A Functional Approach to Algebra: Two Issues that Emerge

Abstract

Although the two previous chapters presented in this book report and reflect on research in a functional approach to the introduction of algebra within a computer environment, they differ greatly in what they have chosen to focus on. This commentary chapter will tackle a central issue in each of the chapters. In my comments on the Kieran et al chapter, I will address the authors’ choice of the pointwise approach to functions and offer some suggestions for broadening their research and development program. The question of “real world problems” is central to Heid’s chapter. In my comments on that chapter, I will explore issues around three implicit assumptions concerning real world problems. Examples of students’ work that arose in my own research will be used to explore the issues and raise the questions that emerge in these chapters.