Free Ideas and Connecting as Shape-Shifting

Posted: November 28, 2013 in The root of the matter

When I read the title to this chapter, I balked: shape-shifting?! How is the ability of a being to physically transform into another form or being have ANYTHING to do with mathematics? I closed the book. Then, I took a moment to reflect on the title…and postulated that maybe we are not talking about the ability for someone to shift into another form but that we are talking about looking at mathematics as a shape shifter; as it can take many different forms, and have many varied outcomes. Furthermore, when we view mathematics as a shape shifter, we see the need to incorporate more problem solving and open ended questions into our curricula. I read the chapter, and discovered this was Jennifer’s reasoning.

Jennifer begins by explaining that “free ideas” (ideas written in the moment) are very important and highlight the need for individual and group collaboration when problem solving. Jennifer structured a problem as an individual activity, and first had students write out their “free ideas” as individuals. Then, students were grouped together and must collaborate-they had to look at each other’s ideas and understand that someone might have a differing or even conflicting idea than their own idea. Shape shifting comes into play when individuals came together as groups and had to find something that both of the graphs had in common (held true to both). Groups had to shift their free ideas. I really appreciate Jennifer’s theory, and I feel that it is applicable to all subjects. I also feel this to be a good lesson to teach students social responsibility and open communication when we interact with one another (your idea is challenged and you need to shift your idea so it holds true).

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