Participatory and anticipatory stages of mathematical concept learning: Further empirical and theoretical development

Martin A. Simon, Nicora Placa, Arnon Avitzur

Research output: Contribution to journalArticle


Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. In this article, we discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment. We describe our modifications to and further explicate and exemplify the theoretical underpinnings of these stage constructs. We introduce a representation scheme and use it to trace the development of a concept from initial activity, through the participatory stage, and to the anticipator}' stage.

Original languageEnglish (US)
Pages (from-to)63-93
Number of pages31
JournalJournal for Research in Mathematics Education
Issue number1
StatePublished - Jan 2016



  • Anticipatory
  • Conceptual learning
  • Learning stages
  • Learning theory
  • Mathematical concept
  • Participatory
  • Reflective abstraction

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education

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