14 - Integrating the History of Mathematics into Activities Introducing Undergraduates to Concepts of Calculus

Summary

Introduction

The history of mathematics may be a useful resource for understanding the processes of formation of mathematical thinking, and for exploring the way in which such understanding can be used in the designing of classroom activities. Such a task demands that mathematics teachers be equipped with a clear theoretical framework for the formation of mathematical knowledge. The theoretical framework has to provide a fruitful articulation of the historical and psychological domains as well as to support a coherent methodology. This articulation between history of mathematics and teaching and learning of mathematics can be varied. Some teaching experiments may use historical texts as essential material for the class, while on the other hand some didactical approaches may integrate historical data in the teaching strategy, and epistemological reflections about it, in such a way that history is not visible in the actual teaching or learning experience.

We used a teaching approach inspired by history. In particular, we used a genetic approach to teaching and learning. According to Tzanakis and Arcavi [17, p. 208]:

It is neither strictly deductive nor strictly historical, but its fundamental thesis is that a subject is studied only after one has been motivated enough to do so, and learned only at the right time in one'smental development. …Thus, the subject (e.g., a new concept or theory) must be seen to be needed for the solution of problems, so that the properties or methods connected with it appear necessary to the learner who then becomes able to solve them. […]