Explanation and Proof in Mathematics (eBook, PDF)

Philosophical and Educational Perspectives

• Format: PDF

Produktbeschreibung

Produktdetails

• Verlag: Springer US
• Erscheinungstermin: 4. Dezember 2009
• Englisch
• ISBN-13: 9781441905765
• Artikelnr.: 37340342

Inhaltsangabe

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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.

Rezensionen

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)