Explanation and proof in mathematics: philosophical and educational perspectives

Developments in the practice of mathematics over the last three decades have led to new types of proof and argumentation, challenging the established normsin this area. These developments originated from the use of computers (both as a heuristic device and as a means of verification), from a new quality in the relations of mathematics to its applications in the empirical sciences and technology, and from a stronger awareness of the social nature of the processesleading to the acceptance of a proof. A large number of philosophers of mathematics have turned their attention more and more from the justificatory to theexplanatory role of proof. Their central questions are no longer only why andhow a proof makes a proposition true, but also how it contributes to an adequate understanding of the proposition in question and what role is played in this process by factors that go beyond logic. Directs the attention of educational researchers to the newest developments in the philosophy and practice of mathematics and to the relevance of these developments for effective mathematicseducation Critical examination of what the most recent literature in the philosophy of mathematics has to say about the ways today's mathematicians devise and judge proof INDICE: From the contents Section 1: The Role of Representations and Diagrams in Proof. Section 2: Proofs as Experiments and Their Role in the EmpiricalSciences.- Section 3: Genesis, Epistemological Functions and Social Practicesof Proof. Section 4: Proof and Mathematical Understanding--Different Types ofArgumentation and Proof.- Understanding, Proving, and the Description of Algorithms in the Book of Mathematical Procedures from China (ca 186 BCE).- Contexts for Approaching at Validation: The Function of Artefacts of Information Technologies.- Proof and Hypotheses.- Operative Proofs.- The Cognitive Development of Different Types of Reasoning and Proof.- Proving as Part of Mathematical Achievement: Concepts and Results from the PISA Study.

• ISBN: 978-1-4419-0575-8
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 280
• Fecha Publicación: 01/07/2009
• Nº Volúmenes: 1
• Idioma: Inglés