Importance of math prerequisites for performance in introductory physics

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 $\mathrm{size}=0.58$ standard deviations, $p<0.001$), even when controlling for students’ physics 1 final exam scores (effect $\mathrm{size}=0.27$ 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.

Figure 1

Rubric for free response question 1.

Figure 2

Rubric for free response question 5.