Abstract by Haley Jeppson
Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation
Students struggle to conceptualize and correctly apply concepts in calculus such as the chain rule, implicit differentiation, and related rates. Students also learn mathematics more deeply when they make connections between different mathematical ideas. I have hypothesized that students can make powerful connections between the chain rule, implicit differentiation, and related rates through the mathematical concept of nested multivariation. Based on this hypothesis, I have created a Hypothetical Learning Trajectory (HLT) rooted in nested multivariation for students to develop an understanding of these three topics. In this study, I explore an HLT through a small-scale teaching experiment with first year calculus students using tasks based on the HLT. I address how students used nested multivariation in developing these three concepts, what understandings they developed, and how the HLT might be improved for the future.