By Gila Hanna,Hans Niels Jahnke,Helmut Pulte
In the 4 many years due to the fact Imre Lakatos declared arithmetic a "quasi-empirical science," expanding cognizance has been paid to the method of facts and argumentation within the box -- a improvement paralleled via the increase of desktop expertise and the mounting curiosity within the logical underpinnings of mathematics. Explanantion and evidence in Mathematics assembles views from arithmetic schooling and from the philosophy and heritage of arithmetic to reinforce mutual knowledge and proportion contemporary findings and advances of their interrelated fields. With examples starting from the geometrists of the seventeenth century and historical chinese language algorithms to cognitive psychology and present academic perform, participants discover the function of refutation in producing proofs, the numerous hyperlinks among scan and deduction, using diagrammatic considering as well as natural good judgment, and the makes use of of facts in arithmetic schooling (including a critique of "authoritative" as opposed to "authoritarian" educating styles).
A sampling of the coverage:
- The conjoint origins of evidence and theoretical physics in historic Greece.
- Proof as bearers of mathematical knowledge.
- Bridging understanding and proving in mathematical reasoning.
- The function of arithmetic in long term cognitive improvement of reasoning.
- Proof as test within the paintings of Wittgenstein.
- Relationships among mathematical facts, problem-solving, and explanation.
Explanation and facts 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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