Methodological considerations on investigating teachers’ beliefs of mathematics and its teaching

Our primary concerns are the methodological considerations on investigating teachers’ beliefs of mathematics teaching using a quantitative as well as qualitative approach. However, a discussion of this type cannot be completely detached from the textual determination that beliefs result from. Hereby, Dionne’s and Ernest’s characterizations of beliefs on mathematics served as a theoretical background; the dominant perspectives on mathematics can be described as toolbox aspect, system aspect and process aspect. Originally, our test subjects numbered a total of 13 experienced German mathematics teachers. However, we will limit the scope of the discussion to research on six representative persons. We used three data-gathering methods: questionnaires, videotaped interviews and graphical as well as numerical self-estimations, respectively. In our investigation a comparison of the self-estimations stands in the foreground. Since this information is mainly overlapping, partly redundant and likely contradictory, we have to question the data in order to describe the beliefs of the teachers. The research was conducted during the spring and summer of 1994.