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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.
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 …