DERIVATIVES AND APPLICATIONS; DEVELO PMENT OF ONE STUDENT'S UNDERSTANDING

Abstract

This paper reports on a longitudinal observation study characterising student’s development in their understanding of derivatives. Through the Dutch context-based curriculum, students learn this concept in relation to applications. In our study, we assess student’s understanding. We used a framework for data analysis, which focuses on representations and their connections as part of understanding derivatives, and it includes applications as well. We followed students from grade 10 to grade 12, and in these years we administered four task-based interviews. In this paper we report on the development of one ‘average’ student Otto. His growth consists of an increasing variety of relations, both between and within representations and also between a physical application and mathematical representations. We also find continuity in his preferences for and avoidances of certain relations.