Introduction

Since the early 1980s, my colleagues and I have been studying the history of algebraic ideas as a component of our research on the teaching and learning of school algebra. In Filloy, Rojano and Puig [6, ch. 1, ch. 3 and ch. 10], we discuss in some detail in which sense our study of the history of algebraic ideas is made from the point of view of mathematics education. What do we mean by studying the history of mathematics from the point of view of mathematics education? First, we mean that the problems of the teaching and learning of algebra is what determines for us which texts must be sought out in history and what questions we should address to them.

Indeed, in our research on the teaching and learning of algebra we have observed that, when dealing with arithmetic-algebraic word problems or with the solution of equations, pupils use a stratified sign system, with strata that come from their previously acquired vernacular and arithmetic language, and also from the concrete models used in the teaching sequences. As a consequence, we conceive the construction by pupils of the language of symbolic algebra as the final identification, within a single language stratum, of those earlier language strata that are irreducible from one stratum to another until the more abstract language has been developed [6, p. 263, and chapter 6].