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Tools and Mathematics in the Real World

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Tools and Mathematics

Part of the book series: Mathematics Education Library ((MELI,volume 110))

Abstract

This chapter considers, with special regard to tool use, mathematics in out-of-school practices and attempts to replicate these practices in school mathematics. Both foci are important and problematic issues in mathematics education. This chapter has four sections. The two central sections address the two main foci. The opening section sets the scene with an historical account of ways that mathematics has been subdivided with regard to its application(s). The last section considers problem issues.

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Notes

  1. 1.

    I use the term ‘school’ loosely to denote any educational institution.

  2. 2.

    I think this ‘use of a specific tool in pure mathematics’ and ‘use of a range of tools in applied mathematics’ is a fairly common phenomena but I do not claim that it is a universal phenomenon.

  3. 3.

    Siller and Greefrath’s (2010, p. 2138) note, ‘The three different worlds shown in Fig. 2 are idealized; they influence each other.’

  4. 4.

    This is not meant to belittle the mathematical potential of artefacts that are not mathematical tools. Many artefacts of this kind enable what the Freudenthal school (see Freudenthal, 1991) call ‘horizontal mathematization’; mathematics can be extracted from the artefact and the artefact can be mathematically structured by the agent.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Agder, Kristiansand, Norway

    John Monaghan

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  1. John Monaghan
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Monaghan, J. (2016). Tools and Mathematics in the Real World. In: Tools and Mathematics. Mathematics Education Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-02396-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-02396-0_14

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