Visualizations in Mathematics


In this paper we discuss visualizations in mathematics from a historical and didactical perspective. We consider historical debates from the 17th and 19th centuries regarding the role of intuition and visualizations in mathematics. We also consider the problem of what a visualization in mathematical learning can achieve. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. We emphasize that a visualization in mathematics should always be considered in its proper context.

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  1. 1.

    Hobbes used the term ‘the angle of Contingence’, instead of ‘the angle of contact’.

  2. 2.

    Hobbes’ term ‘quantity’ can be interpreted as ‘magnitude’, which is used in for example Euclid’s Elements.

  3. 3.

    Stenlund (2005) used this terminology in the context of spoken communication.


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We would like to thank Anders Öberg for many valuable discussions. The research leading to the present article was financially supported by the Bank of Sweden Tercentenary Foundation and the Swedish Research Council.

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Correspondence to Kajsa Bråting.

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Bråting, K., Pejlare, J. Visualizations in Mathematics. Erkenn 68, 345–358 (2008).

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  • Function Concept
  • Mathematical Concept
  • Equilateral Triangle
  • Mathematical Object
  • Mathematical Definition