关于专家在新型绘图任务中推理时数学与物理不可分割性的实证证据
Empirical evidence of the inseparability of mathematics and physics in expert reasoning about novel graphing tasks
AI总结：
本研究通过新型绘图任务证实专家在物理情境中无法脱离物理进行纯数学推理，揭示了数学与物理推理的不可分割性，为教学改进以帮助学生建立联系提供了依据。
摘要：
大学预科数学建模教学通常将数学视为与对现实世界的推理相分离，并且通常将数学推理和对现实世界情境的推理视为建模周期的独立阶段。在本文中，我们提供了有助于表征专家在开发图形模型时如何在物理情境中使用数学的证据。一个重要发现是，基本上没有证据表明专家在处理这些任务时以脱离情境的方式进行推理，相反，他们使用物理推理——要么基于任务情境，要么来自抽象物理模型——来指导他们的数学。物理教师和学生在方法上的差异可能会导致双方期望不匹配并产生挫败感。这项工作丰富了关于数学推理如何在物理中出现的知识体系，并可以帮助研究人员和教师认识到专家数学推理中与现实世界的联系。这可以帮助教师和研究人员更好地开发材料和方法，从而帮助学生也开始建立这些联系。
英文摘要：
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a modeling cycle. In this paper, we present evidence that helps characterize how experts use mathematics in physics contexts while developing graphical models. An important finding is that there was essentially no evidence of experts reasoning in a context-free way with these tasks, but instead they used physical reasoning -- either grounded in the context of the task or from abstract physical models -- to guide their mathematics. The difference in approach of physics instructors and students may lead to a mismatch in expectations, and frustration, for both parties. This work contributes to the body of knowledge about how mathematical reasoning appears in physics, and can help researchers and instructors recognize the connections to the physical world in expert mathematical reasoning. This can help instructors and researchers be better equipped to develop materials and methods that can help students start building those connections as well.
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