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Explanation and proof in mathematics : philosophical and educational perspectives

Author: G Hanna; H N Jahnke; Helmut Pulte
Publisher: New York : Springer, ©2010.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Developments in the practice of mathematics have led to new types of proof and argumentation, challenging the established norms in this area. This book directs the attention of educational  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: G Hanna; H N Jahnke; Helmut Pulte
ISBN: 9781441905758 1441905758 1441905766 9781441905765
OCLC Number: 502399282
Description: viii, 294 pages : illustrations ; 24 cm
Contents: Introduction --
Reflections on the nature and teaching of proof : The conjoint origin of proof and theoretical physics / Hans Niels Jahnke --
Lakatos, Lakoff and Nunez: towards a satisfactory difinition of continuity / Teun Koetsier --
Preaxiomatic mathematical reasoning: an algebraic approach / Mary Leng --
Completions, constructions, and corollaries / Thomas Mormann --
Authoritarian versus authoritative teaching: Polya and Lakatos / Brendan Larvor --
Proofs as bearers of mathematical knowledge / Gila Hanna, Ed Barbeau --
Mathematicians' individual criteria for accepting theorems and proofs: an empirical approach / Aiso Heinze --
Proof and cognitive development : Bridging knowing and proving in mathematics: a didactical perspective / Nicolas Balacheff --
The long-term cognitive development of reasoning and proof / David Tall, Juan Pablo Mejia-Ramos --
Historical artefacts, semiotic mediation and teaching proof / Maria G. Bartolini Bussi --
Proofs, semiotics and artefacts of information technologies / Maria Alessandra Mariotti --
Experiments, diagrams and proofs : Proof as experiment in Wittgenstein / Alfred Nordmann --
Experimentation and proof in mathematics / Michael de Villiers --
Proof, mathematical problem-solving, and explanation in mathematics teaching / Kazuhiko Nunokawa --
Evolving geometric prooofs in the seventeenth century: from icons to symbols / Evelyne Varbin --
Proof in the wording: two modalitics from ancient chinese algorithms / Karine Chemla.
Responsibility: Gila Hanna, Hans Niels Jahnke, Helmut Pulte, editors.

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From the reviews:"The origin of this book is the conference Explanation and Proof in Mathematics: Philosophical and Educational Perspectives (Essen, 2006) and it reflects different views from three Read more...

 
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