Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument

This study extends prior efforts to assess mathematical knowledge for teaching (MKT) by advancing the MKT-Fractions instrument, focusing specifically on teachers’ knowledge for teaching fractions. Building an earlier measure centered on Knowledge of Content and Students (KCS), this phase integrates items targeting Specialized Content Knowledge (SCK) and Knowledge of Content and Teaching (KCT). Drawing on responses from 103 preservice teachers across two teacher preparation programs, we employed Rasch modeling to examine evidence for internal structure and item functioning. Results indicated strong item reliability, unidimensionality, and a coherent item hierarchy aligned with a construct map that represents the developmental trajectory of knowledge needed to teach fractions. The instrument effectively differentiated item difficulty across domains without significant variation in performance across programs. These findings support the use of the MKT-Fractions instrument as a tool for assessing preservice teachers’ readiness and for informing teacher education practices focused on fraction instruction.