Distinguishing two stages of mathematics conceptual learning

Ron Tzur, Marty Simon

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)287-304
Number of pages18
JournalInternational Journal of Science and Mathematics Education
Issue number2
StatePublished - Jun 2004


  • Abstraction
  • Concept development
  • Conceptual learning
  • Conceptualization
  • Epistemology
  • Learning
  • Mathematics learning
  • Stages of learning

ASJC Scopus subject areas

  • Education
  • General Mathematics


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