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 collection of questions. 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
Session IV
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
