Download Explanation and Proof in Mathematics: Philosophical and by Gila Hanna, Hans Niels Jahnke, Helmut Pulte PDF

By Gila Hanna, Hans Niels Jahnke, Helmut Pulte

In the 4 a long time because Imre Lakatos declared arithmetic a "quasi-empirical science," expanding consciousness has been paid to the method of evidence and argumentation within the box -- a improvement paralleled via the increase of desktop expertise 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 background 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 historic chinese language algorithms to cognitive psychology and present academic perform, individuals discover the position of refutation in producing proofs, the numerous hyperlinks among test and deduction, using diagrammatic pondering as well as natural good judgment, and the makes use of of evidence 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 old 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 scan within the paintings of Wittgenstein
  • Relationships among mathematical evidence, problem-solving, and explanation

Explanation and evidence in Mathematics is bound to draw a variety of readers, together with mathematicians, arithmetic schooling pros, researchers, scholars, and philosophers and historians of mathematics.

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Additional resources for Explanation and Proof in Mathematics: Philosophical and Educational Perspectives

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II, pp. 45–51). Paris: PME. Heath, T. L. (Ed. ) (1953). The works of Archimedes. New York: Dover. Heath, T. L. (Ed. ) (1956). The thirteen books of Euclid’s elements. Second edition revised with additions. New York: Dover. Jahnke, H. N. (2005). A genetic approach to proof. In M. ) Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, Sant Feliu de Guíxols 2005, 428–437. Jahnke, H. N. (2007). Proofs and Hypotheses. Zentralblatt für Didaktik der Mathematik (ZDM), 39(2007), 1–2, 79–86.

2 Lagrange Euler’s proof in fact rested upon an element alien to analysis as Euler saw it: the geometrical intermediate value property. However, at the end of the eighteenth century, in a treatise on algebraic equations, Lagrange came up with a simple proof of the intermediate value theorem for polynomials, based on the fundamental theorem of algebra. His proof, which seemed at first sight satisfactory and independent of geometry, runs as follows: He writes a polynomial as a product of linear terms.

Contemporary British Philosophy, first series (pp. 357–383). London: George Allen & Unwin. Szabó, Á. (1960). Anfänge des Euklidischen Axiomensystems. Archive for History of Exact Sciences 1, 38–106. Page numbers refer to the reprint in O. ) (1965) Zur Geschichte der griechischen Mathematik (pp. 355–461). Darmstadt: Wissenschaftliche Buchgesellschaft. Toomer, G. J. (Ed. ) (1984). Ptolemy’s Almagest. London: Duckworth. van der Waerden, B. L. (1988). Science awakening I, Paperback edition. Dordrecht: Kluwer.

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