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Register a new userDeveloping a reasoning inventory for measuring physics quantitative literacy
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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.
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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.
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.
We are developing a new research based assessment (RBA) focused on quantitative reasoning -- rather than conceptual understanding -- in physics contexts. We rapidly moved administration of the RBA online in Spring 2020 due to the COVID-19 pandemic. We present our experiences with online, unproctored administration of an RBA in development to students enrolled in a large-enrollment, calculus-based, introductory physics course. We describe our attempts to adhere to best practices on a limited time frame, and present a preliminary analysis of the results, comparing results from the online administration to earlier results from in-person, proctored administration. We include discussion of online administration of multiple-choice/multiple-response (MCMR) items, which we use on the instrument as a way to probe multiple facets of student reasoning. Our initial comparison indicates little difference between online and paper administrations of the RBA, consistent with previous work by other researchers.
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.
Science is an inherently quantitative endeavor, and general education science courses are taken by a majority of college students. As such, they are a powerful venue for advancing students skills and attitudes toward mathematics. This article reports on the development and validation of the Quantitative Reasoning for College Science (QuaRCS) Assessment, a numeracy assessment instrument designed for college-level general education science students. It has been administered to more than four thousand students over eight semesters of refinement. We show that the QuaRCS is able to distinguish varying levels of quantitative literacy and present performance statistics for both individual items and the instrument as a whole. Responses from a survey of forty-eight Astronomy and Mathematics educators show that these two groups share views regarding which quantitative skills are most important in the contexts of science literacy and educated citizenship, and the skills assessed with the QuaRCS are drawn from these rankings. The fully-developed QuaRCS assessment was administered to nearly two thousand students in nineteen general education science courses and one STEM major course in early 2015, and results reveal that the instrument is valid for both populations.
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