AN INVESTIGATION OF THE ROLE OF SPATIAL PERFORMANCE, LEARNING STYLES, AND KINETIC IMAGERY IN THE LEARNING OF CALCULUS
Abstract
This study was designed to (1) investigate the preference calculus students have for linguistic versus graphical presentations of precalculus and calculus concepts and how that preference is related to spatial and class performance, (2) investigate the effects that viewing of kinetic images via computer-generated graphics and filmloops during the study of elementary calculus concepts has upon student achievement, and (3) investigate the relationship between achievement in elementary calculus and spatial performance. The Purdue Visualization of Rotations Test (PVRT) was used to identify twenty high spatial and twenty low spatial college calculus students. Ten students of each type were randomly assigned to each of two groups. The experimental group was taught the basic concepts of the use of derivatives to graph rational functions using filmloops and computer-generated graphics in addition to the textual material used with the control group. Instruments T4 and MLSQ were developed to measure student performance after the treatment and to assess student preference for mode of presentation, respectively. Analyses of variance revealed no significant difference ((alpha) = 0.25) between methods and no significant interaction for either instrument. There was a large difference between scores on T4 by spatial type with high spatial students tending to perform better and a significant difference ((alpha) = 0.05) between the distributions of MLSQ scores for the two spatial types with the high spatial students preferring graphical presentations more often. Significant correlations ((alpha) = 0.01) were obtained between PVRT and T4 (r = 0.56) as well as PVRT and MLSQ (r = 0.40). Twenty students were interviewed about their performance on T4, MLSQ, or both. These interviews provided insight into learning styles, imagery, and performance of these students. Information about the role of visuals in the learning of calculus was also obtained. Some calculus students have a strong preference for graphical presentations and others strongly prefer linguistic presentations. The majority seem to synthesize the two types of presentations with one of the two playing a dominant role. Spatial performance does affect student performance with those of high spatial performance tending to score higher and tending to prefer graphical presentations.
Degree
Ph.D.
Subject Area
Mathematics education
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.