. Aspects of Factor Analysis Applied to the Force Concept Inventory M. R. Semak and R. D. Dietz Department of Physics and Astronomy University of Northern Colorado, Greeley, CO 80639.
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Aspects of Factor Analysis Applied to the Force Concept Inventory
M. R. Semak and R. D. Dietz
Department of Physics and AstronomyUniversity of Northern Colorado, Greeley, CO 80639
Abstract: The application of factor analysis to the Force Concept Inventory (FCI) has proven to be problematic. Some studies have suggested that factor analysis of test results serves as a helpful tool in assessing the recognition of Newtonian concepts by students. Other work has produced at best ambiguous results. We report on our analysis of over 500 pre- and 400 post-tests. The factor structure is more pronounced in the post-test with a more readily identifiable association between factors and physical concepts.
The exchange of views between Huffman, Heller, Hestenes, and Halloun1,2,3 in the pages of The Physics Teacher back in 1995 brought the concept of factor analysis to the attention of the physics education research community. Recently, Scott, Schumayer, and Gray4 published a detailed account of how they applied factor analysis to investigate how over two thousand students answered the FCI questions after they had completed the mechanics section of an introductory physics course. They determined that five factors could be identified. This agrees in general with our unpublished results. Here we concentrate on comparing student performance on the FCI before and after instruction in mechanics and the consequent evolution of the factor pattern.
The factor analysis was done using the statistics software package, Mplus5, with the WLSMV estimator on tetrachoric correlations and a Quartermin rotation.
The evolution of the FCI results to a situation in which students make more refined associations may be indicative of a mind on the path to grasping certain invaluable physical subtleties. We offer a way to quantify this. Also, given certain loading/correlation values or lack of interpretability, this analysis can help justify examining certain FCI questions as to their effectiveness as a measure of student understanding.
The authors offer great thanks to Susan Hutchinson, Professor of Statistics, Applied Statistics and Research at the University of Northern Colorado for many thoughtful discussions concerning this project.