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Modelling with Heuristic Worked Examples in the KOMMA Learning Environment

Modellieren mit heuristischen Lösungsbeispielen in der Lernumgebung KOMMA

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Abstract

Modelling competency is considered to be an important part of mathematical competency. Although much work has been done with respect to the development and dissemination of modelling tasks, there is hardly any empirical evidence how these tasks should be integrated in the mathematics classroom. In this article we present a teaching approach based on heuristic worked examples which turned out to be a promising way of supporting initial skill acquisition within the field of modelling. We will provide an overview how the learning environment (KOMMA) was conceptualized and will present first results of a large-scale field study examining the effectiveness of example based learning for initial skill acquisition in the field of modelling. The results presented here take into account short-term as well as long-term effects on the learning of 8th-grade students. They suggest, that the participants’ modelling competencies increased significantly during the training but that long-term effects were much smaller.

Zusammenfassung

Modellierungskompetenz wird als wichtiger Teil mathematischer Kompetenz betrachtet. Trotz umfangreicher Forschungen zur Entwicklung und Dissemination von Modellierungsaufgaben gibt es kaum empirische Ergebnisse dazu, wie diese Aufgaben in den Mathematikunterricht integriert werden sollen. Wir beschreiben einen auf heuristischen Lösungsbeispielen basierenden instruktionalen Ansatz, der sich als vielversprechend für den anfänglichen Fähigkeitserwerb beim Modellieren erwiesen hat. Wir beschreiben das Konzept der verwendeten Lernumgebung (KOMMA) und berichten erste Ergebnisse einer größeren Feldstudie zur Untersuchung der Effektivität von beispielbasierten Lernumgebungen für den anfänglichen Erwerb von Modellierungskompetenzen. Die Ergebnisse beschreiben kurzfristige und langfristige Lernzuwächse bei Schülerinnen und Schülern der achten Jahrgangsstufe. Sie legen nahe, dass die Modellierungskompetenzen der Schülerinnen und Schüler während der Intervention signifikant zunahmen, langfristige Effekte aber deutlich kleiner ausfielen.

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Notes

  1. KOMMA is supported by a grant from BMBF, the German Federal Ministry of Education and Research (PLI3032).

  2. SEASITE means self-explanation activity supported by instructional explanations.

  3. The IRT-analysis was based on a sample of 1657 persons who took part in all tests but were assigned to different learning environments (paper and pencil material instead of computer based instruction or material asking for a higher degree of self-regulation; see above for details).

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, München, Deutschland

    Luzia Zöttl

  2. TUM School of Education, Technische Universität München, Schellingstraße 33, 80799, München, Deutschland

    Stefan Ufer & Kristina Reiss

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  1. Luzia Zöttl
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  2. Stefan Ufer
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  3. Kristina Reiss
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Correspondence to Stefan Ufer.

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Zöttl, L., Ufer, S. & Reiss, K. Modelling with Heuristic Worked Examples in the KOMMA Learning Environment. J Math Didakt 31, 143–165 (2010). https://doi.org/10.1007/s13138-010-0008-9

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