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A Companion to Wittgenstein on Education pp 517–526Cite as

What Does Calculating Have to Do with Mathematics? Wittgenstein, Dewey, and Mathematics Education in Sweden

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Abstract

This paper concerns mathematics education in Sweden in relation to Ludwig Wittgenstein and John Dewey . Both Wittgenstein and Dewey were critical of an essentialistic, or dualistic, view of knowledge as a distinct (mental) phenomenon distinguishable from the (physical) result. This kind of view is commonly expressed in the research on mathematics education , where mathematical understanding is seen to take place in the mind or the brain, and the calculation that takes place on paper is a more or less contingent result of the mental process. I will exemplify how this view has influenced the classroom practice in Sweden and will argue that as well as being philosophically problematic in the framework of Wittgenstein and Dewey, it is counterproductive as regards the aims of mathematics education .

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Notes

  1. 1.

    Following convention, titles for Wittgenstein’s works are abbreviated (PI = Philosophical Investigations , BB = The  Blue and Brown Books (Preliminary Notebooks), RFM = Remarks on the Foundations of Mathematics), with section (§) or page number (p.), with full citation and initials (e.g., RFM) in the References.

  2. 2.

    It has been suggested to me that one reason for the extensive manuals is that many mathematics teachers lack the necessary mathematical training to be able to evaluate tests in a more traditional way. This might, of course, be one explanation to the need for extensive manuals.

  3. 3.

    This is not self -evident: In a Finnish study concerning the benefit of word problems in mathematics education , the students were given full points if they modeled the task correctly but reached the wrong result due to lack of numerical skill . The problem concerned “especially multiplication and division with decimal numbers” (Pongsakdi et al. 2016: 33).

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Author information

Authors and Affiliations

  1. Uppsala University, Uppsala, Sweden

    Tove Österman

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  1. Tove Österman
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Correspondence to Tove Österman .

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Editors and Affiliations

  1. University of Waikato, Hamilton, Waikato, New Zealand

    Michael A. Peters

  2. Ontario Institute for Studies in Education, University of Toronto, Toronto, Ontario, Canada

    Jeff Stickney

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Österman, T. (2017). What Does Calculating Have to Do with Mathematics? Wittgenstein, Dewey, and Mathematics Education in Sweden. In: Peters, M., Stickney, J. (eds) A Companion to Wittgenstein on Education. Springer, Singapore. https://doi.org/10.1007/978-981-10-3136-6_34

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  • DOI: https://doi.org/10.1007/978-981-10-3136-6_34

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