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Distinguishing Two Stages of Mathematics Conceptual Learning

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Abstract

In this theoretical article, we distinguish two stages of learning a new mathematical concept – participatory and anticipatory. We use a recently developed mechanism for explaining mathematical conceptual learning – reflection on activity-effect relationship – as well as von Glasersfeld’s tripartite model of a scheme, to explain qualitative distinctions between the two stages. We use this distinction to explain why instructional interventions (including inquiry-based approaches) may not bring about the intended instructional goals.

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Authors and Affiliations

  1. NCSU, 502-k Poe Hall, box 7801, Raleigh, NC 27695-7801, U.S.A.

    Ron Tzur

  2. Department of Curriculum and Instruction, Pennsylvania State University, University Park, PA 16802, U.S.A.

    Marty Simon

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  1. Ron Tzur
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  2. Marty Simon
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Correspondence to Ron Tzur.

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Tzur, R., Simon, M. Distinguishing Two Stages of Mathematics Conceptual Learning. Int J Sci Math Educ 2, 287–304 (2004). https://doi.org/10.1007/s10763-004-7479-4

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  • DOI: https://doi.org/10.1007/s10763-004-7479-4

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