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Register a new userThe Physics Inventory of Quantitative Literacy: A tool for assessing mathematical reasoning in introductory physics
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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, pre/post test scores reveal that this reasoning isnt 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.
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In an effort to improve the quality of citizen engagement in workplace, politics, and other domains in which quantitative reasoning plays an important role, Quantitative Literacy (QL) has become the focus of considerable research and development efforts in mathematics education. QL is characterized by sophisticated reasoning with elementary mathematics. In this project, we extend the notions of QL to include the physics domain and call it Physics Quantitative Literacy (PQL). We report on early stage development from a collaboration that focuses on reasoning inventory design and data analysis methodology for measuring the development of PQL across the introductory physics sequence. We have piloted a prototype assessment designed to measure students PQL in introductory physics: Physics Inventory of Quantitative Literacy (PIQL). This prototype PIQL focuses on two components of PQL: proportional reasoning, and reasoning with negative quantities. We present preliminary results from approximately 1,000 undergraduate and 20 graduate students.
We have developed the Physics Inventory of Quantitative Literacy (PIQL) as a tool to measure students quantitative literacy in the context of introductory physics topics. We present the results from various quantitative analyses used to establish the validity of both the individual items and the PIQL as a whole. We show how examining the results from classical test theory analyses, factor analysis, and item response curves informed decisions regarding the inclusion, removal, or modification of items. We also discuss how the choice to include multiple-choice/multiple-response items has informed both our choices for analyses and the interpretations of their results. We are confident that the most recent version of the PIQL is a valid and reliable instrument for measuring students physics quantitative literacy in calculus-based introductory physics courses at our primary research site. More data are needed to establish its validity for use at other institutions and in other courses.
The Physics Inventory of Quantitative Literacy (PIQL), a reasoning inventory under development, aims to assess students physics quantitative literacy at the introductory level. The PIQLs design presents the challenge of isolating types of mathematical reasoning that are independent of each other in physics questions. In its current form, the PIQL spans three principle reasoning subdomains previously identified in mathematics and physics education research: ratios and proportions, covariation, and signed (negative) quantities. An important psychometric objective is to test the orthogonality of these three reasoning subdomains. We present results from exploratory factor analysis, confirmatory factor analysis, and module analysis that inform interpretations of the underlying structure of the PIQL from a student viewpoint, emphasizing ways in which these results agree and disagree with expert categorization. In addition to informing the development of existing and new PIQL assessment items, these results are also providing exciting insights into students quantitative reasoning at the introductory level.
Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational reasoning in introductory physics contexts. We explore one aspect of covariational reasoning: ``goes like reasoning. ``Goes like reasoning refers to ways physicists relate two quantities through a simplified function. For example, physicists often say that ``the electric field goes like one over r squared. While this reasoning mode is used regularly by physicists and physics instructors, how students make sense of and use it remains unclear. We present evidence from reasoning inventory items which indicate that many students are sense making with tools from prior math instruction, that could be developed into expert ``goes like thinking with direct instruction. Recommendations for further work in characterizing student sense making as a foundation for future development of instruction are made.
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.
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