From Jsarmi

Revision as of 23:27, 5 December 2007

Group Trajectory

 Session 1: Dyad from same school, technical problems, f2f work produces some reported results
 Session 2: Feedback attended to
 Session 3: 
 Session 4: 

Group composition: Stable/ Technical Problems

 Session 1:  tc   ro
 Session 2:           
 Session 3:  
 Session 4:  
  
 (L)                   (N)  

Session I

Work done F2F is reported to the chat... how is this "reporting" deployed? Initially Tc attempts a direct dialog style:

 tcmath 5/9/06 5:12:43 PM EDT: So, Rook, we have the fact that squares is defined as a function of N by the partial sum quadratic for the sequence 1,2,3,4,5....

This whiteboard textbook was created by tcmath before the previous message:

  sequence:1,2,3,4,5
  partial sum sequence:1,3,6,10,15
  Function is quadratic, so these eqautions are true:
  a1^2+b1+c=1

but later, because of technical problems, the style changes to a plural narrative:

 jsarmi 5/9/06 5:19:46 PM EDT: It seems as if the system is giving Rook a lot of trouble, isn't it, tcmath?
 jsarmi 5/9/06 5:21:41 PM EDT: tcmath?
 tcmath 5/9/06 5:24:36 PM EDT: I'm done for now
 tcmath 5/9/06 5:24:48 PM EDT: I was working with Rook since his computer wasn't working
 jsarmi 5/9/06 5:24:57 PM EDT: I see
 tcmath 5/9/06 5:25:16 PM EDT: We figured out the equation for squares, and we should easily solve it for sticks as well in the same manner

Feeback

(No Feedback in between sessions)

Session II

Technical problems seemed to be resolved. Dyad must be in same room or connected otherwise, no greetings. Tc starts with this message after which the board is CLEARED of everything that was posted in the previous session.

tcmath 5/11/06 5:04:13 PM EDT: Okay. You must agree that the squares is defined by the equation squares=1/2N^2+1/2N. 

Tcmath attempts to paste the problem table into a textbox but the formatting does not transfer and he ends up with along list instead.

Are we doing Session 1 still? Lack of coordination?:

tcmath 5/11/06 5:09:53 PM EDT: I'm setting up the problem on the whiteboard
 p M M M
 tcmath 5/11/06 5:10:08 PM EDT: 
 p M M M M
 Rook 5/11/06 5:11:18 PM EDT: Did you solve the sticks as function of N yet?
 Rook 5/11/06 5:11:35 PM EDT: I think the  equation is x^2+3x
 Rook 5/11/06 5:11:50 PM EDT: Found the equation...
 tcmath 5/11/06 5:11:54 PM EDT: The seperate lines here represent the sticks you would "add" when N increases by 1.
 p M M
 Rook 5/11/06 5:12:11 PM EDT: What are you doing?
 p M M
 Rook 5/11/06 5:12:17 PM EDT: !!
 Rook 5/11/06 5:12:40 PM EDT: Are we doing Session 1 still?
 tcmath 5/11/06 5:12:43 PM EDT: Okay. The top 4 sticks are there by default; you have to have them.

Linking Sequences: Squares then Sticks

How do they constitute the two to be related?

tcmath 5/11/06 5:26:20 PM EDT: So, for squares we found the partial sum equation for the sequence 1,2,3,4,5... Now we find it for the sequence 2n+2 (after distribution)

Then we will be done

Definitively in the same room but conversing/coordinationg on the chat. Notice long gaps between postings

 tcmath 5/11/06 5:28:30 PM EDT: Here, you can use my TI-84 to do the whole regression thing and I'll do it algebraically on paper. Tell me your results.
 Rook 5/11/06 5:29:34 PM EDT: oh...
 Rook 5/11/06 5:30:36 PM EDT: x^2+3X
 tcmath 5/11/06 5:31:51 PM EDT: Then we're done with the pattern: 

