Dataset2/D2TASS
From Jsarmi
Contents |
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
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
