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 Université Laval in Québec. 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.
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.
Leslie P. Steffe, Pearla Nesher, Paul Cobb, Bharath Sriraman, Brian Greer
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