A theory of algebra-word-problem comprehension and its implications for the design of learning environments.

A tutoring approach is derived from a model of problem comprehension, based on the van Dijk and Kintsch (1983; Kintsch, 1988) theory of discourse processing. A problem statement is regarded as a text from which the student must glean propositional and situational information and make critical inferences. The competent student must coordinate this information with known problem models so that formal (i.e., algebraic) operations can be applied and exact solutions can be obtained. We argue that this task is a highly reading-oriented one in which poor text comprehension and an inability to access relevant long-term knowledge lead to serious errors. In particular, poor students often omit from their solutions or misspecify necessary mathematical constraints that are based on reading inferences needed to describe fully the problem situation. Furthermore, formal algebraic expressions are so abstract that their meaning is often elusive; this contributes to mistranslations and misinterpretations. The competent app...

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