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Barbara K. Flexer

The relative importance of a group of cognitive variables in explaining the algebra achievement of high-ability eighth graders was investigated. Stepwise multiple regression analyses identified algebra prognosis test scores and performance in seventh-grade mathematics as the most influential predictors of algebra grades, whereas mathematics problem solving, the prognosis test, and IQ were shown to best predict achievement on a standardized algebra test. A discriminant analysis demonstrated the importance of the prognosis test in discriminating between students who successfully completed first-year algebra and those who dropped out of or failed the course. Although the study showed no sex difference in algebra achievement test scores, girls in the sample attained higher percentage grades for the course.

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James J. Roberge and Barbara K. Flexer

Previous investigations of the effects of field dependence-independence or the level of operational development on the mathematics achievement of children in the lower elementary school grades have involved the administration of concrete operational tasks (e.g., classification, conservation, and seriation). The present study was designed to examine the influence of these factors on the mathematics achievement of sixth, seventh, and eighth graders by using formal operational tasks (i.e., combinations, propositional logic, and proportionality). Results were analyzed using total mathematics achievement test scores as well as scores on subtests of computation, concepts, and problem solving. Field-independent students scored significantly higher than field-dependent students on the total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher than their low-operational peers on all tests. Educational implications of the findings are discussed.