Dataset1/D1T5SS
From Jsarmi
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Group Five's Trajectory
This is a relatively stable team that starts with a dyad and ends with four participant (probably the only team that ended with more participants that it started with). Two participants, who where part of other teams in prior sessions join the team in sessions 2 and 3 and stay with it. Interesting bridging activity.
Session I
This dyad generates only two questions. Perhaps because when they have two the facilitator states that they have "very good questions to start with".
(C/W) How far away are the 2 points? (es)
(C/W) What is the shortest path between the two points? (dg)
(C/W) what would the circumcircle be of this triangle drawn / what would the diameter of the circumcircle be (es)
(C/ ) ModeratorM: For example, I could ask how could we find the shortest distance between any two points in this world,
such as between A at (x1, y1) and B at (x2, y2)? ... Can we find a formula for this shortest distance?
They seem to be using the two distances together and having them coexist in the grid world. They work on the first one, get an answer and move to the second one, which leads to this exchange;
dragon: lets go onto the second one? estrickmcnizzle: allright dragon: remember that we can only go on the grid estrickmcnizzle: well, judging by my calculations, any root that does not go along a diagnol is the same length dragon: it should be dragon: except if you go some extra long way for no reason estrickmcnizzle: haha, precisely dragon: but why are they the same? I remember that I proved this once but I forgot... estrickmcnizzle: because you will alsways have to go down and to the right the same amount of times
The moderator contributes the last question and, mostly dragon, engages in thinking about it but time runs out and es has to go:
dragon: I think dragon: is it dragon: absolute value of x1 - x2 dragon: and absolute value of y1-y2 ModeratorM: estrickmcnizzle, are you there? estrickmcnizzle: yes estrickmcnizzle: but i must depart, for the dinner table calls
Will they revisit this formula in the next session?
Session II
This session has dr and es (the original dyad) joined by we and gd. Gd moved from team 2 (was lv). When the moderator introduces the set of questions from all teams, wi, who is new, asks if there are "defined points a and b? or is it for any point, a and b?" and dg (oldtimer) states that "there were definite points originally" and es adds that "but we are just assuming points are there, right now". Dg adds "but the question asked if there were solutions or an equation to find A and B if they had any location" (pointing to his own prior posting) (Is this skip-continuing?). Gd, who just joined asks as well "what are the points?" to which dragon responds "I dont remember / but they were pretty random" See further data. Then they explore for a bit question 6 where you can go off the edge and come back somewhere else but find it "too complicated" so they drop it See data.
Then they agree to work on problem 7 (What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)?). First they want to pick some points and three people place points on the grid resulting in a number of point arrangements. Here we have a bridging episode where dr narrates what es and she did last time (303/304 drago: last time, me and estrick came up / that...). There are some difficulties with the other members understanding dg's report but they work it out (See full analysis of this bridging episode). Dr, who is the one mostly driving the team, tries different candidate formulas without explicitly mentioning the one he thought in session I:
341 dragon: so ) 342 mathwhiz344: it's like, you can't walk in water, and the lines are dry lines 343 dragon: lets also say 344 dragon: that A is point (0,0) 345 gdog: k 346 dragon: so 347 dragon: the shortest distance was 6 over and three down... 348 estrickmcnizzle: yes 349 dragon: we need to find a relationship between the numbers 350 estrickmcnizzle: correctomundo 351 mathwhiz344: yup 352 dragon: like x1, y1, x2, y2 353 gdog: k 354 dragon: but 355 dragon: the relationship needs to work with whatever points 356 dragon: so I guess picking (0,0) was a bad idea, but it still gives a basic idea of what should happen 357 dragon: like 0 + 6 (x1 + x2) or possible absolute value of 0 - 6 ( I x1 - x2 I ) 358 estrickmcnizzle: yea 359 gdog: ya 360 dragon: wait 361 dragon: the first one 362 dragon: O + 6 363 dragon: x1 + x2 364 lemings leaves the room 365 dragon: because absolute value of 0 - -3 = 3 366 dragon: not -3 367 gdog: yes [To 355] 368 mathwhiz344: yeah 369 dragon: yea... 370 dragon: so I guess it is just 371 dragon: x1 + x2, y1 + y2... 372 dragon: but for some reason I don't believe that it is true... 373 mathwhiz344: we could test with some other points 374 dragon: ok 375 mathwhiz344: lets try 376 gdog: ok 377 gdog: how do we clear the canvas
So, for some reason, perhaps the new arrangement of points and where they located the origin, dr and the team are led to a different formula: x1 + x2, y1 + y2. (It seems as if somewhere Dr (and the rest) thought that they needed a formula to take the coordinates of the first point and then produce the coordinates of the second one, using it? Maybe not.) In any event, Dr isn't completely sure ("for some reason I don't believe that it is true") so they decide to try the formula with other points, so they clear the canvas and create a new arrangement of points with the origin in the bottom left corner of the grid and two points at 3,3 and 9,8. They find out that the original formula did not work, but they find a modification that does. Is this "local continuity"?? Notice how Drago marks his "initial suggestion" today as wrong, and then presents the final correct formula as a past thing, a recovered: IT WAS X
424 dragon, 21:02 (12.05): so my initial suggestion was wrong
433 dragon, 21:03 (12.05): I get it now 434 dragon, 21:03 (12.05): I think 435 dragon, 21:04 (12.05): it was absolute value x1-x2, absolute value y1-y2 436 dragon, 21:04 (12.05): because 437 dragon, 21:04 (12.05): length is always positive
Then they make some "future plans"?
