Defining Testlets for Measuring Growth in Students' Physics Quantitative Literacy

The Physics Inventory of Quantitative Literacy (PIQL) is a 20-item multiple-choice test that was created to measure students' mathematical reasoning and quantitative literacy in physics contexts across three facets: ratios and proportions, covariation of two or more quantities, and the meaning of negative or signed quantities in various contexts. We have previously established strong evidence for the validity and reliability of the test as a whole, as well as for individual PIQL items. We present results from our recent efforts to define two 12-item testlets (a.k.a. PIQLets) that are statistically and psychometrically equivalent to each other and to the full PIQL. Having two equivalent shorter versions reduces the amount time needed for students and instructors to engage with the test and allows for pre/post testing with minimal repeated items. We detail our evidence for the equivalence of the two PIQLets based on a data set of student responses to the full PIQL, and present preliminary evidence from their use in five physics courses across two universities.