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1. A Framework for the Natures of Negativity in Introductory Physics

   White Brahmia, Suzanne; Olsho, Alexis; Smith, Trevor I.; Boudreaux, Andrew (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Unlike physics experts, novices struggle to understand the many roles signed numbers can play in physics contexts, and recent evidence shows that unresolved struggle carries over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects. We contribute to the growing body of research that focuses on student reasoning in a physics context about signed quantities and the role of the negative sign. This paper contributes a framework for categorizing the natures of the negative sign in physics contexts, inspired by the research into the natures of negativity in algebra. Using the framework, we analyze several published studies associated with reasoning about negativity drawn from the physics education and mathematics education research communities. We provide implications for mathematics and physics instruction and further re- search. 

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2. The Physics Inventory of Quantitative Reasoning: Assessing Student Reasoning About Sign

   Olsho, Alexis; White Brahmia, Suzanne; Boudreaux, Andrew; Smith, Trevor I. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   An increase in general quantitative literacy and discipline-specific Physics Quantitative Literacy (PQL) is a major course goal of most introductory-level physics sequences—yet there exist no instruments to assess how PQL changes with instruction in these types of courses. To address this need, we are developing the Physics Inventory of Quantitative Literacy (PIQL), a multiple-choice inventory to assess students’ sense-making about arithmetic and algebra concepts that underpin reasoning in introductory physics courses—proportional reasoning, covariational reasoning and reasoning about sign and signed quantities. The PIQL will be used to not only to assess students’ PQL at specific points in time, but also to track changes in and development of PQL that can be attributed to instruction. Data from early versions of the PIQL suggest that students experience difficulty reasoning about sign and signed quantities. 

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3. A Conceptual Blend Analysis of Physics Quantitative Literacy Reasoning Inventory Items

   White Brahmia, Suzanne; Olsho, Alexis; Boudreaux, Andrew; Smith, Trevor I; Zimmerman, Charlotte (January 2020, Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Reed, Z.; Higgins, A. (Ed.)

   Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the “math world” and “physical world” meet. Physics Quantitative Literacy (PQL) is a set of interconnected skills and habits of mind that support quantitative reasoning about the physical world. The Physics Inventory of Quantitative Literacy (PIQL), which we are currently refining and validating, assesses students’ proportional reasoning, co-variational reasoning, and reasoning with signed quantities in physics contexts. In this paper, we apply a Conceptual Blending Theory analysis of two exemplar PIQL items to demonstrate how we are using this theory to help develop an instrument that represents the kind of blended reasoning that characterizes expertise in physics. A Conceptual Blending Theory analysis allows for assessment of hierarchical partially correct reasoning patterns, and thereby holds potential to map the emergence of mathematical reasoning flexibility throughout the introductory physics sequence. 

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4. Developing a Reasoning Inventory for Measuring Physics Quantitative Literacy

   Smith, Trevor I.; White Brahmia, Suzanne; Olsho, Alexis; Boudreaux, Andrew (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   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 signed quantities. We present preliminary results from approximately 1,000 undergraduate and 20 graduate students. 

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5. Physics Students’ Implicit Connections Between Mathematical Ideas

   Smith, Trevor I; White Brahmia, Suzanne; Olsho, Alexis; Boudreaux, Andrew (January 2020, Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Reed, Z.; Higgins, A. (Ed.)

   The Physics Inventory of Quantitative Literacy (PIQL) aims to assess students’ physics quantitative literacy at the introductory level. PIQL’ s design presents the challenge of isolating types of mathematical reasoning that are independent of each other in physics questions. In its current form, PIQL spans three principle reasoning subdomains previously identified in the research literature: 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 that suggest that students’ responses to PIQL questions do not fit this structure. Groupings of correct responses identified in the data provide insight into the ways in which students’ knowledge may be structured. Moreover, questions with multiple correct responses may have different responses in different data-driven groups, suggesting that the both the answer choice and the context of the question may impact how students (implicitly) relate various ideas. 

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