Date of Award

Spring 1984

Project Type

Dissertation

Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

Abstract

The purpose of this study was to develop covariance structural models that would explain, in terms of orthogonal latent variables, the correlations observed among mathematics achievement and participation measures and related cognitive and affective variables. A random sample of college calculus students (N = 268; 124 females and 144 males) was administered: (1) a battery of cognitive tests, including measures of spatial-visual ability, field independence/field dependence, and logical reasoning; and (2) a battery of affective scales, including measures of attitude toward mathematics, confidence, perceived usefulness of mathematics, effectance motivation, and locus of control. Measures of previous academic achievement and participation in mathematics and science, and future academic plans, as well as achievement in the calculus course itself were recorded. The sample was then split into two equal-sized subsamples.

Using one subsample, a test of the hypothesis that males and females have the same covariance structure for the measures was performed. A significant difference (p < .0001) was found. Separate orthogonal factor models were developed for males and females based on these sample correlations. Sample correlations from the second subsample were used to evaluate the adequacy of the developed models by application of Factorial Modeling, a parameter estimation and confirmatory technique for orthogonal factor models. There was evidence of a reasonable fit for both models. Comparison of the two models revealed that academic experience and preparation were clearly the two most important factors in explaining variance in calculus achievement for both males and females, while the affective and cognitive factors contributed very little to variance in calculus achievement. The most profound differences between males and females were found in the affective domain, with the effects of perceived usefulness of mathematics on other affective variables being much stronger for males than females. Slight sex differences were found in the correlational structure of cognitive measures. The results implied that, at least at the level of college calculus, special programs aimed towards changing attitudes, or towards improving cognitive skills such as spatial ability, should not be expected to have a transfer effect to calculus achievement.

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