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Science and Mathematics Education Commons™
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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 …
An Integrated Study Of Children's Construction Of Improper Fractions And The Teacher's Role In Promoting That Learning, Ron Tzur
Ron Tzur
In this constructivist teaching experiment with 2 fourth graders I studied the coemergence of teaching and children's construction of a specific conception that supports the generation of improper fractions. The children's posing and solving tasks in a computer microworld promoted a modification in their fraction schemes. They advanced from thinking about a unit fraction as a part of a whole to thinking about it as standing in a multiplicative relationship with a reference whole (the iterative fraction scheme). In this article I report an intertwined analysis of the children's construction of this multiplicative relationship and an examination of the teacher's …