PIQL: A new assessment of mathematical reasoning development in physics instruction

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. We present the PIQL, Physics Inventory of Quantitative Literacy, which is currently under development in a multi-institution collaboration. PIQL assesses students’ proportional reasoning, co-variational reasoning, and reasoning with signed quantities as they are used in physics. Unlike concept inventories, which assess conceptual mastery of specific physics ideas, PIQL is a reasoning inventory that can provide snapshots of student ideas that are continuously developing. Item distractors are constructed based on the different established natures of the mathematical objects in physics contexts (e.g. the negative sign as a descriptor of charge type and the negative sign as indicator of opposition in Hooke’s law). An analysis of student responses on PIQL will allow for assessment of hierarchical reasoning patterns, and thereby potentially map the emergence of mathematical reasoning flexibility throughout the introductory sequence.