THE USE OF ITEM RESPONSE THEORY (IRT) TO INVESTIGATE THE HIERARCHICALNATURE OF A COLLEGE MATHEMATICS CURRICULUM

The purpose of this study was to investigate the degree to which an un dergraduate math curriculum matched the item difficulty levels of repr esentative mathematics problems based on that sequence. Following a sy stematic process outlined by Hsu and Shermis, an item bank of 120 item s was developed for placement testing at the undergraduate levels. Ran ks for the final 62 item values were calculated and correlated with th e rank order of the math curriculum sequence. Results suggest a congru ence between curricular sequence and item difficulty levels of problem s based on that sequence. This finding indicates that the linear or hi erarchical assumption concerning the undergraduate-level sequence appe ars to be reasonable. The discussion addresses items that were excepti ons to this trend and summarizes implications for computerized adaptiv e testing.