Diagnosing Teachers’ Multiplicative Reasoning (DTMR) is an NSF-funded project investigating how tests may be built that are suitable for use with large samples of teachers and that provide information about teachers’ capacities to support students’ thinking. In particular, we are developing and evaluating a test form that diagnoses middle grades teachers’ multiplicative reasoning in the context of fractions, decimals, and ratios. The test emphasizes knowledge needed to use problem situations and drawn models for developing arithmetic with rational numbers and proportional reasoning.

The DTMR project promises contributions not only to mathematics education but also to psychometrics. In particular, we are developing our test using a new class of psychometric models called diagnostic classification models (DCMs) that classify examinees on multiple categorical latent variables, or attributes. Although a strong research base exists regarding DCMs, researchers have yet to develop instruments for these models from the ground up. Doing so is essential for learning how well DCMs can perform in applications. We are taking this step and are drawing attributes from the research on students’ and teachers’ reasoning with fractions, decimals, and ratios.

The DTMR project is a collaboration between mathematics education researchers and psychometricians at the University of Georgia, University of Massachusetts Dartmouth, and San Diego State University. If successful, our approach to test development could serve as a model for developing further instruments that diagnose reasoning in other areas of science, technology, engineering, and mathematics (STEM) content areas.