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TagExponents in math teaching

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African American smiling woman math teacher stands at black board with pointer.

Reviving the Relational View of Mathematics

Unfortunately, some textbooks teach number rules rather than relationships, so students may not know why the rule matters

While helping a friend’s teenage son with math, I was perusing the textbook used. I was dismayed by the presentation of the topic of translating graphs. More than that, I believe the issue reflects some general problems with how mathematics is typically presented to high school students. Specifically, the text addressed how to do graph transformations for exponential functions. That is, if you have a function with the form y = a ⋅ bx (where a and b are constants), how would you create a new equation whose graph was moved up, down, left, or right? The method the book proposed, while technically correct, misses a huge opportunity to help students. The book presents a general form for transforming exponential…