We present a framework designed to help categorize various sense making moves, allowing for greater specificity in describing and understanding student reasoning and also in the development of curriculum to support this reasoning. The framework disaggregates between the mechanisms of student reasoning (the cognitive tool that they are employing) and what they are reasoning about (the object). Noting that either the tool or object could be mathematical or physical, the framework includes four basic sense making modes: Use of a mathematical tool to understand a mathematical object, use of a mathematical tool to understand a physical object, use of a physical tool to understand a mathematical object, and use of a physical tool to understand a physical object. We identify three fundamental processes by which these modes may be combined (translation, chaining, and coordination) and present a visual representation that captures both the individual reasoning modes and the processes by which they are combined. The utility of the framework as a tool for describing student reasoning is demonstrated through the analysis of two extended reasoning episodes. Finally, implications of this framework for curricular design are discussed.

中文翻译：

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物理数学意义的分类框架

我们提出了一个旨在帮助对各种有意义的动作进行分类的框架，以便在描述和理解学生推理以及开发支持这种推理的课程时提供更大的特异性。该框架将学生推理的机制（他们正在使用的认知工具）和他们的推理依据（对象）进行分类）。注意到该工具或对象可能是数学的或物理的，该框架包括四种基本的意义理解模式：使用数学工具来理解数学对象，使用数学工具来理解物理对象，使用物理工具来实现。了解数学对象，并使用物理工具理解物理对象。我们确定了可以组合这些模式的三个基本过程（翻译，链接和协调）），并提供一个直观的表示形式，它捕获了各个推理模式及其组合的过程。通过分析两个扩展的推理情节，证明了该框架作为描述学生推理的工具的实用性。最后，讨论了该框架对课程设计的影响。