By Gila Hanna, Hans Niels Jahnke, Helmut Pulte
In the 4 many years on account that Imre Lakatos declared arithmetic a "quasi-empirical science," expanding realization has been paid to the method of evidence and argumentation within the box -- a improvement paralleled via the increase of machine know-how and the mounting curiosity within the logical underpinnings of arithmetic. Explanantion and evidence in Mathematics assembles views from arithmetic schooling and from the philosophy and historical past of arithmetic to reinforce mutual understanding and percentage fresh findings and advances of their interrelated fields. With examples starting from the geometrists of the seventeenth century and historic chinese language algorithms to cognitive psychology and present academic perform, participants discover the position of refutation in producing proofs, the various hyperlinks among test and deduction, using diagrammatic considering as well as natural common sense, and the makes use of of facts in arithmetic schooling (including a critique of "authoritative" as opposed to "authoritarian" instructing styles).
A sampling of the coverage:
- The conjoint origins of facts and theoretical physics in historical Greece
- Proof as bearers of mathematical knowledge
- Bridging realizing and proving in mathematical reasoning
- The function of arithmetic in long term cognitive improvement of reasoning
- Proof as scan within the paintings of Wittgenstein
- Relationships among mathematical facts, problem-solving, and explanation
Explanation and evidence in Mathematics is sure to draw a variety of readers, together with mathematicians, arithmetic schooling execs, researchers, scholars, and philosophers and historians of mathematics.
Read Online or Download Explanation and Proof in Mathematics: Philosophical and Educational Perspectives PDF
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Additional resources for Explanation and Proof in Mathematics: Philosophical and Educational Perspectives
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