Seeing through Symbols: The Case of Equivalent Expressions.

Abstract

While going through the research literature on learning and teaching algebra, one is often reminded of the old story about a person who knew a dozen of languages but remained silent all his life just because he had nothing to say in any of them. Time and time again, researchers tell us about students who, even if quite proficient in manipulating algebraic symbols, do not seem able to use formulas as tools for meaningful communication. In particular, mastery of the rules of syntax is only rarely accompanied by an ability to justify these rules. The following excerpt from a conversation with a twelve-year-old student who had just completed an introduction to algebra is not likely to surprise an experienced teacher (I is the interviewer; Gi is the student):

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