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Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?

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Abstract

The study tries to show one line of how the German didactical tradition has evolved in response to new theoretical ideas and new—empirical—research approaches in mathematics education. First, the classical mathematical didactics, notably ‘stoffdidaktik’ as one (besides other) specific German tradition are described. The critiques raised against ‘stoffdidaktik’ concepts [for example, forms of ‘progressive mathematisation’, ‘actively discovering learning processes’ and ‘guided reinvention’ (cf. Freudenthal, Wittmann)] changed the basic views on the roles that ‘mathematical knowledge’, ‘teacher’ and ‘student’ have to play in teaching–learning processes; this conceptual change was supported by empirical studies on the professional knowledge and activities of mathematics teachers [for example, empirical studies of teacher thinking (cf. Bromme)] and of students’ conceptions and misconceptions (for example, psychological research on students’ mathematical thinking). With the interpretative empirical research on everyday mathematical teaching–learning situations (for example, the work of the research group around Bauersfeld) a new research paradigm for mathematics education was constituted: the cultural system of mathematical interaction (for instance, in the classroom) between teacher and students.

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Notes

  1. In this paper ‘stoffdidaktik’ is restricted to a certain fundamentalist form of content related mathematical analysis that is based on ideas on the New Math era. Later there have been further developments and modifications of the stoffdidaktik approach—no longer explicitly linked to the New Math era—that relates the analysis of mathematical content knowledge to the learning processes of students. These kinds of stoffdidaktik still exist; there are also types of stoffdidaktik that emphasize the epistemological analysis of mathematical content matter.

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  1. Universität Duisburg-Essen, Essen, Germany

    Heinz Steinbring

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Correspondence to Heinz Steinbring.

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Many parts of this contribution are based on Steinbring, 2005. A first version of this paper was presented at the Seminar Series: “Mathematical Knowledge in Teaching”, Conceptualising and theorising mathematical knowledge in teaching (11–12 January 2007—2 days—Cambridge), organized by Kenneth Ruthven and Tim Rowland, University of Cambridge).

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Steinbring, H. Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?. ZDM Mathematics Education 40, 303–316 (2008). https://doi.org/10.1007/s11858-008-0077-0

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