Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

TLDR

Concerns in the US and Europe question whether teacher training equips educators with the professional knowledge needed for consistently high‑quality instruction. This study examines how teachers’ content knowledge and pedagogical content knowledge influence high‑quality instruction and student progress in secondary‑level mathematics. A one‑year, representative German study of Grade 10 classes and their mathematics teachers collected data to assess these relationships. Pedagogical content knowledge is distinct from content knowledge and has a substantial positive effect on students’ learning gains, mediated by cognitive activation and individualized support.

Abstract

In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers’ content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers’ pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains that was mediated by the provision of cognitive activation and individual learning support.