This paper extends prior work establishing an operationalized framework of mathematical sense making (MSM) in physics. The framework differentiates between the object being understood (either physical or mathematical) and various tools (physical or mathematical) used to mediate the sense-making process. This results in four modes of MSM that can be coordinated and linked in various ways. Here, the framework is applied to novel modalities of student written work (both short answer and multiple choice). In detailed studies of student reasoning about the photoelectric effect, we associate these MSM modes with particular multiple choice answers, and substantiate this association by linking both the MSM modes and multiple choice answers with finer-grained reasoning elements that students use in solving a specific problem. Through the multiple associations between MSM mode, distributions of reasoning elements, and multiple-choice answers, we confirm the applicability of this framework to analyzing these sparser modalities of student work and its utility for analyzing larger-scale ($N>100$) datasets. The association between individual reasoning elements and both MSM modes and MC answers suggest that it is possible to cue particular modes of student reasoning and answer selection. Such findings suggest potential for this framework to be applicable to the analysis and design of curriculum.

中文翻译：

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将数学意义上的构架应用于学生作业及其在课程设计中的潜力

本文扩展了先前的工作，建立了物理学中的数学意义生成（MSM）的可操作框架。该框架区分了被理解的对象（物理的或数学的）和用于调解感官过程的各种工具（物理的或数学的）。这导致可以以各种方式进行协调和链接的MSM的四种模式。在这里，该框架适用于学生书面作品的新颖形式（简短答案和多项选择）。在对有关光电效应的学生推理的详细研究中，我们将这些MSM模式与特定的多项选择答案相关联，并通过将MSM模式和多项选择答案与学生用于解决特定问题的细粒度推理元素相链接来证实这种关联。$ñ>100$）数据集。各个推理元素与MSM模式和MC答案之间的关联表明，可以提示学生推理和答案选择的特定模式。这些发现表明该框架可能适用于课程的分析和设计。