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.
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!