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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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Mathematical Knowledge in Teaching

Part of the book series: Mathematics Education Library ((MELI,volume 50))

Abstract

This chapter shows how the German didactical tradition has evolved in response to new theoretical ideas and new – empirical – research approaches in mathematics education. First, classical mathematical didactics, notably the tradition of ‘stoffdidaktik’, is described. The critiques raised against ‘stoffdidaktik’ [for example, forms of ‘progressive mathematisation’, ‘actively discovering learning processes’ and ‘guided reinvention’ (cf. Freudenthal, Wittmann)] changed basic views on the roles that ‘mathematical knowledge’, ‘teacher’ and ‘student’ 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). Through interpretative empirical research on everyday mathematical teaching-learning situations (for example, by the research group around Bauersfeld) a new research paradigm for mathematics education was constituted: the cultural system of mathematical interaction between teacher and students.

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Notes

  1. 1.

    One can suppose that this is where the famous didactical triangle originates.

  2. 2.

    In this paper ‘stoffdidaktik’ is restricted to a certain fundamentalist form of content-related mathematical analysis based on ideas from the New Math era. Later, there were further developments and modifications of the stoffdidaktik approach – no longer explicitly linked to the New Math era – that relate 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.

  3. 3.

    Concerning the individual-psychological perspective, see e.g. Cobb, Yackel, and Wood (1991); and for the collectivistic perspective, see Solomon (1989).

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Acknowledgement

With kind permission from Springer Science+Business Media: Steinbring, H. (2008). Changed views on mathematical knowledge in the course of didactical theory development – independent corpus of scientific knowledge or result of social constructions? Zentralblatt für Didaktik der Mathematik, 40(2), 303–316. Many parts of this contribution are based on Steinbring, 2005.

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  1. Fakultät für Mathematik, Universität Duisburg-Essen, Essen, D-45117, Germany

    Heinz Steinbring

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  1. Fac. Education, University of Cambridge, Hills Road 184, Cambridge, CB2 2PQ, United Kingdom

    Tim Rowland

  2. Fac. Education, University of Cambridge, Hills Road 184, Cambridge, CB2 2PQ, United Kingdom

    Kenneth Ruthven

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Steinbring, H. (2011). Changed Views on Mathematical Knowledge in the Course of Didactical Theory Development: Independent Corpus of Scientific Knowledge or Result of Social Constructions?. In: Rowland, T., Ruthven, K. (eds) Mathematical Knowledge in Teaching. Mathematics Education Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9766-8_4

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