Explanation and Proof in Mathematics Philosophical and Educational Perspectives /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Hanna, Gila (Editor), Jahnke, Hans Niels (Editor), Pulte, Helmut (Editor)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2010.
• Subjects: Education.; Philosophy and social sciences.; Mathematics.; Mathematics > Study and teaching.; Learning & Instruction.; Popular Science in Education.; Mathematics, general.; Mathematics Education.; Philosophy of Education.

In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpi...

Table of Contents:

• 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.