts: so it wuld be 1/2 + (1/2)^2 + (1/2)^3 .... EatUrSqRts: any questions ... (goes on for a long time but team seems to be following) ... EatUrSqRts: so, 10/12 is eaten, how much is left? Jason: 2/12 FooFoo: 1/6 Jason: .5/3 ... (but then Jason challenges the connection with the problem they are supposed to be discussing) ... EatUrSqRts: k, lets change it to 6 ppl, 7 cookies EatUrSqRts: the infinite series will be... Jason: well can we relate that to this problem? Jason: we're trying to find the shortest path EatUrSqRts: thats 10 Jason: ok, lets stop constipating the process and get to the problem EatUrSqRts: which 1? Jason: the one we're supposed to be discussing ... (then Ih goes back to his formula from Session III) ... EatUrSqRts: (collumns+1)(rows)(2) EatUrSqRts: anyone disagree? Jason: check it EatUrSqRts: 56? Jason: that can't be the area EatUrSqRts: no, the # of short paths
No discussion. Then time runs out. This session seems very unproductive. Moderator pastes the moderators' answer to the question about the number of paths. Ih seems interested but does not say much after the answers are posted.
Group composition: Stable
Session 1: js* fo ih ss sg** Session 2: js fo ih wb(L/***) Session 3: js ih/eu ss su Session 4: js fo ih/eu (*) Jason moves briefly to Team 3 instructed by the facilitator of room 4. (**) Contributes one question but low participation in general. Does not return (L) Late (***) Little math participation. Weisbari might be same user as rweisbac in Team 1, frind of Jason. Jason visited Team 1 at the beginning.
Grid-World vs. Diagonals
Session 1: Session 2: Session 3: Session 4:
