Day 39: Confused about Fractions

 

Today in precalculus, I was beat over the head about how important it is for students to truly understand the conceptual underpinnings of learned procedures.  I asked students to evaluate a difference quotient expression where the function was the inverse function:

Simplify the expression  when  :   Then evaluate when x = 3 and h = 0.

Did I learn a lot about what students had memorized poorly as well as misconceptions.  What a great opportunity to explore via asking the right questions their misunderstandings as well as give them tools for figuring things out when they are not sure how the mechanics work.

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This problem also gave us an opportunity to revisit the idea of an undefined value when it is indeterminant in nature; i.e. 0/0 and how that is related to the point discontinuity.  Good stuff today!

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Posted on October 30, 2015, in Uncategorized and tagged , , . Bookmark the permalink. Leave a comment.

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