发表机构
University of Göttingen; University of Geneva; Friedrich-Alexander-Universität Erlangen-Nürnberg（哥廷根大学; 日内瓦大学; 埃尔朗根-纽伦堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文区分物理方程的六种认识论功能及六种核心策略，为物理方程的感知理解提供系统化词汇，并基于对31位物理学家的调查，指出策略教学需加强。
AI 中文摘要
在物理教学中，方程往往主要被视为获取数值结果的工具。然而，物理学家也使用方程来描述依赖关系、解释这些依赖关系为何成立、预测新情境中会发生什么、根据物理知识检验表达式，以及探索那些并非立即可见的后果。尽管这些用途在物理教育文献中随处可见，但它们尚未被系统地整合在一起，且用于描述它们的术语也仍然不一致。借鉴数学教育中关于符号意识和函数概念的研究，我们区分了物理方程的六种认识论功能：计算、描述、解释、预测、评估和探索。随后，我们描述了实现这些功能的六种策略：量纲分析、数量级分析、协变分析、特例分析、极限情形分析和形式类比，并分别用基础物理中的例子加以说明。为了考察这些策略在学科内的看法，我们调查了一所大学院系中的31位物理学家，涉及其中五种策略。受访者认为这些策略对物理学不可或缺，判断极限情形分析对学生而言比量纲分析更难，并报告他们自己的课程可以投入更多时间在这些策略上。通过区分物理学家使用方程的目的与实现这些目的所采用的策略，本文为物理方程的感知理解提供了词汇，并明确了对这些策略进行显式教学所涉及的内容。
英文摘要
In physics instruction, equations are often treated primarily as tools for obtaining numerical results. Yet physicists also use them to describe dependencies, explain why those dependencies hold, predict what happens in new situations, test expressions against physical knowledge, and explore consequences that are not immediately apparent. Although such uses appear throughout the physics education literature, they have not been brought together in a systematic account, and the terminology used to describe them remains inconsistent. Drawing on research in mathematics education on symbol sense and the function concept, we distinguish six epistemic functions of physics equations: calculating, describing, explaining, predicting, evaluating, and exploring. We then characterize six strategies through which these functions can be realized: dimensional analysis, order of magnitude analysis, covariational analysis, special case analysis, limiting case analysis, and formal analogies, illustrating each with examples from introductory physics. To examine how these strategies are viewed within the discipline, we surveyed 31 physicists at one university faculty about five of the strategies. Respondents regarded the strategies as indispensable to physics, judged limiting case analysis to be more difficult for students than dimensional analysis, and reported that their own courses could devote more time to them. By distinguishing what physicists use equations for from the strategies by which they do so, the paper provides a vocabulary for sensemaking of physics equations and specifies what explicit instruction in these strategies involves.
Comments34 pages, 1 figure, 3 tables
