The Validity of Cognitive, Affective, and Demographic Variables in the Prediction of Achievement in High School Algebra and Geometry: Implications for the Definition of Mathematical Aptitude

Abstract

For a sample of 300 high school students who had completed two semesters of algebra and two semesters of plane geometry the validity coefficients of each of 21 cognitive measures, three personality factor scales, seven attitude and/or interest measures, two indicators of previous musical experience, and five demographic characteristics were determined with respect to each of five criterion measures. Three stepwise multiple regression analyses were completed, and one-way analyses of variance were carried out on each of the 31 predictor measures to determine whether significant differences were present in mean scores of three subgroups representing distinctly different levels of achievement and teacher-rated aptitude. In general, highest validity coefficients were registered for cognitive measures, although some affective variables contributed significant proportions of variance to the coefficients of multiple determination. Statistically reliable differences among the means of the three subgroups were present for all except one of the cognitive measures but absent for every one of the affective and demographic variables. Language and verbal-oriented tasks appeared to be substantially more prognostic of success in geometry than of success in algebra. Implications for the definition of mathematical aptitude are discussed.