Reflective Abstraction and Mathematics Education: The Genetic Decomposition of the Chain Rule-Work in Progress

Abstract

Students have experienced difficulty in understanding and using the chain rule. This study aims at assisting the students to understand and apply the chain rule and thus inform the author’s teaching for future learning of students. A questionnaire will be designed to explore the conceptual understanding of the concept of the chain rule by first year university of technology students using APOS (action-processes-objects-schema) which proposes in the form of the genetic decomposition a set of mental constructions that the students might make in order to learn the concept of the chain rule in calculus and accessing it when needed. This instrument will be used to collect data on how students learn derivatives of trigonometric functions in calculus, using the chain rule. This will be with a view to clarify their understanding of the composition of functions, derivative and the chain rule. The study consists of two phases, both using a qualitative approach. A structured way to describe an individual student’s understanding of the chain rule is developed and applied to analyzing the evolution of the understanding for each of 30 first year students. Other ways to collect data include tests, written exercises and classroom observations. The purpose of the questionnaire will be to establish the correlation between the students’ ability to deal with composition of functions and using the chain rule successfully. Students (n = 10) will then be interviewed based on their written responses to elicit their thinking involved when answering. The analysis of written responses and interviews should establish whether the instrument provided substantial information for identification of certain mental constructions that the researches proposed to consider.