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Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science

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Transformation - A Fundamental Idea of Mathematics Education

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Abstract

Interpreting calculations as sequences of transformations on arithmetical expressions, like 3 × 12, opens new opportunities for understanding and modelling arithmetical competence. Arithmeticus is a computer program that produces sequences of transformations, which can be applied to arithmetical expressions. It can analyse the sequence of transformations used in a student’s calculation, store them and try to apply them on other expressions. In this paper it will be explained how these features are a basis of a dynamic model of arithmetical competence. Additionally, informatical educational science will be proposed as a special approach of investigating learning and teaching processes by informatical methods: in the case of Arithmeticus, by the dynamical modelling of arithmetical competence and learning and teaching processes.

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Notes

  1. 1.

    In this chapter ‘production’ is not meant in an industrial or technical meaning but in the original Latin meaning of ‘to create and to reveal something’, ‘bringing out something’, or ‘to bring up something’.

  2. 2.

    In German, the nouns ‘Bearbeitungshilfe’ and ‘Veranschaulichungsmittel’.

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Authors and Affiliations

  1. Leemptstraat 6, 6512 EN, Nijmegen, Netherlands

    Joost Klep

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  1. Joost Klep
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Correspondence to Joost Klep .

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Editors and Affiliations

  1. IEIM - Institut für Mathematik, Universität Paderborn, Paderborn, Germany

    Sebastian Rezat

  2. Fakultät für Mathematik - IDM, Universität Bielefeld, Bielefeld, Germany

    Mathias Hattermann

  3. Fakultät für Mathematik - IDM, Universität Bielefeld, Bielefeld, Germany

    Andrea Peter-Koop

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Klep, J. (2014). Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science. In: Rezat, S., Hattermann, M., Peter-Koop, A. (eds) Transformation - A Fundamental Idea of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3489-4_17

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