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The Physics Inventory of Quantitative Literacy (PIQL), a reasoning inventoryunder development, aims to assess students' physics quantitative literacy atthe introductory level. The PIQL's design presents the challenge of isolatingtypes of mathematical reasoning that are independent of each other in physicsquestions. In its current form, the PIQL spans three principle reasoningsubdomains previously identified in mathematics and physics education research:ratios and proportions, covariation, and signed (negative) quantities. Animportant psychometric objective is to test the orthogonality of these threereasoning subdomains. We present results from exploratory factor analysis,confirmatory factor analysis, and module analysis that inform interpretationsof the underlying structure of the PIQL from a student viewpoint, emphasizingways in which these results agree and disagree with expert categorization. Inaddition to informing the development of existing and new PIQL assessmentitems, these results are also providing exciting insights into students'quantitative reasoning at the introductory level.

Using psychometric tools as a window into students' quantitative reasoning in introductory physics