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# 数学代写|数学建模代写Mathematical Modeling代考|MATH4413 Will’s Classroom Observation

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## 数学代写|数学建模代写Mathematical Modeling代考|Will’s Classroom Observation

Will was a member of a different group within the same class. He was often quiet during the discussions that took place. We, therefore, have very few excerpts in which he spoke.

By all outward appearances, there were few opportunities for Will to share his own ideas. He did not assert himself at all. However, when the teacher walked over to his group and asked the group a question, he occasionally answered her questions, especially those directed specifically at him. We infer that “Stay out of Trouble” was the primary structure active for Will for most of the sessions, as his main focus was on avoiding interactions that might lead to conflict. We will provide evidence for this in excerpts of observation and interview data below.

In the following excerpt, occurring at the beginning of the session, it is important to note that one of Will’s group members drew a 40 unit by 10 unit rectangle on chart paper before the teacher walked over. In response to the teacher’s questions about that rectangle, Will made one suggestion to try different numbers. Will’s group members ignored this idea.
Teacher: How can you prove that this is the maximum area?
Will: $\quad$ You can try different numbers and see if [they] will work.
Teacher: Okay, so how would you try different numbers? Do you want to try that and I’ll be back?
Dana: Why we can’t just leave our maximum length like this?
Teacher: I didn’t say you couldn’t leave it like this. I was just asking do you know….how do you know that’s the maximum length?

The other students in the group continued to discuss this with the teacher as Will began to write and draw silently.

We infer that Will’s silent drawing and writing may have been an attempt to fulfill a desire to understand how to construct a rectangle with a perimeter of 100 feet, indicating the activation of “Check this Out”.

## 数学代写|数学建模代写Mathematical Modeling代考|Will’s Retrospective Interview

Retrospective interviews revealed a lot more information about Will’s mathematical understanding, reasons for his lack of social interactions with peers, motivations, emotions and engagement. In this case, the interview was especially important, since Will did not say much, and rarely interacted with peers, during the problem solving session.

During the classroom observation, as noted above, Will’s group member, Dana, only drew one rectangle on his group’s chart paper. This was not the one that Will had drawn on his crumpled up sheet of paper. From Will’s retrospective interview, we found out that he realized that it is possible to construct rectangles with different dimensions for this problem, which indicates a shift in his mathematical thinking.

We are not sure if this mathematical shift occurred during the problem solving session or some time after. Consequently we did not list it on Table 2 . The interview data did reveal that he knew that his rectangle and the rectangle chosen by his group would both have a perimeter of 100 .

By his statements in the retrospective interview, we infer that he did not know that his 30 by 20 rectangle had a greater area than the 40 by 10 rectangle chosen by his group. He believed his solution and the solution chosen by the group were equally likely to be correct. However, he was reluctant for the group to choose his solution, for fear of backlash.
Interviewer: So what made you crumple it up?
Will: $\quad$..I was just thinking not to use it anymore, just use [Ghee’s], just saying, we don’t need it anymore so we just tossed it away.
Interviewer: How did that make you feel?
Will: $\quad$..If they had chosen my wrong one, and the right one they tossed it away, they might’d get mad at me.
Interviewer: Why did you take it back out?
Will: $\quad$ Cause Ms. B wants it, wanted to see…
Interviewer: So how did that make you feel?
Will: $\quad$ That raised up my happiness back for me. Like I said, it, when they chose [Gee’s], my happiness came down a little bit, but when she wanted to see mine, it came up.

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