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Algebraic Understanding of Equalities in Primary Classes

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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Learning of mathematics in primary classes should not be reduced to learning algorithms and routines or procedures. It is more important to foster children’s thinking and reasoning of meaningful relations between objects and operations. In addition, from our point of view, the algebraic concepts should be more relevant than the algebraic symbols. In this sense, the conceptual understanding of equalities seems to be an essential basis for a flexible and sophisticated understanding of equations. Hence, discussing and explaining equalities should play a prominent role in the teaching and learning of mathematics from the beginning of primary school. In our design study we develop learning opportunities for primary school children that involve comparing terms and tasks with a view toward the underlying mathematical structures . In this chapter we discuss our theoretical background and some results of our video-based qualitative analysis of learning situations in the area of reasoning about equalities.

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Notes

  1. 1.

    Note that the raised dot is used here to signify the operation of multiplication.

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Author information

Authors and Affiliations

  1. Carl v. Ossietzky Universität, Oldenburg, Germany

    Ralph Schwarzkopf

  2. Technische Universität, Dortmund, Germany

    Marcus Nührenbörger & Carolin Mayer

Authors
  1. Ralph Schwarzkopf
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  2. Marcus Nührenbörger
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  3. Carolin Mayer
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Corresponding author

Correspondence to Ralph Schwarzkopf .

Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec, Canada

    Carolyn Kieran

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Schwarzkopf, R., Nührenbörger, M., Mayer, C. (2018). Algebraic Understanding of Equalities in Primary Classes. In: Kieran, C. (eds) Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68351-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-68351-5_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68350-8

  • Online ISBN: 978-3-319-68351-5

  • eBook Packages: EducationEducation (R0)

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