Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects—both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebraic contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond.

中文翻译：

---

入门物理负性本质的框架

数学推理技能是许多物理入门课程（尤其是基于微积分的物理课程）的期望成果。新手可以艰难地理解带符号的数字在物理学中所扮演的许多角色，最近的证据表明，尚未解决的斗争可以延续到随后的物理学课程中。正负物理量在物理学中无处不在，并且该符号具有重要而多样的含义。数学教育研究文献记录了将负数概念化为数学对象的认知挑战，包括专家，历史学家和初学者。我们为物理学领域中规模较小但不断发展的研究做出了贡献，该研究旨在检查学生对有符号数的推理以及在数学模型中对符号的使用和解释的推理。在本文中，我们受到数学教育研究界在代数情境中已建立工作的启发，提出了一种在物理学情境中对负号的各种含义和解释进行分类的框架。这样的框架可以支持创新，可以在入门课程及以后的课程中促进对带符号数量的更深入的数学概念化。