Validating Psychometric Classification of Teachers' Fraction Arithmetic Reasoning

In prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial interpretations of the reasoning characteristic of each latent class. Our results suggested increasing facility reasoning about fraction arithmetic from one class to the next. The present study contributes two further arguments for the validity of our initial interpretations. First, we administered the same survey to a new sample of future middle grades mathematics teachers before and after 20 weeks of instruction on multiplication, division, and fractions, and we found that from pretest to posttest future teachers transitioned from one latent class to another in ways consistent with increased proficiency in fraction arithmetic. Second, we interviewed 8 of the future teachers before and after the instruction and found that future teachers' reasoning during interviews was largely consistent with our original interpretation of the 3 latent classes. These results provide further support for our original interpretation of the mixture Rasch analysis, demonstrate the utility of our approach for capturing growth and change in future teachers' reasoning during teacher education coursework, and contribute innovative applications of psychometric models for surveying teachers' reasoning at scale.