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Journal für Mathematik-Didaktik

, Volume 31, Issue 1, pp 9–29 | Cite as

Reconceptualising Word Problems as Exercises in Mathematical Modelling

  • Lieven VerschaffelEmail author
  • Wim Van Dooren
  • Brian Greer
  • Swapna Mukhopadhyay
Originalarbeit

Abstract

During the last 20 years, many scholars have argued in various ways that the (traditional) practice of word problems in school mathematics does not foster in students, indeed inhibits, a genuine disposition towards mathematical modelling and applied problem solving. In this article we give a brief review and discussion of this research, including a summary of earlier work culminating in the book by Verschaffel et al. (2000) and with special attention to the more recent empirical work. We begin with presenting the ascertaining studies documenting and illuminating the phenomenon of “suspension of sense-making” when doing school arithmetic word problems. Then we move to studies that have contributed to the explanation of the observed effects. This explanation is followed by a review of some recent design experiments wherein the modelling perspective has been implemented and tested. Afterwards we discuss some recent studies on the difficulties encountered by teachers who try to implement this new perspective into their daily classroom practices. Finally, we discuss a number of educational implications of the research done so far and some challenges for the future of teaching mathematical modelling.

Keywords

Word problems Mathematical sense-making Didactical contract Socio-mathematical norms Classroom practices 

Die Rekonzeptualisierung von Textaufgaben als Übungen in mathematischer Modellierung

Zusammenfassung

Im Verlauf der letzten 20 Jahre haben zahlreiche Wissenschaftler in verschiedenen Studien gezeigt, dass die traditionelle Art und Weise der schulischen Behandlung mathematischer Textaufgaben die Lernenden nicht hinsichtlich ihrer Modellierungskompetenzen fördert, sondern eher sogar behindert, dass sie angemessene Voraussetzungen für das Lösen angewandter Probleme erwerben. In diesem Artikel geben wir zunächst einen kurzen Überblick über die Forschung zu Textaufgaben und beziehen uns – mit einem Fokus auf neuere empirische Untersuchungen – u.a. auch auf diesbezügliche frühere Arbeiten, die im Buch von Verschaffel et al. (2000) veröffentlicht sind. Dabei beginnen wir mit der Beschreibung von Studien, die sich mit der Beschreibung und Erklärung des Phänomens des “suspension of sense-making” im Rahmen der schulischen Bearbeitung von arithmetischen Textaufgaben auseinandersetzen. Hierauf folgt die Analyse einiger experimenteller Untersuchungen, die sich mit einer verstärkten Implementation und Evaluation von Unterrichtsexperimenten befassen, in denen Modellierungsaspekten im Vordergrund stehen. Im Anschluss daran werden verschiedene Studien hinsichtlich der Schwierigkeiten analysiert, die sich bei der Implementation einer veränderten Herangehensweise in das tägliche Unterrichten ergeben.

Abschließend werden einige sich aus den Forschungsergebnissen ergebende didaktische Implikationen sowie sich daraus abzuleitende Herausforderungen noch zu leistender Forschung zur Vermittlung von Modellierungskompetenz diskutiert.

Mathematics Subject Classification (2000)

97A40 97M99 97D50 97D70 97D70 

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Copyright information

© GDM 2010

Authors and Affiliations

  • Lieven Verschaffel
    • 1
    Email author
  • Wim Van Dooren
    • 1
  • Brian Greer
    • 2
  • Swapna Mukhopadhyay
    • 2
  1. 1.Katholieke Universiteit LeuvenLeuvenBelgien
  2. 2.Portland State UniversityPortlandUSA

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