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Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. 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. 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 algebra 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.
One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills invo
Computational Thinking (CT) is still a relatively new term in the lexicon of learning objectives and science standards. There is not yet widespread agreement on the precise definition or implementation of CT, and efforts to assess CT are still maturi
A goal of Introductory Physics for Life Sciences (IPLS) curricula is to prepare students to effectively use physical models and quantitative reasoning in biological and medical settings. To assess whether this goal is being met, we conducted a longit
Energy is a complex idea that cuts across scientific disciplines. For life science students, an approach to energy that incorporates chemical bonds and chemical reactions is better equipped to meet the needs of life sciences students than a tradition
Incorporating computer programming exercises in introductory physics is a delicate task that involves a number of choices that may have a strong affect on student learning. We present an approach that speaks to a number of common concerns that arise