Date of Award

Fall 1980

Project Type


Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy


The primary purpose of this study was to investigate the effects of spatial training upon calculus achievement, spatial visualization, and tendency and ability to visualize solids of revolution in calculus, for college males and females. A random sample of 250 first-semester calculus students at the University of New Hampshire was apportioned into seven experimental groups, each containing males and females. Students were pretested on precalculus background, spatial visualization, and calculus background, and were assigned to one of three treatment conditions: audiovisual spatial training (AV), audio-vidual-tactual spatial training (AVT), and a control condition. The spatial training materials were organized into six slide-tape modules which were presented in programmed form. The content of the six modules was: two-dimensional spatial tasks, three-dimensional spatial tasks, rotations from two- into three-dimensional space, area discrimination, and the development of three-dimensional images from two-dimensional images. The AVT training was distinguished from the AV training by the inclusion of supplementary manipulatives and models, which corresponded to the spatial tasks presented on the slides.

Following the training period, students were posttested on spatial visualization. Calculus achievement was assessed by means of course grades. In addition, each student was assigned a score representing tendency and ability to visualize solids of revolution in calculus problems. That score is referred to as VSRSC.

The analysis revealed significant correlations between spatial visualization and precalculus scores, between spatial visualization and VSRSC scores, and among the mathematics achievement measures. Multivariate and univariate analyses of covariance indicated several significant main effects and interaction effects. A significant sex difference favoring males was found on the spatial visualization posttest; a significant sex difference favoring females was found on a calculus test of applications of the definite integral to area, volume, and work problems; and a significant treatment-by-sex interaction on the calculus total grade suggested that the AV training was more influential for females than for males, and that the AVT training was more influential for males than was the AV training. A 2 x 2, treatment-by-sex analysis of variance of VSRSC resulted in a significant treatment effect favoring the groups which received spatial training, as well as a significant treatment-by-sex interaction indicating a more positive influence of training on VSRSC scores for females than for males. A significant gain in spatial visualization scores from pretest to posttest, for the entire sample was demonstrated using a t-test.

The results suggest that sex differences in college calculus students on measures of calculus achievement may be less pronounced than in other populations, and that in fact, females studying calculus may possess ability characteristics which distinguish them from other females. The combined experience of taking first-semester calculus and participating in concurrent course work appears to enhance spatial ability, and may do so in different ways for males and females. Spatial training may play a role in the solution of certain types of calculus problems, and that role may be more influential for females than for males. Other hypotheses and questions suitable for future research in the areas of spatial ability, mathematics achievement, and the study of sex differences are generated.