Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction

Martin A. Simon; Ron Tzur; Karen Heinz; Margaret T. Kinzel

doi:10.2307/30034818

Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction

Martin A. Simon, Ron Tzur, Karen Heinz, Margaret T. Kinzel

Mathematics Department

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

127 Scopus citations

Abstract

We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstraction and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified. (Contains 2 figures and 9 footnotes.)

Original language	American English
Pages (from-to)	305-329
Number of pages	25
Journal	Journal for Research in Mathematics Education
Volume	35
Issue number	5
DOIs	https://doi.org/10.2307/30034818
State	Published - Nov 2004

Keywords

Cognitive Development
Concept Formation
Constructivism (Learning)
Epistemology
Instructional Design
Learning Theories
Lesson Plans
Logical Thinking
Mathematical Concepts
Mathematical Logic
Mathematics Instruction
Transformative Learning

EGS Disciplines

Mathematics

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10.2307/30034818

Cite this

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abstract = " We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstraction and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified. (Contains 2 figures and 9 footnotes.)",

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N2 - We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstraction and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified. (Contains 2 figures and 9 footnotes.)

AB - We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstraction and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified. (Contains 2 figures and 9 footnotes.)

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KW - Concept Formation

KW - Constructivism (Learning)

KW - Epistemology

KW - Instructional Design

KW - Learning Theories

KW - Lesson Plans

KW - Logical Thinking

KW - Mathematical Concepts

KW - Mathematical Logic

KW - Mathematics Instruction

KW - Transformative Learning

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Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction

Abstract

Keywords

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