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An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: triangular numbers

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Abstract

This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils’ spontaneous production using a triangular numbers activity. Based on a specific collaborative learning methodology, this study explores the possibility of constructing an Arithmetic-Algebraic Work Space around the process of constructing signs as framed by both activity theory and a technological approach, showing the spontaneous representations produced by seventh grade pupils and their evolution in a socio-cultural environment.

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Authors and Affiliations

  1. Département de Mathématiques, Université du Québec à Montréal, 201 Président Kennedy, Montréal, QC, H2X 3Y7, Canada

    Fernando Hitt, Mireille Saboya & Carlos Cortés Zavala

  2. Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico

    Fernando Hitt, Mireille Saboya & Carlos Cortés Zavala

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  1. Fernando Hitt
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  2. Mireille Saboya
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  3. Carlos Cortés Zavala
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Correspondence to Fernando Hitt.

Appendix: Pentagonal numbers

Appendix: Pentagonal numbers

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Hitt, F., Saboya, M. & Cortés Zavala, C. An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: triangular numbers. ZDM Mathematics Education 48, 775–791 (2016). https://doi.org/10.1007/s11858-015-0749-5

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