Effects of instruction on pedagogical content knowledge about fractions in sixth-grade mathematics on content knowledge and pedagogical knowledge

Abstract

German pre-service teacher education aims to foster the concurrent formation of content knowledge, pedagogical knowledge, and pedagogical content knowledge. Accordingly, the coordination, sequencing, and prioritization of learning opportunities for the three areas of professional knowledge represent vital issues of the organization of teacher education at German universities. In this context, reanalyzing selected data of a previous experiment, we examined effects of instruction on pedagogical content knowledge about fractions in sixth-grade mathematics on the formation of corresponding content knowledge and generic pedagogical knowledge. Totaling 59 pre-service elementary school teachers, three groups had received seven hours of intervention on either content knowledge, pedagogical knowledge, or pedagogical content knowledge. Analyses of video recordings, ratings of treatment quality, and tests of professional knowledge revealed strong internal validity of the data. We found small effects of instruction on pedagogical content knowledge on the formation of both content knowledge and pedagogical knowledge. However, contrary to our expectations, effects on pedagogical knowledge were more consistent and statistically robust than effects on content knowledge. For the development of pedagogical knowledge in teacher education, this finding highlights the potential of parallel or integrated coursework, in which pre-service teachers use specific instructional strategies and student conceptions as examples to derive generic principles of teaching and learning.