学生在数学和物理背景下思考散度和旋度
Student thinking about the divergence and curl in mathematics and physics contexts
摘要：
物理系本科生在理解数学工具和将数学知识应用于物理环境方面存在困难。使用基于学生访谈和开放式问题的书面答复的调查报表，我们调查了数学和物理学生中关于向量场的散度和旋度的正确和不正确概念的流行率。我们比较和对比前指令的反应，从中级E&M学生在KU鲁汶和圣安德鲁斯大学，与后指令的反应，从圣安德鲁斯的学生就读于向量微积分课程。这些学生群体之间的差异主要是在与物理相关的概念和向量场的图形表示方面。我们的比较前和教学后的反应，从E&M的学生表明，他们的理解的分歧和旋度显着改善，在大多数地区，虽然没有那么多的期望。
英文摘要：
Undergraduate physics students are known to have difficulties with understanding mathematical tools, and with applying their knowledge of mathematics to physical contexts. Using survey statements based on student interviews and written responses to open-ended questions, we investigated the prevalence of correct and incorrect conceptions regarding the divergence and curl of vector fields, among both mathematics and physics students. We compare and contrast pre-instruction responses from intermediate-level E&M students at KU Leuven and the University of St Andrews, with post-instruction responses from St Andrews students enrolled in a vector calculus course. The differences between these student populations were primarily in areas having to do with physics-related concepts and graphical representations of vector fields. Our comparison of pre- and post-instruction responses from E&M students shows that their understanding of the divergence and curl improved significantly in most areas, though not as much as would be desired.
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