Cognitive Models Underlying Students' Formulation of Simple Linear Equations

Data are presented to show that errors in formulating algebraic equations are not primarily due to syntactic translation, as has been assumed in the literature. Furthermore, it is shown that the reversal error is common even when none of the previously published causes of the error is applicable. A new explanation is required and is proposed in this paper. An examination of students' errors leads us to suggest that students generally construct from the natural language statement a cognitive model of compared unequal quantities. They formulate equations by trying to represent the model directly or by drawing information from it. This hypothesis is supported by research on the comprehension of relationships by linguists, pyscholinguists and psychologists. Data were collected from 281 students in grade 9 in free response format and from 1048 students in grades 8, 9, and 10 who completed a multiple-choice item.

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