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Journal für Mathematik-Didaktik

, Volume 11, Issue 4, pp 273–296 | Cite as

Zum Rechtfertigungsproblem didaktischer Konzeptionen — Ein Beitrag zur Bruchrechendidaktik — Teil I

  • Hans Joachim Burscheid
  • Wemer Mellis
Article

Abstract

The paper presents arguments of a methodological kind to overcome the arbitrariness of educational reasoning. The point of view taken is that a researcher, who wants to make suggestions for mathematics education on a given subject, has to give explicit constraints for the selection, structuring and presentation of the knowledge to be taught. In order to have a provable claim on his suggestions, the knowledge to be taught has to be described as a theory. His claim than is, that the theory satisfies the given constraints.

As an example constraints are given for the treatment of fractions as measurements. The knowledge to be taught about the fractions as measurements is reconstructed as an empirical theory in the structuralist’s view following J.D. Sneed. This certain kind of reconstruction ist justified by the point of view on children’s learning as adopted here. In order not to divert the reader’s attention from the paper’s goal, the form of the theory is not discussed in its own right. But the theory is described in detail, specially in respect to its fundamentals (part I). A series of stages and variations in the introduction of the theory shall ease the reader’s understanding of the formal reasoning (part II). In the final section the presented constraints and the theory of fractions as measurements is compared to the traditional treatment of fractions in mathematics education. This suggests a way to a rational reconstruction of the traditional concepts in teaching fractions.

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Literatur

  1. BALZER, W., Mathematical Structures as Representations of Intellectual Structures. Dialectica 34 (1980), 247–262CrossRefGoogle Scholar
  2. BALZER, W., Empirische Theorien: Modelle — Strukturen — Beispiele. Braunschweig 1982CrossRefGoogle Scholar
  3. BAUERSFELD, H., Ergebnisse und Probleme von Mikroanalysen mathematischen Unterrichts. In: W. Dörfler — R. Fischer (Hrsg.), Empirische Untersuchungen zum Lehren und Lernen von Mathematik. Schriftenreihe Didaktik der Mathematik. Univ. für Bildungs-wissenschaften in Klagenfurt, Bd. 10. Wien — Stuttgart 1985. S. 7–25Google Scholar
  4. BURSCHEID, H.J. — MELLIS, W., The construction of the fraction-concept and the addition of fractions as content of an empirical theory. Proceedings of the 2nd TME — Conference „Foundations and Methodology of the Discipline Mathematics Education (Didactics of Mathematics)”. Bielefeld — Antwerpen 1988. S. 226–235Google Scholar
  5. KARASCHEWSKI, H., Wesen und Weg des ganzheitlichen Rechenunter-richts. Stuttgart 1966Google Scholar
  6. MELLIS, W., Eine strukturalistische Betrachtung der Conservation-ability. Unveroffentliches Manuskript 1984Google Scholar
  7. RESNICK, L.B., Mathematics and Science Learning: A New Conception. Science 220 (1983), 477–478CrossRefGoogle Scholar
  8. SCHMIDT, S. — WEISER, W., Zählen und Zahlenverstandnis von Schulanfängern: Zählen und der kardinale Aspekt. Journal für Mathematikdidaktik 3 (1982), 227–263Google Scholar
  9. SNEED, J.D., The Logical Structure of Mathematical Physics. Dordrecht — Boston — London 1971CrossRefGoogle Scholar
  10. SNEED, J.D., Quantities as Theoretical with Respect to Qualities. Epistemologia II (1979), 215–250Google Scholar
  11. SPECK, J. (Hrsg.), Handbuch wissenschaftstheoretischer Begriffe. 3 Bde. Gottingen 1980Google Scholar
  12. STEGMOLLER, W., Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie. Band II. Theorie und Erfahrung. Studienausgabe, Teil D und Teil E. Berlin — Heidelberg 1973Google Scholar
  13. WEIDIG, I., Zahlbereichserweiterungen in didaktischer Sicht. Der mathematische und naturwissenschaftliche Unterricht 26 (1973), 482–486Google Scholar

Copyright information

© GDM - Gesellschaft für Didaktik der Mathematik 1990

Authors and Affiliations

  • Hans Joachim Burscheid
    • 1
  • Wemer Mellis
    • 1
  1. 1.Seminar für Mathematik und ihre DidaktikUniversität zu KölnKöln 41Deutschland

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