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

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...

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Bibliographic Details
Published inJournal for research in mathematics education Vol. 35; no. 5; pp. 305 - 329
Main Authors Simon, Martin A, Tzur, Ron, Heinz, Karen, Kinzel, Margaret
Format Journal Article
LanguageEnglish
Published National Council of Teachers of Mathematics 01.11.2004
Subjects
Cognitive Development
Concept Formation
Constructivism (Learning)
Epistemology
Instructional Design
Learning Theories
Lesson Plans
Logical Thinking
Mathematical Concepts
Mathematical Logic
Mathematics Instruction
Transformative Learning
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Summary: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.)
ISSN:0021-8251
DOI:10.2307/30034818