Abstract
Research about education in mathematics is influenced by the ongoing dispute about qualitative and quantitative research methods. Especially in the domain of professional knowledge of teachers one can find a clear distinction between qualitative, interpretive studies on the one hand and large-scale quantitative assessment studies on the other hand. Thereby the question of how professional knowledge of teachers can be measured and whether the applied constructs are developed on a solid theoretical base is heavily debated. Most studies in this area limit themselves to the use of either qualitative or quantitative methods and data. In this chapter we discuss the limitations of such mono-method studies and we show how a combination of research methods within a “mixed methods design” can overcome these problems. Thereby we lay special emphasis on different possibilities a mixed methods approach offers for a mutual validation of both qualitative and quantitative findings. For this purpose, we draw on data and results coming from an empirical study about a teacher training program in mathematics, where quantitative data measuring the development of professional knowledge of student teachers were related to qualitative in-depth interviews about the training program.
Keywords
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- 1.
Beck and Maier distinguish slightly differently between the “normative” and the “interpretive paradigm” going back on Wilson (1970).
- 2.
It should be clear from the preceding discussion that this is not so much a problem of quantitative research per se—it may occur if one strictly follows a hypothetico-deductive approach (which is for many reasons advisable if quantitative methods are applied) and if researchers lack empirically contentful hypotheses, workable theories and/or specific knowledge about the domain under study. The latter is often not so much the fault of uninformed researchers but a consequence of the fact that social action is often structured by culture-bound rules and “local knowledge”.
- 3.
A methodological adjustment of the treatment groups by measures of treatment evaluation (e.g. propensity score matching) has been omitted so far as the use of elaborate statistical methods to determine treatment effects appeared disproportionate due to the small group sizes. Furthermore, the group differences in Abitur grades are not significant and the relationship of school-related pre-cognitions considering the attendance at Advanced or Basic course merely reflects the pre-cognitions of local convenience samples.
- 4.
It needs to be noted that performance on the level of individual items can vary due to chance and thus should not be over-interpreted.
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Kelle, U., Buchholtz, N. (2015). The Combination of Qualitative and Quantitative Research Methods in Mathematics Education: A “Mixed Methods” Study on the Development of the Professional Knowledge of Teachers. In: Bikner-Ahsbahs, A., Knipping, C., Presmeg, N. (eds) Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_12
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DOI: https://doi.org/10.1007/978-94-017-9181-6_12
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