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 used 15 years of institutional data at a US-based 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. In other words, students could be using invalid data about their introductory physics performance to make their decision about whether physics is the right field for them to pursue, and those invalid data in introductory physics favor male students. 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.
Physics Inventory of Quantitative Literacy: A tool for assessing mathematical reasoning in introductory physics
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Abstract -
Physical systems are characterized by inherent symmetries, one of which is encapsulated in theunits of their parameters and system states. These symmetries enable a lossless order-reduction, e.g.,via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machinelearning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/ornumerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantlyenhance the interpretability and generalizability of ML-discovered secondary laws. Ournumerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysisenables both deep neural networks and sparse regression to reproduce old results, e.g., Stokes law fora sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction.Our results suggest the need to incorporate other physics-based symmetries and invariancesinto ML-based techniques for equation discovery.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevPhysEducRes.17.020129
