Math Education Concepts

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Do They Get It? The Instantaneous Rate of Change Exactly

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Continuous Everywhere but Differentiable Nowhere

Today in calculus I wanted to check if students really understood what they were doing when they were finding the instantaneous rate of change. (We haven’t learned the word derivative yet, but this is the formal definition of the derivative.)

So I handed out this worked out problem.

And I had them next to each of the letters write a note answering the following individually (not as a group):

A: write what the expression represents graphically and conceptually

B: write what the notation $latex \lim_{h\rightarrow0}$ actually means. Why does it need to be there to calculate the instantaneous rate of change. (Be sure to address with h means.)

C: write what mathematical simplification is happening, and why were are allowed to do that

D: write what the reasoning is behind why were are allowed to make this mathematical move

E: explain what this number (-1) means, both conceptually and graphically

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Author: Math Education Concepts

I am a Co-founder of and Program Coordinator for Math Corps Philadelphia, a combined academic enrichment and mentoring program. I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I hold a Master of Education degree in Secondary Mathematics and have several years of experience teaching secondary and post-secondary mathematics.

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