Physical Sciences and Mathematics Commons^™

Developing Understanding Of The Chain Rule, Implicit Differentiation, And Related Rates: Towards A Hypothetical Learning Trajectory Rooted In Nested Multivariation, Haley Paige Jeppson

Theses and Dissertations

There is an overemphasis on procedures and manipulation of symbols in calculus and not enough emphasis on conceptual understanding of the subject. Specifically, students struggle to understand and correctly apply concepts in calculus such as the chain rule, implicit differentiation, and related rates. Students can 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 created a hypothetical learning trajectory (HLT) rooted in nested multivariation for students to …