Interactive Graphics System for the Study of Variance/Covariance Structures ofBivariate and Multivariate Normal Populations

摘要

This research created a graphics oriented computer program which was used as partof a Visualization, Verbalization, Algorithization and Mathematization (VVAM) learning protocol. The curriculum for this research was the study of variance/covariance structures of bivariate and multivariate normal populations. The program displays the geometric images corresponding to the various possible covariance structures. These images facilitate and encourage experiment-based self discovery learning. The program encourages the student to take an active role in their own education. The program created is self contained, calculating all the statistical values it requires to create the various geometric images. The students have complete control in choosing what scenario they wish to study. The program was tested using four specific scenarios which represented a cross section of all possible scenarios. Within each of these scenarios were several options which were designed to encapsulate different aspects of the curriculum. The results of the research showed that the program, under the aegis of the VVAM, does facilitate the visualization and verbalization of the complex mathematical concepts associated with covariance structures. The learning environment was found to promote the creation of new knowledge on three distinct levels.... Statistics, Learning, Computer, Covariance, Variance, Graphics, Geometric Approach.