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Mathematical interaction shaped by communication, epistemological constraints and enactivism

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Abstract

On the surface, mathematical interaction often appears as an immediately transparent event that could be directly understood by careful observation. Theoretical considerations, however, clearly show that mathematical speaking and conversation in teaching–learning situations are highly complex social structures comprising many preconditions. Communication does not generate direct understanding and the object of communication—mathematics—is, as knowledge of abstract relations, not directly accessible. The learning agents—the teacher and students in the mathematics classroom—have to cope with these difficulties in a way of reciprocal actions between social communication and individual consciousness.

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Notes

  1. To be clear: researchers in mathematics education would completely disagree with such a conception of teaching as a transmission of unambiguous mathematical knowledge (see Ernest 2010). But in everyday mathematics teaching the teaching–learning processes of mathematical knowledge often transform to interactions in which mathematical knowledge is intended to be directly transported from the teacher to the students (see the criticisms made by von Glasersfeld 1995, p. 83).

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  1. Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Thea-Leymann-Straße 9, 45127, Essen, Germany

    Heinz Steinbring

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Steinbring, H. Mathematical interaction shaped by communication, epistemological constraints and enactivism. ZDM Mathematics Education 47, 281–293 (2015). https://doi.org/10.1007/s11858-014-0629-4

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