Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic

Abstract

Questions concerning the emergence and development of algebraic thinking in a problem-solving context oblige us to reflect, firstly, on the nature of the problems that are given to students and on their relative difficulty, and secondly, on the repertory of procedures available for handling them. More specifically, given the arithmetic experience students have already acquired in problem solving when algebra is introduced, an analysis of the problems presented in the two domains (arithmetic and algebra) is essential. Confronting their spontaneous arithmetic reasoning in these problems with that which is normally expected in algebra, we can get a better understanding of the fundamental changes required of pupils in the passage from one mode of treatment to the other (conflicts, necessary adjustments, new constructions). Any didactic setting (choice of appropriate situations and interventions) necessarily relies upon this knowledge.