, Volume 27, Issue 1, pp 59-78

A cognitive gap between arithmetic and algebra

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Abstract

Serious attempts are being made to improve the students' preparation for algebra. However, without a clear-cut demarcation between arithmetic and algebra, most of these undertakings merely provide either an earlier introduction of the topic or simply spread it out over a longer period of instruction. The present study investigates the upper limits of the students' informal processes in the solution of first degree equations in one unknown prior to any instruction. The results indicate the existence of acognitive gap between arithmetic and algebra, a cognitive gap that can be characterized asthe students' inability to operate spontaneously with or on the unknown. Furthermore, the study reveals other difficulties of a pre-algebraic nature such as a tendency to detach a numeral from the preceding minus sign in the grouping of numerical terms and problems in the acceptance of the equal symbol to denote a decomposition into a difference as in 23=37−n which leads some students to read such equations from right to left.

This research was funded by the Quebec Ministry of Education (Fonds FCAR-92-ER-1032).
The authors wish to thank Patricia Lytle for her many helpful suggestions in the preparation of this paper.