  The Physics Inventory of Quantitative Literacy (PIQL), a reasoning inventory
under development, aims to assess students' physics quantitative literacy at
the introductory level. The 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, 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.
