Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

Inbunden, Engelska, 2009

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Beskrivning

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 researchers to the newest developments in the philosophy and practice of mathematics.

Produktinformation

Utgivningsdatum:2009-12-17
Mått:155 x 235 x 28 mm
Vikt:587 g
Format:Inbunden
Språk:Engelska
Antal sidor:294
Upplaga:2010
Förlag:Springer-Verlag New York Inc.
ISBN:9781441905758

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Recensioner i media

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 fields: mathematics educators, philosophy of mathematics and history of mathematics. ... The authors and editors made a fine job providing a useful resource for all interested in proofs and proving in mathematical education."--- (Claudi Alsina, Zentralblatt MATH, Vol. 1196, 2010)

Innehållsförteckning

Reflections on the Nature and Teaching of Proof.- The Conjoint Origin of Proof and Theoretical Physics.- Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity.- Preaxiomatic Mathematical Reasoning: An Algebraic Approach.- Completions, Constructions, and Corollaries.- Authoritarian Versus Authoritative Teaching: Polya and Lakatos.- Proofs as Bearers of Mathematical Knowledge.- Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach.- Proof and Cognitive Development.- Bridging Knowing and Proving in Mathematics: A Didactical Perspective.- The Long-Term Cognitive Development of Reasoning and Proof.- Historical Artefacts, Semiotic Mediation and Teaching Proof.- Proofs, Semiotics and Artefacts of Information Technologies.- Experiments, Diagrams and Proofs.- Proof as Experiment in Wittgenstein.- Experimentation and Proof in Mathematics.- Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching.- Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols.- Proof in the Wording: Two Modalities from Ancient Chinese Algorithms.