Abstract
Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have been completed in addition to high school preparation. Using multiple linear regression including these measures of prior preparation, we examine the correlation between taking various math courses in college and final exam scores in introductory physics courses at a highly selective west coast university. In physics 1, we find that prior college math coursework is not a predictor of physics 1 final exam score. In physics 2, we find that having taken a course in vector calculus is a strong predictor of physics 2 exam performance (effect size=0.58 standard deviations, p<0.001), even when controlling for students’ physics 1 final exam scores (effect size=0.27 standard deviations, p<0.01). These effect sizes are similar in magnitude to other measures of students’ incoming physics and math preparation. Qualitative analysis of student exams from physics 2 reveal that this “vector calculus gap” is due to differences in reasoning about vectors and geometry and some differences in conceptual understanding of circuits, as vector calculus itself is not required to perform well on the final exam. That is, basic reasoning related to vector calculus appears to be important, but the formalisms of vector calculus do not.Received 10 November 2020Accepted 1 February 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.17.010108Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStudent preparationPhysics Education Research
Highlights
Researchers in physics education research (PER) have recently started to focus on what factors explain the variation in student outcomes on various assessments such as course final exams [1,2,3,4] and concept inventories [5,6,7,8,9]
Because Stanford is a highly selective institution, we might think there would be more variation in SAT and ACT math scores at other schools, and that this factor might be more predictive performance than it is here. These results show that for this student population which calculus courses a student has taken has little to no correlation with physics 1 performance, but vector calculus preparation has a significant correlation with physics
2 performance after controlling for baseline physics preparation. This suggests that a student who starts their college career by taking calculus 1 concurrently with physics 1 may not experience trouble in physics 1, but they might be significantly disadvantaged in physics 2 because they do not have any vector calculus experience
Summary
Researchers in physics education research (PER) have recently started to focus on what factors explain the variation in student outcomes on various assessments such as course final exams [1,2,3,4] and concept inventories [5,6,7,8,9]. These investigations have largely focused on issues of equity—determining whether there are demographic performance gaps in these assessment outcomes, what factors might affect these gaps, and how they can be eliminated.
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