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Geometrical Conceptualization

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International Handbook of Mathematical Learning Difficulties

Abstract

This chapter reviews the challenges of learning and teaching geometric conceptualization. We describe how geometry appears differently during the various stages of learning in institutionalized education. The earlier conceptual stages of geometry always form the foundation for the next interpretation of geometry that the learner will encounter. This stratified structure of geometrical thinking is visible in geometrical conceptualization and teaching geometry as a prolific dialogue between the concrete and the conceptual approaches. This chapter places particular focus on the central nature of prototypical conceptualization and figurativeness in the early stages of learning geometry, the gradual development of the ability to categorize and form definitions, and the roles these have in the process of shaping a pupil’s structured conceptual geometric knowledge. Theoretical observations are illustrated with examples.

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Notes

  1. 1.

    Source: Textbook Silfverberg, Viilo & Pippola. Matematiikan Taito 3. Geometria, Weilin+Göös, s. 48

  2. 2.

    Source: Textbook Silfverberg, Viilo & Pippola. Matematiikan Taito 3. Geometria, Weilin+Göös, s. 47

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Author information

Authors and Affiliations

  1. Department of Teacher Education, University of Turku, Turku, Finland

    Harry Silfverberg

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  1. Harry Silfverberg
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Correspondence to Harry Silfverberg .

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Editors and Affiliations

  1. Faculty of Education Sciences, Department of Psychology, University of Duisburg-Essen, Essen, Germany

    Annemarie Fritz

  2. Faculty of Education, Centre for Education Practice Research, University of Johannesburg, Johannesburg, South Africa

    Annemarie Fritz

  3. Departamento de Psicologia, Faculdade de Filosofia e Ciências Humanas, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Vitor Geraldi Haase

  4. Niilo Mäki Institute, Jyväskylä, Finland

    Pekka Räsänen

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Silfverberg, H. (2019). Geometrical Conceptualization. In: Fritz, A., Haase, V.G., Räsänen, P. (eds) International Handbook of Mathematical Learning Difficulties. Springer, Cham. https://doi.org/10.1007/978-3-319-97148-3_36

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  • DOI: https://doi.org/10.1007/978-3-319-97148-3_36

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