用物理中的数学分析问题解决：通过授权的认识论框架
Analyzing Problem Solving Using Math in Physics: Epistemological Framing via Warrants
摘要：
发展物理学专业知识需要学习有效和高效地使用数学，应用于物理环境。这样做涉及协调各种概念和技能，包括数学处理，计算，将辅助信息与数学混合，以及从数学中读出物理含义，反之亦然。从中级水平的学生解决小组问题的录像观察，我们注意到，学生经常“卡住”使用有限的一组技能或推理，没有注意到，一套不同的工具（他们拥有并知道如何有效地使用）可以快速，轻松地解决他们的问题。我们把学生对某种知识的感知/判断称为认识论框架，这种知识在特定情况下是适当的。虽然认识论框架通常是不明确的（甚至是无意识的），但在小组解决问题的情况下，学生有时会对如何进步产生分歧。在这些分歧中，他们提出明确的理由或论据来支持他们的观点。针对数学在物理问题解决中的应用，我们提出了一个分类系统，物理学生的认股权证。这种分析为他们的认识论框架提供了切实的证据。
英文摘要：
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical processing, computation, blending ancillary information with the math, and reading out physical implications from the math and vice versa. From videotaped observations of intermediate level students solving problems in groups, we note that students often "get stuck" using a limited group of skills or reasoning and fail to notice that a different set of tools (which they possess and know how to use effectively) could quickly and easily solve their problem. We refer to a student's perception/judgment of the kind of knowledge that is appropriate to bring to bear in a particular situation as epistemological framing. Although epistemological framing is often unstated (and even unconscious), in group problem solving situations students sometimes get into disagreements about how to progress. During these disagreements, they bring forth explicit reasons or warrants in support of their point of view. For the context of mathematics use in physics problem solving, we present a system for classifying physics students' warrants. This warrant analysis offers tangible evidence of their epistemological framing.
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