Exploring Teachers' Pedagogical Content Knowledge of Teaching Fractions

The quality of teachers' mathematical knowledge for teaching (MKT) is critical for effective teaching and mathematical learning of students. However, most efforts on measuring MKT tend to focus on teachers' content knowledge (CK), with less attention to teachers' pedagogical content knowledge for teaching (PCK). This study reports on our initial efforts to develop and pilot a measure for assessing teachers' PCK for fractions. Analysis of cognitive interviews from two expert teachers combined with Rasch modeling of 85 pre-service and in-service teachers was conducted to examine validity evidence for the PCK-Fractions measure. Results provide useful validity evidence for the initial validity argument of the measure. Namely, evidence suggests differences between pre-service (PSTs) and in-service teachers' (ISTs) scores based on their professional level (junior PSTs, senior PSTs, & ISTs). Implications of this and additional validity evidence suggest a measure useful for assessing the effect of teacher education and professional experience initiatives, as well as indicators for revising this initial measure.