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 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.

Show description

Read Online or Download Explanation and Proof in Mathematics: Philosophical and Educational Perspectives PDF

Best educational philosophy books

Education in Divided Societies (Ethnic and Intercommunity Conflict)

All societies include ethnic divisions. typically, schooling has acted to advertise social integration, yet with the acknowledgement of range will we recognize which approach top promotes optimistic inter-community relatives? schooling in Divided Societies examines the event of a number of structures, together with these which offer universal colleges and people which position minorities in separate colleges.

Deans of Men and the Shaping of Modern College Culture

Deans of guys in American faculties and universities have been created within the past due 19th and early 20th centuries to aid deal with a becoming pupil inhabitants. The early deans usually had a character that allowed them to have interaction simply with scholars. over the years, many deans observed their places of work raise in dimension and accountability.

Wartime Schooling and Education Policy in the Second World War: Catholic Education, Memory and the Government in Occupied Belgium

This publication bargains with the advance of non-public secondary education through the moment international warfare in Belgium. It specializes in how the German occupier used schooling to achieve attractiveness of the regime, and discusses the attitudes of Belgian schooling professionals, faculties, lecturers and students in the direction of the German profession.

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

Sample text

Logical Atomism. In J. M. ), 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.

Methods and problems in Greek science (pp. 248–277). Cambridge: Cambridge University Press. Lloyd, G. E. R. (2000). Der Beweis und die Idee der Wissenschaft. In J. Brunschwig, & G. E. R. ) Das Wissen der Griechen. Eine Enzyklopädie (pp. 238–258). München: Wilhelm Fink. Mach, E. (1976). Die Mechanik. Historisch-kritisch dargestellt (Unveränderter Nachdruck der 9. Auflage, Leipzig 1933, 1. Auflage 1883). Darmstadt: Wissenschaftliche Buchgesellschaft. Maddy, P. (1990). Realism in mathematics. Oxford: Clarendon Press.

In CERME 6 Proceedings, to appear. Bartolini Bussi, M. , Mariotti, M. , & Garuti, R. (1997). Approaching geometry theorems in contexts: from history and epistemology to cognition. In Proceedings of the 21st conference of the international group for the psychology of mathematics education (Lahti) (Vol. 1, pp. 180–195). Duhem, P. (1994). Sozein ta Phainomena. Essai sur la notion de théorie physique de Platon à Galilée. Paris: Vrin (Original publication 1908). Freudenthal, H. (1973). Mathematics as an educational task.

Download PDF sample

Rated 4.85 of 5 – based on 34 votes