Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning. This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Universite Laval in Quebec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past…mehr
Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning. This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Universite Laval in Quebec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.First Published in 1996. Routledge is an imprint of Taylor & Francis, an informa company.
Leslie P. Steffe, Pearla Nesher, Paul Cobb, Bharath Sriraman, Brian Greer
Inhaltsangabe
Contents: Preface. Part I: P. Cobb Sociological and Anthropological Perspectives on Mathematics Learning.P. Cobb B. Jaworski N. Presmeg Emergent and Sociocultural Views of Mathematical Activity. J. Voigt Negotiation of Mathematical Meaning in Classroom Processes: Social Interaction and Learning Mathematics. G.B. Saxe T. Bermudez Emergent Mathematical Environments in Children's Games. J. Richards Negotiating the Negotiation of Meaning: Comments on Voigt (1992) and Saxe and Bermudez (1992). A.D. Schliemann D.W. Carraher Negotiationg Mathematical Meanings In and Out of School. E. Yackel Social Interaction and Individual Cognition. B. van Oers Learning Mathematics as a Meaningful Activity. E.A. Forman Learning Mathematics as Participation in Classroom Practice: Implications of Sociocultural Theory for Educational Reform. K. Crawford Cultural Processes and Learning: Expectations Actions and Outcomes. J.W. Stigler C. Fernandez M. Yoshida Traditions of School Mathematics in Japanese and American Elementary Classrooms. Part II: B. Greer Cognitive Science Theories and Their Contributions to the Learning of Mathematics.B. Greer Theories of Mathematics Education: The Role of Cognitive Analyses. G. Hatano A Conception of Knowledge Acquisition and Its Implications for Mathematics Education. G. Vergnaud The Theory of Conceptual Fields. D.W. Carraher Learning About Fractions. P.W. Thompson Imagery and the Development of Mathematical Reasoning. R.B. Davis Cognition Mathematics and Education. Part III: G.A. Goldin The Contribution of Constructivism to the Learning of Mathematics.G.A. Goldin Theory of Mathematics Education: The Contributions of Constructivism. E. von Glasersfeld Aspects of Radical Constructivism and Its Educational Recommendations. F. Marton D. Neuman Phenomenography and Children's Experience of Division. P. Ernest Varieties of Constructivism: A Framework for Comparison. N. Herscovics The Construction of Conceptual Schemes in Mathematics. G. Booker Constructing Mathematical Conventions Formed by the Abstraction and Generalization of Earlier Ideas: The Development of Initial Fraction Ideas. G.A. Goldin J.J. Kaput A Joint Perspective on the Idea of Representation in Learning and Doing Mathematics. C.A. Maher A.M. Martino Young Children Invent Methods of Proof: The Gang of Four. C. Janvier Constructivism and Its Consequences for Training Teachers. Part IV: Perspectives on the Nature of Mathematical Learning.W. Dörfler Is the Metaphor of Mental Object Appropriate for a Theory of Learning Mathematics? L.P. Steffe H.G. Wiegel On the Nature of a Model of Mathematical Learning.
Contents: Preface. Part I: P. Cobb Sociological and Anthropological Perspectives on Mathematics Learning.P. Cobb B. Jaworski N. Presmeg Emergent and Sociocultural Views of Mathematical Activity. J. Voigt Negotiation of Mathematical Meaning in Classroom Processes: Social Interaction and Learning Mathematics. G.B. Saxe T. Bermudez Emergent Mathematical Environments in Children's Games. J. Richards Negotiating the Negotiation of Meaning: Comments on Voigt (1992) and Saxe and Bermudez (1992). A.D. Schliemann D.W. Carraher Negotiationg Mathematical Meanings In and Out of School. E. Yackel Social Interaction and Individual Cognition. B. van Oers Learning Mathematics as a Meaningful Activity. E.A. Forman Learning Mathematics as Participation in Classroom Practice: Implications of Sociocultural Theory for Educational Reform. K. Crawford Cultural Processes and Learning: Expectations Actions and Outcomes. J.W. Stigler C. Fernandez M. Yoshida Traditions of School Mathematics in Japanese and American Elementary Classrooms. Part II: B. Greer Cognitive Science Theories and Their Contributions to the Learning of Mathematics.B. Greer Theories of Mathematics Education: The Role of Cognitive Analyses. G. Hatano A Conception of Knowledge Acquisition and Its Implications for Mathematics Education. G. Vergnaud The Theory of Conceptual Fields. D.W. Carraher Learning About Fractions. P.W. Thompson Imagery and the Development of Mathematical Reasoning. R.B. Davis Cognition Mathematics and Education. Part III: G.A. Goldin The Contribution of Constructivism to the Learning of Mathematics.G.A. Goldin Theory of Mathematics Education: The Contributions of Constructivism. E. von Glasersfeld Aspects of Radical Constructivism and Its Educational Recommendations. F. Marton D. Neuman Phenomenography and Children's Experience of Division. P. Ernest Varieties of Constructivism: A Framework for Comparison. N. Herscovics The Construction of Conceptual Schemes in Mathematics. G. Booker Constructing Mathematical Conventions Formed by the Abstraction and Generalization of Earlier Ideas: The Development of Initial Fraction Ideas. G.A. Goldin J.J. Kaput A Joint Perspective on the Idea of Representation in Learning and Doing Mathematics. C.A. Maher A.M. Martino Young Children Invent Methods of Proof: The Gang of Four. C. Janvier Constructivism and Its Consequences for Training Teachers. Part IV: Perspectives on the Nature of Mathematical Learning.W. Dörfler Is the Metaphor of Mental Object Appropriate for a Theory of Learning Mathematics? L.P. Steffe H.G. Wiegel On the Nature of a Model of Mathematical Learning.
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