more_than_meets_the_eye.pdf |
Consider the example of a problem about structure found on pages 38-40 in Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009). Why do you think this problem is considered to be an exemplary model? Discuss your reasons and whether or not you use problems of this type/structure in your classroom.
3 Comments
Rich Fochtman
10/21/2013 12:16:10 pm
I definitely believe that this is an excellent problem. It is a great way to introduce and reinforce the idea of polynomials. This problem requires students to think "outside of the box." It supports the idea of multiple solution strategies and supports the upper levels of Webb's Depth of Knowledge Spectrum. I do have a hard time picturing my inclusion Algebra I class generating these types of responses. Some of these students are extremely low functioning.
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Amanda Olson
10/25/2013 10:30:11 pm
I couldn't agree with you more, Rich. I would love to have that type of conversation with my students. It would show that they understand how to calculate results given a function, and how to relate algebraic functions through the interpretation of their graphs. I do feel that some of my gifted students could come to this conclusion, but they only make up a tiny part of my classes. I would be afraid that the rest of my students would be staring off into space, and I would lose their attention. It would be something I could try in a small group instruction and get more beneficial results.
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Maria Hausman
10/23/2013 04:29:34 am
This is an exemplary problem because it shows how a linear function is a type of polynomial and how different functions can be used to represent or fit certain values or data. In calculus, we actually do the opposite and linearize curves because every curve looks like a line if you zoom in close enough. Seeing structure is easier at the higher levels of mathematics because you have a greater picture of how the mathematics connects and works at each level. Using algebra to show structure in numbers is more realistic than showing them structure in functions in the Algebra I class.
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