Multidimensional data visualization in the statistical analysis of curricula

Abstract

A method has been developed for the analysis of curricula via the statistical analysis of examination results. It is based on the visualization of a set of academic subjects characterized by their correlation matrix obtained on the basis of examination results. The method integrates two methods for data mapping: Sammon's mapping and the self-organizing map (SOM). These are based on different principles, and, therefore, they supplement each other when used jointly. The results of analysis of the correlations of subjects by one of the factor analysis methods—centroid method—are presented for comparison. The main proposition that grounds the method of analysis is that, in most cases, a student gets similar marks in the related subjects. If a student is gifted for the humanities, he will be successful in most of the humanities. Mathematical aptitude yields good marks in mathematical subjects. When analysing the curriculum of studies, we know in advance which subjects are mathematical and which of the humanities. However, there are subjects that cannot be assigned to any well-defined class of subjects. Computer science subjects may serve as an example of such subjects. The proposed method made it possible to evaluate the level of mathematization of different computer science subjects or their nearness to the humanities. The necessary data were the results of examination, only. This level is never quantified, but it may be estimated considering the whole complex of subjects that compose the curriculum. The investigator draws qualitative conclusions about the graphically presented numerical results. The analysis gives us a detailed knowledge of the interaction and similarity of subjects. The knowledge makes a basis both for revising the present curriculum of studies and preparing new ones.