Surveying Middle-Grades Teachers’ Reasoning About Fraction Arithmetic in Terms of Measured Quantities

The authors report a novel survey that narrows the gap between information about teachers’ knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. Our results provide insight into teachers’ knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling.