The Diagnosing Teachers’ Multiplicative Reasoning (DTMR) tests are designed for in-service middle grades teachers and emphasize knowledge needed (a) to think about fractions and proportional relationships as quantities and (b) to use drawn models (e.g., number line and area models) as the basis for solving problems. Given that the tests focus on content knowledge, these test could be used with preservice teachers as well. One test is on fractions and one is on proportional relationships.
The DTMR tests are designed for use with diagnostic classification models, a family of recently developed psychometric models. They use categorical latent variables called "attributes" to model the probability of an item response, and they generate attribute mastery profiles for each examinee that summarize areas of strength and weakness. The attached document describes the attributes used for the DTMR project in detail and demonstrates how they are grounded in the
research literature. To date, the test on fractions has been calibrated using a large national sample. The project hopes to calibrate the proportional reasoning test by Summer 2013.