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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Notes
In the book, L’arithmétique des écoles (1927), we find the following definition of algebra which illustrates well the role it played in teaching: “Algebra is a science which simplifies problem solving and generalizes solutions by establishing formulas to solve problems of the same type.” This role was put into practice in problems without numeric data and which were explicitly aimed at a general solution as, for example, the following problems: “A sum of money is divided between two children such that one receives twice what the other gets. How much did each receive?” “Two cyclists set off in the same direction with one traveling a certain number of kilometers more than the other. What is the distance between them after a certain number of hours?”
For an analysis of problems involving different types of relations between the quantities (transformation problems, rate problems, comparison problems,…), see Bednarz et al., 1992; Bednarz & Janvier, 1994.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bednarz, N., Janvier, B. (1996). Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic. In: Bernarz, N., Kieran, C., Lee, L. (eds) Approaches to Algebra. Mathematics Education Library, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1732-3_8
Download citation
DOI: https://doi.org/10.1007/978-94-009-1732-3_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-4168-0
Online ISBN: 978-94-009-1732-3
eBook Packages: Springer Book Archive