Typing on the Wiki

 tcmath 5/11/06 5:42:32 PM EDT: we're here--we're just typing up our patterns observed on VMT Wiki

Reading the Wiki, Finding the "next" topic

 jsarmi 5/11/06 5:47:28 PM EDT: Well.. any ideas suggested by the notes from other groups in the Wiki?
 tcmath 5/11/06 5:48:02 PM EDT: Well, they figured out the same thing for squares, but their approach was unique for the sticks.
 tcmath 5/11/06 5:48:33 PM EDT: We used the same technique for both teh sticks and the squares (partial sums on a sequence), while they used two different ones.
 jsarmi 5/11/06 5:48:41 PM EDT: how about the values of the table?
 Rook 5/11/06 5:49:02 PM EDT: they got the same
 Rook 5/11/06 5:49:33 PM EDT: and we checked with the other groups--same answers...
 tcmath 5/11/06 5:49:38 PM EDT: They were ahead one row, though, starting with row 4 since it was the first row without a given answer.
 Rook 5/11/06 5:49:53 PM EDT: on the 1st website (VMT Wiki)
 jsarmi 5/11/06 5:50:12 PM EDT: Oh... I see
 tcmath 5/11/06 5:50:31 PM EDT: For our discussion: I think that mathematiciancs would usually generalize a lot, finding a method that fit the problem even if initial values were changed.
Rook 5/11/06 5:50:46 PM EDT: Yeah
Rook 5/11/06 5:50:54 PM EDT: that's the next topic

Our method would still work

tcmath 5/11/06 5:51:39 PM EDT: For example, if every column in the diagram increased by 2 instead of 1.
 Rook 5/11/06 5:52:20 PM EDT: I think that the polygons/figures have to be regular to have a chance at this problem, of course--or else there's really no pattern
 Rook 5/11/06 5:52:39 PM EDT: Assume that the rest of the answers would just be doubled?
 tcmath 5/11/06 5:52:57 PM EDT: If this happened, then our method would still work becuase we would determine the original sequence and then generalize it in a closed form, quadratic equation, for the partial sums.
 Rook 5/11/06 5:53:02 PM EDT: The 2 wouldn't make a difference really
 Rook 5/11/06 5:53:22 PM EDT: Yeah, or solve it as written, jumping by 2...
 Rook 5/11/06 5:53:37 PM EDT: so, it should also work for n-gons that are regular
 tcmath 5/11/06 5:54:18 PM EDT: Probably not for three since the sticks really depends on the number of squares we're increasing by. In ours, we had 4 in our equation, while if we increased by three, that number would be 10, I think.
 Rook 5/11/06 5:54:34 PM EDT: Yeah, the equation, such as the initial starting point, would have to change to fit more or less starting sticks

Projecting

 tcmath 5/11/06 5:58:42 PM EDT: We should try looking at the specific case of, say pentagons.
 p M
 Rook 5/11/06 5:59:11 PM EDT: Yeah
 Rook 5/11/06 5:59:18 PM EDT: though do you have to leave?
 tcmath 5/11/06 5:59:28 PM EDT: That'll have to wait till next time. I have to leave. 
                                I wonder if we could even replicate the problem with regular pentagons?
 Rook 5/11/06 5:59:45 PM EDT: mb in our spare time we could look at it and talk next session

Feedback

 Dear tcmath and Rook,
 
 We were very interested in the way you combined several approaches to find the formula 
 for the pattern of growth of sticks and squares.   Using a regression method and thinking about 
 the difference between one step of the pattern and the next seem to work very nicely.  
 You also posted very complete descriptions of your ideas on the Wiki. 
 
 In your previous session you started to explore what the patterns would look like with other polygons and in 3-D, 
 and you made a couple of conjectures about them (e.g. “the methods for solving general situations like this would be the same”).   
 For the next step we will encourage you to continue thinking about the different approaches and the problems 
 that you can discover of your own and that are interesting to pursue.  
 
 -The VMT Team

Session III