Book
Explanation and proof in mathematics
philosophical and educational perspectives
Abstract
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 underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Details | Table of Contents
pp.17-32
https://doi.org/10.1007/978-1-4419-0576-5_2towards a satisfactory definition of continuity
pp.33-46
https://doi.org/10.1007/978-1-4419-0576-5_3an algebraic approach
pp.47-57
https://doi.org/10.1007/978-1-4419-0576-5_4Polya and Lakatos
pp.71-83
https://doi.org/10.1007/978-1-4419-0576-5_6an empirical approach
pp.101-111
https://doi.org/10.1007/978-1-4419-0576-5_8a didactical perspective
pp.115-135
https://doi.org/10.1007/978-1-4419-0576-5_9pp.137-149
https://doi.org/10.1007/978-1-4419-0576-5_10pp.151-167
https://doi.org/10.1007/978-1-4419-0576-5_11pp.169-188
https://doi.org/10.1007/978-1-4419-0576-5_12pp.223-236
https://doi.org/10.1007/978-1-4419-0576-5_15from icons to symbols
pp.237-251
https://doi.org/10.1007/978-1-4419-0576-5_16two modalities from ancient Chinese algorithms
pp.253-285
https://doi.org/10.1007/978-1-4419-0576-5_17Publication details
Publisher: Springer
Place: Dordrecht
Year: 2010
Pages: 294
DOI: 10.1007/978-1-4419-0576-5
ISBN (hardback): 978-1-4419-0575-8
ISBN (digital): 978-1-4419-0576-5
Full citation:
Hanna Gila, Jahnke Hans Niels, Pulte Helmut (2010) Explanation and proof in mathematics: philosophical and educational perspectives. Dordrecht, Springer.