Learning Functions of Two Variables Based on Mathematical Thinking Approach

Abstract

Multivariable function is one of the most important concepts in the learning of advanced mathematics. We had implemented a teaching approach to support students in the learning of two-variable functions by promoting mathematical thinking in face-to-face Multivariable Calculus classroom. This study investigates the obstacles and difficulties faced by students in the learning of two-variable functions based on the mathematical thinking approach. The findings indicated that students displayed various difficulties in finding the range and sketching the graph of two-variable functions. The students’ difficulties and obstacles such as poor mastery of algebraic manipulation, poor grasp of prior knowledge or lack of it, idiosyncrasy attributed from previous mathematical experience, and restricted mental images of two-variable functions could be classified as difficulties with techniques, concepts, and studying mathematics. Based on students’ responses, the difficulties were considered mainly conceptual in nature and few were related to techniques and studying mathematics.