Slope conception as rate of change starter kit: Malaysian pre-service secondary mathematics teachers’ subject matter knowledge in rate of change

Abstract

Past research on calculus has shown that students often struggle to understand derivatives due to an overemphasis on algebraic manipulation and procedures rather than grasping the underlying concept. A key factor contributing to this challenge is the lack of a solid understanding of slope as a rate of change. Conceptualizing slope as a rate of change is essential, as it serves as the basis for comprehending derivative concepts. To address this gap, our research explored subject matter knowledge of rate of change, specifically focusing on the slope concept, among Malaysian pre-service mathematics teachers. Our research followed a qualitative methodology, conducting task-based interviews with two pre-service mathematics teachers, Zheng and Amitha, who are majoring in mathematics. The interviews included seven tasks related to slope and ratio concepts. The findings revealed inconsistencies in their notion of rate of change, as they have a loose connection between rate of change and slope concepts, along with its multiplicative property. While they recognized that equivalent values of rate of change indicate a constant rate, they did not grasp that slope also represents a rate of change. Their knowledge appeared limited to viewing derivatives as a method to calculate rate of change, without conceiving the changes occurring between quantities and their multiplicative relationship.