454 dragon: with my original idea of x1 + x2... 455 dragon, 21:05 (12.05): 0 + -3 = -3 456 dragon, 21:05 (12.05): so it didn't work 457 gdog : yea 458 mathwhiz344: yeah, ok 459 dragon: and plus 460 dragon: notice how you can go two ways 461 gdog: yea ok 462 dragon: actually there are a lot more than two...but here are the most simple ones I guess [To 460] 463 mathwhiz344: yeah 464 gdog: yep 465 dragon: so... 466 dragon: either way you go like 5 up and 6 over... 467 mathwhiz344: yeah 468 dragon: but how would you determine whether you were going down or left? I don't know 469 mathwhiz344: and the x1-x2 thingy works 470 gdog: yes 471 gdog: we could solve that next time 472 dragon: yea 473 dragon: I can't think straight right now anyways 474 gdog: lol 478 estrickmcnizzle: no doubt no doubt peac out peace out 479 estrickmcnizzle: leaves the room 480 mathwhiz344: cya all next week
Interestingly, es is very silent during this session, even after dr's narrative about their prior activity.
Session III
Fa joins the team for the first time. At the beginnign there seems to be an agreement that they are going to work on question 2 (number of paths) but when fa asks if they "want to first see the distance between points A and B first?" the two questions seem to get combined.
Notice how GD asks the team to select an origin (gdog, 20:22 (18.05): so where's the origin...) a "practice" the team developed in the last session
Fa is in fact very active and introduces some of the ideas he explored with Rw in Session II of team 1 (his first session). He picks a horizontal arrangement of points and wi remarks that "if it's a straight line, it doesn't represent the majority of the lines, though does it?" At the end fa moves the points to where they are not horizontally connected and with wi, try to convince mo (newcomer) that if you follow the grid there can be more than one shortest path between 2 points. For a while they are trying to clarify if you do have to follow the grid lines. Fa is the one who suggest that you do, more emphatically. The moderator posts a textbox with the original problem description, sort of clarifying that point. Fa sees that as validation. Mo then shifts and starts working on different grid cases ("a one by one square has two paths"). Fa states that to have a formula you need "BLAH = blah / where BLAH = to the distance between the points / and blah = to the number of paths." Here Mo exhibits what might be "solution fitting" instead of "problem solving" even though he is exploring the problem: "can we find 13 paths in this rectangle (a 2 by 3 rectangle) / If so, then X squared + Y squared = the number of paths"
What happens in the rest of the session, I think is a very good case of how extremely difficult intersubjective meaning making can be. There is a lot of individual reasoning externalized but through answers (I see 6, I see 9, etc.) and only vague terms (e.g. an "x-y turn"). Session 4 could be a very good contrast when a smart way of labeling and counting emerges. REVIEW IN DETAIL
It is interesting how GD's participation in this chat is so very different than in the previous one. FA, on the other hand, is as active here as he was with his previous team (1). Perhaps GD's change is not so surprising if seen as a contributor to a team activity where he is now playing a different "role". At the end he states that MO "was the brains tonight" His contributions are almost all questions
Towards the end of this session fa and Mo create this "projective?" summary in the chat:
meets 8:58:58 PM EDT: okay so... meets 8:59:03 PM EDT: 1by1 --> 2 meets 8:59:13 PM EDT: 2 by 2 ..> 6 Mons 8:59:14 PM EDT: 2 by 1 meets 8:59:19 PM EDT: 3 by 2 --> 8 meets 8:59:22 PM EDT: any pattersns? c344 8:59:22 PM EDT: i'm really sorry, but it's 6 o'clock an i have to go by 6 05 at latest Mons 8:59:28 PM EDT: 3 meets 8:59:38 PM EDT: ? c344 8:59:40 PM EDT: so i'll c you on thursday Mons 8:59:42 PM EDT: I mean that one c344 8:59:49 PM EDT: bye
But it is late, wi has to go, Mo is tired, so they do not continue. Seems like a useful summary that they can restart on Session IV.
Interesting comment by Mo: "I dunno whether my problems developed from my stupidity, my absence for the first 2 sessions, or both"
Session IV
Will they continue on the work they started last time, trying to find a pattern for the number of shortest paths between two points? The moderator tries to steer them in that direction:
114 MFmod: 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 axes 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.
This is a very interesting episode where the team together tries to remember what they did, in the sense of using past resources to constitute a present joint activity See more about this. Specially dr and fa work in great coordination to advanced this exploratory work but the other two team members, gd and es do not get involved so at some point they complain. This is interesting because if it signals that they want to participate, they don't want just the team to find and answer. There is, again, an assessment of the fact that the problem might be too complex.:
218 estrickmcnizzle: we arent getting anything done 219 meet_the_fangs: any suggestion? 220 estrickmcnizzle: i dont know, maybe just a more simple problem 221 estrickmcnizzle: less time consuming 222 gdog: drop the questoin 223 dragon: I think I know the answer... 224 gdog: more simpel one that i can understnad plz :) 225 meet_the_fangs: ask the mod to put up the questions 226 meet_the_fangs: or we can do the summer one 227 meet_the_fangs: wat is it [To 223] 228 dragon: not quite sure... [To 227] 229 MFmod: what would you like? 230 gdog: lol 231 dragon: but it is a series of multiplication 232 gdog: i was watchin gu guys do the work 233 gdog: seems like u got smthign but not enough
Group composition: Stable
Session 1: es dr Session 2: es dr gd* wi Session 3: gd wi fa mo Session 4: es dr gd fa (*) Gd was lv from team 2
Grid-World vs. Diagonals
Session 1: define shortest way (grid) and straight distance (diagonal), work on grid Session 2: grid? Session 3: grid Session 4: 3D grid?
