While the SAT-Math test is designed to measure one “construct” – i.e. overall mathematical aptitude at the High School level, – it surely could be analyzed to reveal different abilities for algebra and geometry, for example. When analyzing a semester-long course, one would naturally expect different abilities on different topics (e.g. energy vs. momentum); on different types of problems (e.g. conceptual vs. calculational), or within one lesson (e.g. Newton’s 2nd law vs Newton’s 3rd law). Hence RELATE has done considerable work on multi-dimensional analyses like factor analysis, or generalizations of IRT where the discriminations or questions and the abilities of students are multidimensional.
BRS12 Multidimensional Student Skill with Collaborative Filtering. Y. Bergner, S. Rayyan, D. T. Seaton, and D. E. Pritchard, Physics Education Research Conference 2012, Philadelphia, PA
PSD 19 Mining Students Pre-instruction Beliefs for Improved Learning Angel Perez-Lemonche, John Stewart, Byron Drury, Rachael Henderson, Alex Shconski, and David E Pritchard LAS 2019 Proceedings
PCP18 Mining Student Misconceptions from Pre- and Post-Test Data. Angel Perez-Lemonche, Byron Coffin Drury, David Pritchard EDM Proceedings 2018 KE Boyer and M Yudelson eds p 449 (2018)
SDW21 Examining the relation of correct knowledge and misconceptions using the nominal response model John Stewart , Byron Drury, James Wells, Aaron Adair, Rachel Henderson, Yunfei Ma, Ángel P´erez-Lemonche, and David Pritchard PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH 17,010122 (2021)