In recent years, there has been an increased interest in conceptual blending in physics and mathematics education research as a theoretical framework to study student reasoning. In this paper, we adapt the conceptual blending framework to construct a blending diagram that not only captures the product but also the process of student reasoning when they interpret a mathematical description of a physical system. We describe how to construct a dynamic blending diagram (DBD) and illustrate this using two cases from an interview study. In the interview, we asked pairs of undergraduate physics and mathematics students about the physical meaning of boundary conditions for the heat equation. The selected examples show different aspects of the DBD as an analysis method. We show that by using a DBD, we can judge the degree to which students integrate their understandings of mathematics and physics. The DBD also enables the reader to follow the line of reasoning of the students. Moreover, a DBD can be used to diagnose difficulties in student reasoning.

中文翻译：

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动态概念融合分析可在数学和物理相结合的同时为学生推理过程建模，以热方程为例

近年来，对物理和数学教育研究中的概念融合作为研究学生推理的理论框架的兴趣日益浓厚。在本文中，我们采用概念混合框架来构建混合图，该混合图不仅可以捕获产品，而且还可以解释学生在解释物理系统的数学描述时进行推理的过程。我们描述了如何构建动态混合图（DBD），并使用访谈研究中的两个案例对此进行了说明。在访谈中，我们询问成对的物理和数学专业的本科生有关热方程边界条件的物理含义。所选示例显示了DBD作为分析方法的不同方面。我们展示了通过使用DBD，我们可以判断学生对数学和物理的理解融合的程度。DBD还使读者能够遵循学生的推理路线。此外，DBD可用于诊断学生推理中的困难。