Activity and Sign: Grounding Mathematics Education

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Michael H.G. Hoffmann, Johannes Lenhard, Falk Seeger
Springer Science & Business Media, Dec 6, 2005 - Education - 392 pages
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The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community’s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers of mathematics education by bringing together all the new and fascinating perspectives created through his career as a bridge builder in the field of interdisciplinary research and cooperation. The perspectives elaborated here are for the greatest part motivated by the impressing variety of Otte’s thoughts; however, the idea is not to look back, but to find out where the research agenda might lead us in the future.

This volume provides new sources of knowledge based on Michael Otte’s fundamental insight that understanding the problems of mathematics education – how to teach, how to learn, how to communicate, how to do, and how to represent mathematics – depends on means, mainly philosophical and semiotic, that have to be created first of all, and to be reflected from the perspectives of a multitude of diverse disciplines.

 

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Contents

MICHAEL OTTE Mathematics Sign and Activity
9
PAUL ERNEST Agency and Creativity in the Semiotics of Learning Mathematics
23
SUSANNA MARIETTI The Semiotic Approach to Mathematical Evidence
35
MICHAEL HOFFMAN N Signs as Means for Discoveries Peirce and His Concepts
45
WILLIB ALD DORFLER Diagrammatic Thinking Affordances and Constraints
57
FALK SEEGER Notes on a Semiotically Inspired Theory of Teaching and Learning
67
MARIA G BARTOLINI BUSSI MARIA ALESSANDRA MARIOTTI AND FRANCA
77
HEINZ STEINBRING Do Mathematical Symbols Serve to Describe or Construct
91
THOMAS MIES The Cognitive Unconscious Recalling the History of the Concept
203
HANS NIELS JAHNKEI Hilbert Weyl and the Philosophy of Mathematics
215
THOMAS MORMANN Mathematical Metaphors in Natorps NeoKantian
229
KARLNORBERT IHMIG Newtons Program of Mathematizing Nature
241
MIRCEA RADU Did Hermann and Robert Grafimann Contribute to
263
The Notion of Multiplication
275
CIRCE MARY SILVA DA SILVA DYNNIKOV Some German Contributions
287
On the Inventiveness
299

NORMA PRESMEGI Metaphor and Metonymy in Processes of Semiosis in Mathematics
105
ANNA SIERPINSKA On Practical and Theoretical Thinking and Other False
117
LUIS RADFORD The Semiotics of the Schema Kant Piaget and the Calculator
137
KENNETH RUTHVEN Towards a Normal Science of Mathematics Education?
153
GUY BROUSSEAU The Study of the Didactical Conditions of School Learning
159
Variations on
169
FICHTNER Reflective learning Problems and Questions Concerning
179
A Plea for
191
HERMANN DINGES Variables in Particular Random Variables
305
The Two Peirces
313
MARCO PANZA Some Sober Conceptions of Mathematical Truth
335
JEAN PAUL VAN BENDEGEM Can There Be an Alternative Mathematics Real ly?
349
ROLAND FISCHER An Interview with Michael Otte
361
INDEX
379
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