Qualitative investigation into students' use of divergence and curl in electromagnetism
Qualitative investigation into students' use of divergence and curl in electromagnetism
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DOI：
10.1103/physrevphyseducres.12.020134
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发表时间：
2016-10-19
影响因子：
3.1
通讯作者：
De Cock, Mieke
中科院分区：
文献类型：
--
作者：
Bollen, Laurens;van Kampen, Paul;De Cock, Mieke
许多学生在物理课程中使用数学时遇到了困难。虽然他们通常在死记硬背的数学计算方面受过良好的训练，但他们往往缺乏将所获得的技能应用于物理环境的能力。这种学生的困难在大学生电动力学中尤其明显，因为电动力学在很大程度上依赖于向量微积分的使用。为了深入了解学生的推理时，解决问题的分歧和旋度，我们进行了8个半结构化的个别学生访谈。在这些访谈中，学生讨论了发散和旋度的电磁场使用图形表示，数学计算，和微分形式的麦克斯韦方程。我们观察到，虽然许多学生试图通过绘制电磁场的草图来澄清问题，但他们很难用散度和旋度来解释矢量场的图形表示。此外，有些学生混淆了场线图和场矢量图的特征。通过解释我们的结果的概念混合框架内，我们展示了如何缺乏概念上的理解的矢量算子和图形表示的困难可以占一个不正确的理解麦克斯韦方程的微分形式。因此，需要基于多重表示方法的特定学习材料来阐明麦克斯韦方程。
Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector calculus. To gain insight into student reasoning when solving problems involving divergence and curl, we conducted eight semistructured individual student interviews. During these interviews, students discussed the divergence and curl of electromagnetic fields using graphical representations, mathematical calculations, and the differential form of Maxwell's equations. We observed that while many students attempt to clarify the problem by making a sketch of the electromagnetic field, they struggle to interpret graphical representations of vector fields in terms of divergence and curl. In addition, some students confuse the characteristics of field line diagrams and field vector plots. By interpreting our results within the conceptual blending framework, we show how a lack of conceptual understanding of the vector operators and difficulties with graphical representations can account for an improper understanding of Maxwell's equations in differential form. Consequently, specific learning materials based on a multiple representation approach are required to clarify Maxwell's equations.