What did you learn?

I had done the app with the quadrilaterals before, but in a different context. Doing it in a new context, thinking about the situation with different questions, made it an entirely different lesson. I learned that it can sometimes be a really good thing to use the same materials in different ways, to give students a chance to see that there are many ways to use and approach the same problem/situation/tools.

What questions do you still have?

One thing that struck me right off from the reading was the paragraph on page 25 talking about how some problems are framed toward algebraic thinking and others toward geometric, but that it can be difficult to see how to think the other way in each. That made me wonder if this was because it’s difficult to write problems in such a way that both kinds of thinking seem an equally good choice, or if something else was behind it.

How can it apply to classroom practice?

Aside from what I mentioned in the first answer, I am also thinking I might try to design some tasks for my students that suggest both algebraic and geometric solutions, to see if students choose to solve them geometrically. I am teaching algebra and advanced algebra. I could see my advanced algebra students perhaps using some geometry, as they have already studied it, but I am not sure about the algebra students. I’d like to give them the opportunity, though.

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