Abstract
Students of Grade 7 were given a test followed by individual interviews; at the end of Grade 8 the same students were subject to an analogous test and interviews. Each student had to simplify certain algebraic expressions. This article is focussed on what types of procedures were used by the students performing the task and how they were explained during the interviews. The author identifies seven types of procedures used by students, labelled: (A) Automatization, (F) Formulas, (GS) Guessing-Substituting, (PM) Preparatory Modification of the expression (this includes a subtype: Atomization), (C) Concretization, (R) Rules, (QR) Quasi-rules. Part of the students' procedures led to correct results, others were wrong. Most of the procedures appeared spontaneous in the sense that they had not been taught in the classroom. Prior to the tests, the teachers (in accordance with the curriculum) had done their best to explain the validity of algebraic transformations by referring to the commutativity of addition and multiplication, distributivity, and to geometric interpretation; however, the interviewees (even explicitly asked) seldom used such arguments.
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Demby, A. ALGEBRAIC PROCEDURES USED BY 13-TO-15-YEAR-OLDS. Educational Studies in Mathematics 33, 45–70 (1997). https://doi.org/10.1023/A:1002963922234
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DOI: https://doi.org/10.1023/A:1002963922234