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Science and Mathematics Education Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Science and Mathematics Education
Explicating A Mechanism For Conceptual Learning: Elaborating The Construct Of Reflective Abstraction, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel
Explicating A Mechanism For Conceptual Learning: Elaborating The Construct Of Reflective Abstraction, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel
Ron Tzur
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.
Characterizing A Perspective Underlying The Practice Of Mathematics Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Characterizing A Perspective Underlying The Practice Of Mathematics Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Ron Tzur
We postulate a construct, perception-based perspective, that we consider to be fundamental to the practices of many teachers currently participating in mathematics education reform in the United States. The postulation of the construct resulted from analyses of data from teaching experiments in teacher education classes with a combined group of prospective and practicing teachers and from case studies with individuals from that group. A perception-based perspective is grounded in a view of mathematics as a connected, logical, and universally accessible part of an ontological reality. From this perspective, learning mathematics with understanding requires learners' direct (firsthand) perception of relevant mathematical …
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Ron Tzur
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.
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Ron Tzur
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.