An Investigation of Content Knowledge for Teaching: Understanding its Development and its Influence on Pedagogy

Abstract

This study explores the complex relationship between teachers’ understandings of mathematics and their classroom practices. The study details students’ engagement in a segment of a university course designed to position pre-service teachers to develop a coherent understanding of functions as covariation of quantities. With regards to this instruction, this study was guided by two research questions that dealt with understanding (a) the pre-service teachers’ mathematical development and then (b) how the pre-service teachers’ emerging understanding of function as covariation impact how they envision and enact instruction, with particular emphasis on the pre-service teachers’ ability to orchestrate conceptual conversations about significant mathematical ideas. Analyses highlight the fact that one teaches what they know – pre-service teachers’ particular understandings of mathematical content have a significant impact on their pedagogical conceptualizations of the content. It is these pedagogical conceptualizations of content and the related images that serve to guide the pre-service teachers’ decisions and instructional actions. The study concludes with suggestions for ways in which appropriate pedagogical conceptualizations of the content might be developed.