Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development

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 anticipatory stage.

Contributor Notes

Martin A. Simon, Department of Teaching and Learning, New York University, 420 East Building, New York, NY 10003; msimon@nyu.edu

Nicora Placa, Department of Teaching and Learning, New York University, 420 East Building, New York, NY 10003; np874@nyu.edu

Arnon Avitzur, Department of Teaching and Learning, New York University, 420 East Building, New York, NY 10003; arnon.avitzur@nyu.edu

(Corresponding author is Simon msimon@nyu.edu)(Corresponding author is Placa np874@nyu.edu)(Corresponding author is Avitzur arnon.avitzur@nyu.edu)
Journal for Research in Mathematics Education

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