Cognitive and metacognitive characteristics of eighth grade students' mathematical problem solving

Abstract

The purpose of this study was to investigate the cognitive and metacognitive characteristics of eighth grade students in mathematical problem solving. Differences among high achieving (HA), average achieving (AA), low achieving (LA), and learning disabled (LD) students ( N = 60) on measures of mathematical achievement; reasoning; mathematical problem solving; and strategy knowledge, use, and control were studied. One-way analyses of variance and multivariate analyses of variance were employed to detect differences on a variety of dependent variables derived from a reasoning test, mathematical achievement tests, and a structured interview. Results indicated that LD and LA students differ significantly from AA and HA students in both general mathematical achievement and mathematical problem solving. Another finding suggested that poor problem solving performance of LD students may be related less to computational errors than to other factors such as prediction and selection of appropriate operations for solving problems. Finally, the results suggested that LD students are less aware of problem solving strategies than their peers and may be deficient in regulating strategy selection and application when solving mathematical problems.