Promoting Prospective Mathematics Teachers' Understanding of Derivative across Different Real-life Contexts

Abstract

This study investigates prospective secondary school mathematics teachers' developing conceptions about the meaning of derivative (as rate of change) while working on a series of tasks involving different non-motion real-life contexts. The study was conducted by employing a case study method. The participants of the study were 25 prospective secondary school mathematics teachers enrolled in the mathematics teaching methods course. A series of contextual tasks involving different real-life situations about derivative was designed and implemented in the form of problem-based learning as a regular part of the course. Pre and post questionnaires, written group solutions to the tasks, individual reflection papers, and video-recorded online classroom discussions were the data sources. A constant comparative analysis method was employed in analysing the data. The results showed that prospective teachers have difficulties in interpreting the meaning of derivative in different real-life contexts. While they were frequently using “amount of change” and “slope” interpretations, they started to use “rate of change” interpretation. However, the classroom discussions showed that most of the prospective teachers were using the “rate of change” expression as a memorized term without engaging in its contextual meaning. We made some inferences about the teaching and learning of derivative and also the professional development needs for teachers.