Educational Studies in Mathematics

, Volume 27, Issue 1, pp 59–78 | Cite as

A cognitive gap between arithmetic and algebra

  • Nicolas Herscovics
  • Liora Linchevski
Article

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.

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Nicolas Herscovics
    • 1
    • 2
  • Liora Linchevski
    • 1
    • 2
  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada
  2. 2.School of EducationHebrew UniversityJerusalemIsrael

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