From Jsarmi

Revision as of 21:17, 21 November 2007

Group Trajectory

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

Group composition: Stable

 Session 1:  bw   qs   az
 Session 2:            
 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

 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

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

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?