物理高年级学生数学应用的剖析
Unpacking Students' Use of Mathematics in Upper-division Physics
摘要：
在大学一年级之后的物理学研究中-在美国称为高年级，许多学生的主要学习机会来自于解决长期复杂的书本式问题，以及试图通过解决这些问题来理解基础物理学。在高年级的一些研究集中在学生如何使用数学在这些问题，以及学生在前进的道路上遇到什么挑战。关于高年级学生使用数学的情况，有许多不同的研究。这些通常利用两种广泛的方法之一，一些研究人员主要寻找和解决学生面临的挑战，其他人主要致力于解开学生的即时推理。在本文中，我们提出并讨论了这两种方法，然后回顾研究努力，努力连接这两种方法，以使学生的数学使用的意义，以及发现学生遇到的特殊挑战。这些最近的努力代表了一小步，综合这两种方法，我们认为这是必要的，更有意义地影响学生的学习在高年级。我们关闭我们的审查和讨论，为未来的研究问题提出改进建议，供物理教育研究界考虑，同时它的工作，以了解学生如何使用数学在高年级课程。
英文摘要：
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop an understanding of the underlying physics through solving such problems. Some of the research at the upper-division focuses on how students use mathematics in these problems, and what challenges students encounter along the way. There are a number of different and diverse research studies on students' use of mathematics in the upper-division. These typically utilize one of two broad approaches, with some researchers primarily seeking out and addressing challenges students face, and others working chiefly to unpack students' in-the-moment reasoning. In this paper, we present and discuss both approaches, and then review research efforts that strive to connect these two approaches in order to make sense of students' use of mathematics as well as to uncover particular challenges that students encounter. These recent efforts represent a small step towards synthesizing the two approaches, which we argue is necessary to more meaningfully impact student learning at the upper-division. We close our review and discussion with suggested refinements for future research questions for the physics education research community to consider while it works to understand how students use math in upper-division courses.
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