Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

  • Gila Hanna
  • Hans Niels Jahnke
  • Helmut Pulte

Table of contents

  1. Front Matter
    Pages i-viii
  2. Reflections on the Nature and Teaching of Proof

  3. Proof and Cognitive Development

    1. Front Matter
      Pages 114-114
    2. David Tall, Juan Pablo Mejia-Ramos
      Pages 137-149
    3. Maria G. Bartolini Bussi
      Pages 151-167
    4. Maria Alessandra Mariotti
      Pages 169-188
  4. Experiments, Diagrams and Proofs

  5. Back Matter
    Pages 287-294

About this book


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:

  • 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 long-term cognitive development of reasoning
  • Proof as experiment in the work of Wittgenstein
  • Relationships between mathematical proof, problem-solving, 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.


Hans Niels Jahnke Mathematical Understanding Problem Solving Proof and Idealization Proofs as Experiments Representations and Diagrams in Proof algebra education science

Editors and affiliations

  • Gila Hanna
    • 1
  • Hans Niels Jahnke
    • 2
  • Helmut Pulte
    • 3
  1. 1.Ontario Institute for Studies inUniversity of TorontoTorontoCanada
  2. 2.FB MathematikUniversität Duisburg-EssenEssenGermany
  3. 3.Inst. PhilosophieUniversität BochumBochumGermany

Bibliographic information