  Analysis of institutional data for physics majors showing predictive
relationships between required mathematics and physics courses in various years
is important for contemplating how the courses build on each other and whether
there is need to make changes to the curriculum for the majors to strengthen
these relationships. We use 15 years of institutional data at a large research
university to investigate how introductory physics and mathematics courses
predict male and female physics majors' performance on required advanced
physics and mathematics courses. We used Structure Equation Modeling (SEM) to
investigate these predictive relationships and find that among introductory and
advanced physics and mathematics courses, there are gender differences in
performance in favor of male students only in the introductory physics courses
after controlling for high school GPA. We found that a measurement invariance
fully holds in a multi-group SEM by gender, so it was possible to carry out
analysis with gender mediated by introductory physics and high school GPA.
Moreover, we find that these introductory physics courses that have gender
differences do not predict performance in advanced physics courses. Also,
introductory mathematics courses predict performance in advanced mathematics
courses which in turn predict performance in advanced physics courses.
Furthermore, apart from the introductory physics courses that do not predict
performance in future physics courses, there is a strong predictive
relationship between the sophomore, junior and senior level physics courses.
