Joyce Leslie with Elaine Weiland - Columbia High School, South Orange/Maplewood
Teaching Calculus to a Heterogeneous Class
This talk builds upon the talk of the same name that I gave in 2018. I have refined the methodology I described in the 2018 talk and I have been working with a colleague who is using this method for the first time.
After many years of teaching multi-level calculus classes I have been developing an approach which has been successful in focusing on the big ideas in calculus while strengthening student’s algebra skills – skills necessary for applying differential and integral calculus to interesting problems.
I will share how we review functions through a calculus lens, and develop the derivative to promote an understanding of two important ideas that students often struggle with: the derivative is the slope of the tangent to a function at a single point; and the derivative is also a function. This approach develops the idea and mathematics of the derivative incrementally; students develop and explore the algebra of the derivative as they explore this new and powerful idea.
I am drawing upon years of experience teaching a multi-level Calculus class with some students who are very weak in algebra (yes this happens even to accelerated students!), students who have approached learning math in meaningless and formulaic way, and students who found that 4 AP classes was too much, so they dropped from AP Calc to honors.
This year, another colleague, Elaine Weiland, is experimenting with the same approach in her calculus class and will join me to discuss her “first year experience” using it.
I will also share ideas in introducing integral calculus that appear to soften the tedium of adding the areas of a large but limited number of rectangles. Finally, I will conclude with suggestions for teachers that focus on better preparing students to learn calculus.