Framework for the natures of negativity in introductory physics

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

Physics Inventory of Quantitative Literacy: A tool for assessing mathematical reasoning in introductory physics

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 involved in reasoning productively about physics quantities, which is different from either understanding of physics concepts or problem-solving abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL) as a tool for measuring Quantitative Literacy, a foundation of mathematical reasoning, in the context of introductory physics. We present the development of the PIQL and evidence of its validity for use in calculus-based introductory physics courses. Unlike concept inventories, the PIQL is a reasoning inventory, and can be used to assess reasoning over the span of students’ instruction in introductory physics. Although mathematical reasoning associated with the PIQL is taught in prior mathematics courses, pretest and post-test scores reveal that this reasoning is not readily used by most students in physics, nor does it develop as part of physics instruction—even in courses that use high-quality, research-based curricular materials. As has been the case with many inventories in physics education, we expect use of the PIQL to support the development of instructional strategies and materials—in this case, designed to meet the course objective that all students become quantitatively literate in introductory physics

Toward a framework for the natures of proportional reasoning in introductory physics

We present a set of modes of reasoning about ratio and proportion as a means of operationalizing expert practice in physics. These modes, or natures of proportional reasoning, stem from consideration of how physicists reason in context and are informed by prior work in physics and mathematics education. We frame the natures as the core of an emerging framework for proportional reasoning in introductory physics, that will categorize the uses of proportional reasoning in introductory physics contexts, and provide guidance for the development of reliable assessments. We share results from preliminary assessment items indicating that university physics students have difficulty interpreting and applying ratios in context

Scientific abilities and their assessment.

The paper introduces a set of formative assessment tasks and rubrics that were developed for use in an introductory physics instruction to help students acquire and self-assess various scientific process abilities. We will describe the rubrics, tasks, and the student outcomes in courses where the tasks and rubrics were used