Explanation and Proof in Mathematics Philosophical and Educational Perspectives /
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...
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| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Lenguaje: | English |
| Publicado: |
New York, NY :
Springer US : Imprint: Springer,
2010.
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| Edición: | 1st ed. 2010. |
| Materias: | |
| Acceso en línea: | https://doi.org/10.1007/978-1-4419-0576-5 |
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Tabla de Contenidos:
- 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.