A cognitive gap between arithmetic and algebra
 Nicolas Herscovics,
 Liora Linchevski
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Serious attempts are being made to improve the students' preparation for algebra. However, without a clearcut 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 prealgebraic 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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 Title
 A cognitive gap between arithmetic and algebra
 Journal

Educational Studies in Mathematics
Volume 27, Issue 1 , pp 5978
 Cover Date
 19940701
 DOI
 10.1007/BF01284528
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Authors

 Nicolas Herscovics ^{(1)} ^{(2)}
 Liora Linchevski ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Statistics, Concordia University, Montreal, Canada
 2. School of Education, Hebrew University, Jerusalem, Israel