Abstract Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms . Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.

Anastasios Kapodistrias

John Airey

European Journal of Physics

EUROPEAN JOURNAL OF PHYSICS 是欧洲物理学会的期刊，其主要任务是协助维持和提高大学和其他高等教育机构的物理教学标准。提交文章的作者必须表明其材料对物理教育的有用性并明确文章的目标读者群体（本科或研究生）。忽略此信息或出版商认为对上述任务没有贡献的提交将不被考虑出版。为此，我们欢迎提供原创见解并旨在加强一个或多个领域学习的文章它们通常应至少包括以下内容之一： 解释当代研究如何帮助理解大学水平的物理学：例如，在学生可以理解的水平上对研究领域的调查，解释它如何说明一些一般原则。对结果推导的原始见解。这些应该是一些普遍的兴趣，不仅仅是对教科书的更正。对新颖的实验室练习的描述，说明了普遍感兴趣的新技术。尤其欢迎那些基于相对便宜的设备的练习。文章具有学术或反思性质，旨在引起物理学兴趣并达到适合物理学的水平学生或应届毕业生。成功和原创学生项目的描述，实验，理论或计算。在物理学生和教师可以访问的水平上讨论物理的历史，哲学和认识论。物理课程和技术的新发展报告用于物理教学。物理教育研究报告：提供与大学物理教学直接相关的原创实验和/或理论研究贡献的文章。

The European Journal of Physics is a journal of the European Physical Society, aimed at assisting in maintaining and enhancing the standards of physics education in universities and other higher education institutions. Authors submitting articles must indicate the usefulness of their material for physics education and clearly specify the target audience of their articles (undergraduate or graduate students). Submissions that omit this information or are deemed by the publisher to contribute little to the aforementioned goals will not be considered for publication. We welcome articles that provide original insights and aim to strengthen learning in one or more areas, typically including at least one of the following: explanations of how contemporary research aids in understanding university-level physics, such as surveys of research fields at a level comprehensible to students, illustrating how it elucidates general principles; original insights into the derivation of results, which should be of general interest rather than mere corrections to textbooks; descriptions of novel laboratory exercises that demonstrate new techniques of general interest, especially those based on relatively inexpensive equipment; articles of an academic or reflective nature that aim to stimulate interest in physics and are suitable for physics students or recent graduates; descriptions of successful and original student projects, whether experimental, theoretical, or computational; discussions of the history, philosophy, and epistemology of physics at a level accessible to physics students and teachers; reports on new developments in physics courses and techniques for physics education; and reports of original experimental and/or theoretical research contributions directly related to university physics teaching.

《European Journal of Physics》是欧洲物理学会的期刊，旨在协助维持和提高大学及其他高等教育机构的物理教学标准。提交文章的作者必须明确其材料对物理教育的贡献，并清楚说明文章的目标读者群体（本科生或研究生）。如果忽略这些信息，或出版商认为提交的内容未能对上述任务做出贡献，则将不予考虑出版。我们欢迎提供原创见解的文章，旨在加强一个或多个领域的学习，通常应至少包括以下内容之一：解释当代研究如何帮助理解大学水平的物理学，例如在学生能够理解的层面上对研究领域的调查，阐明它如何说明一些一般原则；对结果推导的原创见解，这些应是普遍感兴趣的内容，而不仅仅是对教科书的更正；对新颖实验室练习的描述，展示普遍感兴趣的新技术，尤其欢迎那些基于相对便宜设备的练习；具有学术或反思性质的文章，旨在引起物理学的兴趣，适合物理学学生或应届毕业生；成功和原创学生项目的描述，包括实验、理论或计算；在物理学生和教师可以理解的层面上讨论物理的历史、哲学和认识论；关于物理课程和技术的新发展报告，用于物理教学；以及与大学物理教学直接相关的原创实验和/或理论研究贡献的物理教育研究报告。

Category	Quartile
教育学	4
教育学, 学科教育	4
教育学, 物理综合	4

Rearranging equations to develop physics reasoning

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Category	Quartile
PHYSICS, MULTIDISCIPLINARY	4