Matematikkens sproglighed som didaktisk potentiale

Authors

  • Carl Winsløw

DOI:

https://doi.org/10.7146/nomad.v6i2.146640

Abstract

Med udgangspunkt i klassiske og nyere matematikfilosofiske synspunkter redegøres kort for hvorledes matematik som fænomen kan beskrives i sprogteoretiske termer. Derpå diskuteres konsekvenserne af en sådan beskrivelse for to grundlæggende matematikdidaktiske problemkredse: Hvordan begrundes matematikundervisning? Hvordan kan matematikundervisning sætte den lærende i stand til at udvikle kreative (i modsætning til automatiske) kompetencer i udøvelse og anvendelse af faget?

References

Benacerraf, P. (1983). Philosophy of mathematics. Cambridge University Press. Bishop, A. (1988). Mathematical enculturation. Kluwer Dordrecht.

Brouwer, L. (1952). Historical background, principles and methods of intuitionism. Søuth African Journal of Science 49, 139-146.

Davis, P. J. & Hersh, R. (1986). Descartes' dream. Penguin books London.

Ernest, P. (1992). The nature of mathematics: towards a social constructivist account. Science and Education 1, 89-100. https://doi.org/10.1007/BF00430212

Ernest, P. (1994). Mathematics, education and philosophy: an international perspective. The Falmer Press London.

Fitzgerald, A. (1985). New technology and mathematics in employment: the main report. University of Birmingham.

Frege, G. (1967). The thought: a logical enquiry. I P.Strawson, Philosophical logic. Oxford University Press.

Gödel, K. (1931). Über formal unentscheidbare Satze der Principia Mathematica und Vervandter Systeme. Monatshefte für Mathematik und Physik 38, 173-198. https://doi.org/10.1007/BF01700692

Hersh, R. (1979). Some proposals for reviving the philosophy of mathematics. Advances in Mathematics 31,31-50. https://doi.org/10.1016/0001-8708(79)90018-5

Hilbert, D. & Bernays, P. (1934). Grundlagen der Mathematik, I, Springer, Berlin.

Jessen, B. (1945). Den aksiomatiske metode. Matematisk Tidskrift A, 37-47.

Kemeny, J. (1988). How computers have changed the way I teach. I AMS-MAA, Joint lecture series. Atlanta, Georgia, USA.

Kline, M. (1972). Mathematics in western culture. Pelican London.

Lakatos, I. (1976). Proofs and refutations. Cambridge University Press. https://doi.org/10.1017/CBO9781139171472

Nissen, G. (1994). Matematikundervisning i en demokratisk kultur. I M. Blomhøj et al. (Eds). Hul i kulturen. Spektrum København.

Pimm, D. (1987). Speaking mathematically, Kegan Paul, London.

Rotman, B. (1988). Toward a semiotics of mathematics, Semiotica 72, 1-35. https://doi.org/10.1515/semi.1988.72.1-2.1

Russell, B. (1919). Introduction to mathematical philosophy. George Alwin and Unwin Ltd. London.

Russell, B. (1967). The autobiography of Bertrand Russell. George Alwin and Unwin Ltd. London.

Skemp, R. (1982). Communicating mathematics: Surface Structures and Deep Structures. I Visible language XVI 3, 281-288.

Thomassen, N. (1981). Dannelse og ideologikritik eller om humaniora og humanisme. I C. Bengt-Pedersen m.fl., Studier ifilosofi. Odense Universitetsforlag.

Tymoczko, T. (1986).New directions in thephilosphy of mathematics. Birkhauser, Boston.

Winsløw, C. (1998). A linguistic approach to the justification problem in mathematics education. For the learning of mathematics, 18(1) 17-23.

Winsløw, C. (1998). On the role of transformations in mathematical discourse. Fortryk.

Downloads

Published

1998-06-01

How to Cite

Winsløw, C. (1998). Matematikkens sproglighed som didaktisk potentiale. NOMAD Nordic Studies in Mathematics Education, 6(2), 29–40. https://doi.org/10.7146/nomad.v6i2.146640

Issue

Section

Articles