Distinguishing two stages of mathematics conceptual learning

Ron Tzur; Marty Simon

doi:10.1007/s10763-004-7479-4

Distinguishing two stages of mathematics conceptual learning

Ron Tzur, Marty Simon

Teaching and Learning

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	287-304
Number of pages	18
Journal	International Journal of Science and Mathematics Education
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/s10763-004-7479-4
State	Published - Jun 2004

Keywords

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

ASJC Scopus subject areas

Education
General Mathematics

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10.1007/s10763-004-7479-4

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title = "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",

author = "Ron Tzur and Marty Simon",

note = "Funding Information: This research was supported by the National Science Foundation (REC 9600023) and by the National Academy of Education – Spencer Foundation. The opinions expressed do not necessarily reflect the views of these foundations.",

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AB - 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.

KW - Abstraction

KW - Concept development

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KW - Conceptualization

KW - Epistemology

KW - Learning

KW - Mathematics learning

KW - Stages of learning

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Distinguishing two stages of mathematics conceptual learning

Abstract

Keywords

ASJC Scopus subject areas

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