A Comprehensive Hypothetical Learning Trajectory for the Chain Rule, Implicit Differentiation, and Related Rates: Part II, a Small-Scale Teaching Experience
Abstract/Description:
Students learn more deeply when conceptual understanding is at the forefront and connections are made between topics. While previous work has examined the chain rule, implicit differentiation, and related rates separately, we have created a hypothetical learning trajectory (HLT) for these topics to teach them in a conceptual, connected way. In a previous paper we outlined the creation of the HLT based on the construct of nested multivariation (NM). In this second paper, we describe a small-scale teaching experiment done to test the HLT. Our results suggest NM was an appropriate construct to base the HLT on, and we present the students’ developing understandings as they progressed through the HLT. Based on the results, we made final adjustments to the HLT, in preparation for a full-scale classroom teaching experiment.
Presenters:
Steven Jones and Haley Jeppson, Brigham Young University