Dataset1/D1T1SS
From Jsarmi
Contents |
Group Trajectory
Summary
Session I
Very democratic. Most of the session, the team orients to the grid as having diagonals and representing the normal geometric world with slope, triangles, etc. They produce the following list of questions mostly presented on the chat:
(C/W*d) Do the points have (X,Y) values (rw) (Briefly in a textbox as "Is there a cartesian plaine to this grid or not") ( /W) wat do we do with the points? (mp) (C/W*s) So we can find the distance between them by doing the distance formula (rw/mm) (C/W*s) Lets make a right triangle with (the points) We know what the hypotenuse is so lets find what sides A and B are (rb) (C/W*s) slope of line AB (mm) (C/ ) altitude to hypoteneuse (mp) (C/ ) try finding the area of a circumscribed circle (mm) (C/ ) inscribed circle? (mp) (C ) quickest route from a to b (rw) (*s) Stated as solutions on the whiteboard; e.g distance between points = rt. 52
Session II
Only rw comes back and a new participant joins: fa. Rw welcomes him. Moderator presents the following collection of questions:
Team 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? Moderator Questions inspired in Teams work 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?
Rw remarks that "these are our questions." Moderator encourages them to "invent new questions or try to answer the questions you already have" Fa remarks that the points are missing. They create two points that are NOT in the same locations as in session I (in contrast to what many other teams did). Since they draw a diagonal (again) the moderator, as in session I, remarks that this is a different "world." Following this comment Fa draws the staircase, deletes it and then draws the vertical and horizontal sides of the triangle (ABX). Interestingly, rw (oldtimer) is the one that suggest that they calculate the straight distance. Fa asks "diagonally or on the line" but Rw (after 10 secs) says "diagonally". Perhaps because the points are in a different place it makes sense to calculate the distance again? They calculate the diagonal distance using Pythagorean theorem and label it on the whiteboard's diagram. Then Fa suggests that they work on the circumscribed triangle (Q#5). They create the diagram of a circumscribed circle, draw some lines but then "get stuck" and Fa suggests doing a different problem (after all rw had said that he wanted to do the circle problem only if fa knew how to).
They move to question 1. Interestingly, it seems as if they are working on 2 different grids (the original and a new one) and talking across their diagrams without realizing it. At the end, it seems as if drawing a path that is the shortest between the points they are considering is sufficient answer to question 1 (what is the shortest path along the grid between the two points?). Then they move to question 2, but this time they seem to be working on the same grid. Fa starts drawing paths and counting but Rw complains that that is not "Efficient" (it is not efficient to just sit there and count). Fa agrees but he has "an organized way of counting" -doubts- then mentions algebra. Interestingly, the paths they are considering are not shortest paths, nor are they of the same length??? Fa suggests permutations and "branching off" Rw seems to be following but then Fa accepts that it is going to get "really messy" (/right/maybe not actually/it is it is) so they drop it because time is running out.
Notice that Fa goes on to join Team 5 in session III and he introduces a similar arrangement of points (horizontal) and the same way of clustering paths of different length. He also mentions permutations as a way to find the number of paths. (See Team 5 Session 3) Rw comes back to this team in Session III, and mentions Fa's idea about the solution being a permutation (See next section).
Session III
Rw asks other team members who missed the previous session where they were (21 Rweisbac, 19:58 (17.05): hi mathman and mathpudding where were u last time); they allude to technical problems. Sh joins the group for the first time. The moderator makes a recap of what has happened with all teams in the first two sessions (During the first two sessions of this program the groups have at times explored...) and when he asks if anyone thought of any other questions after the last session (131) Rw responds: ITS A PERMUTATION!!! (132). This comes from his work with fa in session 2. Sh asks what Rw meant, but Rw says that he will explain later. Once the moderator sets up the teams task by providing a series of questions for them to select from, Rw initiates the problem-solving activity of the team around the same question (#2) that he and fa had been working on in the previous session (145 so lets draw some points on two diagonal corners). Rw suggests 12^2 but Sh (newcomer) says that he got 11^2 which mm supports. There is little discussion of how these values match the number of paths and they move to question #3 (grid with connected edges).
Rw reminds the group (and specially Sh) that you can't travel on the diagonal (233 we do not need slope because you can't go diagonally you can only go hrizontally or vertically / 257 There us no x axis every x coordinate is equal for three and just for three). Rw seems in charge. He summarizes the answer for 3 which seems to be derived from a very particular arrangement of 2 points aligned horizontally (253 yes for three the distance =hieght because all horizontal distances=0). Rw proposes that they move to #4 and the group seems to agree byt mm states that he did not understand the reason for the answer to #3 (271 mathman i didnt understand the reasoning for this Points to message 257). This reopens problem #3. Rw attempts to explain with some participation of Sh who seem to side with mm, and in the midst of that Tp joins the room. Tp immediately disagrees with Rw's idea that there is no horizontal distance (315 Rw: because there is no horizontal distance on the plaine for this problem / 317 Tp: there is). It is very intersting how Tp takes a very active role right away. He suggests that they view the connected grid differently (328 Tp : could you imagine the grid as a piece of paper and you can connect the two sides makin somethin like a cylinder) and they go with that idea for a while but it is hard to see how mm's original request for clarity, or the divergence of answers for that matter, get resolved. They move to #4 and work on it for a bit but time runs out. Rw invites Tp to come back (422: hey templar come back here on thursday your welcome anytime).
Session IV
Tp does come back. Rw and Sh do not. Moderator frames the initiation activity (54): 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. However, after this, the moderator also introduces the "grid-circle" problem and that is what they mostly concentrate on. They orient to this problem not as a grid-world problem but as a normal geometry problem despite the Moderators interjection (132): hey, guys, do you recall that you cannot go on diagonals Despite this, all they do is compute a number of values in a circle (not a grid-circle) and end the session there. It is a bit surprising that after three sessions and no newcomers the team could not make that distinction. One possibility is that they treated every problem as a separate situation to which they could apply a different logic or for which the "constraints" of the grid world did not necessarily apply. Also, they could see both perspectives (grid/no grid) as overlapping?
Group composition: Semi-Stable
Session 1: ma mp rw Session 2: rw fa Session 3: ma mp rw s tp Session 4: ma mp tp(L) tf(N) (L) Late at 8:31:54 PM (N) Did not participate in problem solving activity
Grid-World vs. Diagonals
Session 1: Starts with diagonals, thanks to moderator grid perspective Session 2: Moderator frames grid, rw diagonals, fa puzzled, diagonals and grid coexist Session 3: Explicit mention: you cant' go on diagonals BUT??? Session 4: Back to diagonals, circles, triangles, etc. no grid
