Mental constructions formed in the conceptual understanding of the chain rule

Abstract

This paper reports on how first year engineering University of Technology students, in South Africa conceptualised mathematical learning in the context of calculus with specific reference to the chain rule. Mental constructions made are analysed using reflective abstractions at the heart of which is APOS (Actions-Process-Object-Schema). This was a qualitative study where mental constructions made within twelve groups of 76 first year engineering students were analysed using a proposed initial genetic decomposition. The Triad was later used to analyse the constructions made in learning and understanding the chain rule. Results indicated that students could use and understand the chain rule even though they did not understand the composition of functions. This helped to inform pedagogy to be used in order to enable the students to understand the concept of the chain rule and improve their understanding in calculus.