How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling

Abstract

The purpose of this study is to design a modeling task to facilitate students’ inquiries into the chain rule in calculus and to analyze the results after implementation of the task. Researchers have pointed out that students may encounter difficulties in understanding the chain rule due to the formal approaches used to teach and learn this concept. In this study, we take a modeling approach to the teaching and learning of the chain rule by facilitating the generalization of students’ models and modeling activities. We assumed abductive reasoning to be one of the key factors which can support the generalization of students’ models and modeling activities. We believe that analogical reasoning and diagrammatic reasoning are key factors in fostering students’ use of abduction. As a result, we determined that the students’ models and modeling activities were generalized to the chain rule by their use of abductive reasoning, and the students found the chain rule to be a generalized rule for describing changes of various quantities.