Distinguishing Two Stages of Mathematics Conceptual Learning

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.

Keywords

abstraction concept development conceptual learning conceptualization epistemology learning mathematics learning stages of learning 

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Copyright information

© National Science Council, Taiwan 2004

Authors and Affiliations

  1. 1.NCSURaleighU.S.A.
  2. 2.Department of Curriculum and InstructionPennsylvania State UniversityU.S.A.

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