Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction

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

Teaching and Learning

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

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.

Original language	English (US)
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
Conceptual knowledge
Constructivism
Epistemology
Learning theories
Piaget

ASJC Scopus subject areas

Mathematics (miscellaneous)
Education

Access to Document

10.2307/30034818

Cite this

@article{6739b91b423f441fb9a633a7651ed92e,

title = "Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction",

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.",

keywords = "Cognitive development, Conceptual knowledge, Constructivism, Epistemology, Learning theories, Piaget",

author = "Simon, {Martin A.} and Ron Tzur and Karen Heinz and Margaret Kinzel",

year = "2004",

month = nov,

doi = "10.2307/30034818",

language = "English (US)",

volume = "35",

pages = "305--329",

journal = "Journal for Research in Mathematics Education",

issn = "0021-8251",

publisher = "National Council of Teachers of Mathematics",

number = "5",

}

TY - JOUR

T1 - Explicating a mechanism for conceptual learning

T2 - Elaborating the construct of reflective abstraction

AU - Simon, Martin A.

AU - Tzur, Ron

AU - Heinz, Karen

AU - Kinzel, Margaret

PY - 2004/11

Y1 - 2004/11

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.

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.

KW - Cognitive development

KW - Conceptual knowledge

KW - Constructivism

KW - Epistemology

KW - Learning theories

KW - Piaget

UR - http://www.scopus.com/inward/record.url?scp=8644222004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8644222004&partnerID=8YFLogxK

U2 - 10.2307/30034818

DO - 10.2307/30034818

M3 - Article

AN - SCOPUS:8644222004

SN - 0021-8251

VL - 35

SP - 305

EP - 329

JO - Journal for Research in Mathematics Education

JF - Journal for Research in Mathematics Education

IS - 5

ER -

Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this