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.

中文翻译：

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入门物理的数学前提条件的重要性

以前的工作研究了基于微积分的入门力学（物理1）课程中高中准备与学生成绩之间的关系。在这里，我们将这项工作扩展到基于演算的电和磁（物理2）的性能上，并且除了高中预备课程外，还要研究完成哪些大学数学课程的重要性。使用包括这些预先准备措施的多元线性回归，我们研究了在大学中选择各种数学课程与在高选择性西海岸大学的入门物理课程中的期末考试成绩之间的相关性。在物理学1中，我们发现以前的大学数学课程不能预测物理学1最终考试成绩。在物理学2中$\mathrm{尺寸}=0.58$ 标准偏差， $p<0.001$），即使控制学生的物理成绩1最终考试成绩（效果 $\mathrm{尺寸}=0.27$ 标准偏差， $p<0.01$）。这些效果的大小与学生对即将到来的物理和数学准备的其他衡量方式在大小上相似。对来自物理学2的学生考试的定性分析表明，这种“向量微积分差距”是由于对向量和几何的推理不同，以及对电路的概念理解上的某些差异，因为向量微积分本身并不需要在期末考试中表现良好。也就是说，与矢量演算有关的基本推理似乎很重要，但是矢量演算的形式主义并不重要。