Integrated testlets and the immediate feedback assessment technique Am. J. Phys. 81, 782 (2013) Ontario section (OAPT) newsletter www.oapt.ca/newsletter/ Phys. Teach. 51, 382 (2013) Incorporating Sustainability and 21st-Century Problem Solving into Physics Courses Phys. Teach. 51, 372 (2013) Response times to conceptual questions Am. J. Phys. 81, 703 (2013) Can free-response questions be approximated by multiple-choice equivalents? Am.The ability of adult students to reason on the basis of the control of variables was the subject of an extended investigation. This paper describes the part of the study that focused on the reasoning required to decide whether or not a given variable influences the behavior of a system. The participants were undergraduates taking introductory Physics and K-8 teachers studying physics and physical science in inservice institutes and workshops. Although most of the students recognized the need to control variables, many had significant difficulty with the underlying reasoning. The results indicate serious shortcomings in the preparation of future scientists and in the education of a scientifically literate citizenry. There are also strong implications for the professional development of teachers, many of whom are expected to teach control of variables to young students.

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.

Student understanding of the equilibrium coexistence of a liquid and its vapor was the subject of an extended investigation. Written assessment questions were administered to undergraduates enrolled in introductory physics and chemistry courses. Responses have been analyzed to document conceptual and reasoning difficulties in sufficient detail to be of practical use to instructors. Even after instruction on the relevant material, many students fail to recognize that for one-component systems in which a liquid and its vapor coexist in equilibrium, the pressure is controlled solely by the temperature. Although most students seem to realize that vaporization and condensation both take place, few are able to construct a coherent, step-by-step explanation for how dynamic phase equilibrium is established. Implications for instruction are discussed.

Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory physics graphing problems. Here, graduate students are considered experts for the introductory level material, as they often take the role of instructor at large research universities. Drawing on work from Research in Undergraduate Mathematics Education (RUME), we replicated a study of mathematics experts' covariational reasoning done by Hobson and Moore with physics experts [N. L. F. Hobson and K. C. Moore, in RUME Conference Proceedings, pp. 664-672 (2017)]. We conducted think-aloud interviews with 10 physics graduate students using tasks minimally adapted from the mathematics study. Adaptations were made solely for the purpose of participant understanding of the question, and validated by preliminary interviews. Preliminary findings suggest physics experts approach covariational reasoning problems significantly differently than mathematics experts. In particular, two behaviors are identified in the reasoning of expert physicists that were not seen in the mathematics study. We introduce these two behaviors, which we call Using Compiled Relationships and Neighborhood Analysis, and articulate their differences from the behaviors articulated by Hobson and Moore. Finally, we share implications for instruction and questions for further research.

One desired outcome of introductory physics instruction is that students will be able to reason mathematically about physical phenomena. Little research has been done regarding how students develop the knowledge and skills needed to reason productively about physics quantities, which is different from either conceptual understanding or problem-solving abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL) as a tool for measuring quantitative literacy (i.e., mathematical reasoning) in the context of introductory physics. We present the development of the PIQL and results showing its validity for use in calculus-based introductory physics courses. As has been the case with many inventories in physics education, we expect large-scale use of the PIQL to catalyze the development of instructional materials and strategies-in this case, designed to meet the course objective that all students become quantitatively literate in introductory physics. 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.