This doctoral thesis is within the academic field of mathematics education and presents results from both quantitative and qualitative research.
The quantitative part is based on data from 356 teachers answering a test and a questionnaire. Three main findings are reported. First, findings from the test confirm empirically the existence of the constructs of SCK (specialized content knowledge) and CCK (common content knowledge) in a Norwegian context. Second, findings from the questionnaire established the two constructs of rules and reasoning. Third, findings from a study of the connection between beliefs and knowledge indicates that connections between knowledge and both education and experience varies with different emphasis on rules and reasoning.
The qualitative part is the larger part of the thesis. The data in this part comes from videotaping five of the 356 teachers practice, all teaching at upper primary level (grade 5-7, students aged 10-13). All mathematics teaching for one week was filmed, typically four or five lessons of 45 minutes. Also in this part there are three main findings. First, a framework for describing teachers’ comments were developed using a grounded approach. The redirecting, progressing and focusing actions framework consists of thirteen categories describing how teachers use or not use student comments to work with mathematics. Second, a similar framework describing student comments were developed. Third, the categories of teacher and student comments were used to study student comments and the subsequent teacher comments. This revealed how one teacher used redirecting, progressing and focusing actions differently when responding to different types of student comments.
The frameworks developed in the qualitative part are the main contribution to the academic field of mathematics education and might be used both as research tools and in teacher education to understand or change teaching practices.