Explanation and Proof in Mathematics
Philosophical and Educational Perspectives
Editors: Hanna, Gila, Jahnke, Hans Niels, Pulte, Helmut (Eds.)
Free Preview Directs attention of educational researchers to newest developments in the philosophy and practice of mathematics and their relevance
 Critically examines recent literature in the philosophy of mathematics on mathematicians’ methods for devising and judging proof
 Creates a much needed bridge between the discipline of philosophy of mathematics and mathematics education
 Demonstrates that mathematical practice has lessons for instructional practice
 Stresses the relevance of pragmatic dimensions of mathematics for current philosophy of mathematics
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 About this book

In the four decades since Imre Lakatos declared mathematics a "quasiempirical 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:
 The conjoint origins of proof and theoretical physics in ancient Greece
 Proof as bearers of mathematical knowledge
 Bridging knowing and proving in mathematical reasoning
 The role of mathematics in longterm cognitive development of reasoning
 Proof as experiment in the work of Wittgenstein
 Relationships between mathematical proof, problemsolving, and explanation
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.
 Reviews

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)
 Table of contents (17 chapters)


Introduction
Pages 113

The Conjoint Origin of Proof and Theoretical Physics
Pages 1732

Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity
Pages 3346

Preaxiomatic Mathematical Reasoning: An Algebraic Approach
Pages 4757

Completions, Constructions, and Corollaries
Pages 5970

Table of contents (17 chapters)
 Download Sample pages 1 PDF (607.8 KB)
 Download Table of contents PDF (413.4 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Explanation and Proof in Mathematics
 Book Subtitle
 Philosophical and Educational Perspectives
 Editors

 Gila Hanna
 Hans Niels Jahnke
 Helmut Pulte
 Copyright
 2010
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag US
 eBook ISBN
 9781441905765
 DOI
 10.1007/9781441905765
 Hardcover ISBN
 9781441905758
 Softcover ISBN
 9781489982735
 Edition Number
 1
 Number of Pages
 VIII, 294
 Topics