Classification Scheme for Modelling Tasks
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Classification Scheme for Modelling Tasks Katja Maaß
Received: 3 July 2009 / Accepted: 20 April 2010 / Published online: 8 May 2010 © GDM 2010
Abstract There are many different types of reality-related and modelling tasks, not to mention the many different classifications for these tasks, so it is difficult to obtain a clear overview of the subject. Therefore, following the idea of design research and based on modelling theory, the aim of this paper is to develop a comprehensive classification scheme that systematizes existing classifications. The scheme is intended to provide an overview of the different features of modelling tasks, thereby offering guidance in the task design and selection processes for specific aims and predefined objectives and target groups. The usefulness of the classification scheme will be shown by means of a concrete example. Klassifikationsschema für Modellierungsaufgaben Zusammenfassung Es gibt sehr viele verschiedene Arten von realitätsbezogenen Aufgaben und Modellierungsaufgaben und darüber hinaus auch sehr viele verschiedene Klassifikationen, was zu einem Mangel an Übersicht führt. In diesem Aufsatz soll daher der Idee des Design Research folgend basierend auf der Theorie zum Modellieren ein umfassendes, und bisherige Klassifikationen systematisierende Klassifikationsschema entwickelt werden. Ziel des Schemas soll sein, einen Überblick über die verschiedenen Eigenschaften von Modellierungsaufgaben zu geben und somit den Design- und Auswahlprozess von Modellierungsaufgaben für bestimmte Ziele und Zielgruppen zu steuern. Die Nützlichkeit des Modells wird anschließend exemplarisch an einer Zielgruppe aufgezeigt. Keywords Modelling · Modelling tasks · Classification of tasks · Design of tasks Mathematics Subject Classification (2000) 97M99 · 97-02 K. Maaß () Pädagogische Hochschule, Kunzenweg 21, 79117 Freiburg, Germany e-mail: [email protected]
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1 Introduction In day-to-day mathematics teaching, modelling happens rarely (Blum et al. 2002, p. 275). Furthermore, new empirical studies show that many teachers have almost no knowledge of modelling and do not integrate modelling tasks into their lessons (Maaß and Gurlitt 2009). In order to implement changes in daily teaching, adequate concepts of mathematics lessons are required, together with effective concepts of teacher education (Bruder 2009), continuous professional development and above all tasks related to the changes aimed at. Tasks are a fundamental part of mathematical lessons and thus have a central position within mathematics education (Krainer 1993, p. 65). For modelling there are a huge variety of tasks to choose from; consequently, selecting the appropriate task according to specific aims and target groups can be difficult. Furthermore, there are a number of classifications which often classify modelling tasks with respect to one or sometimes also a mixture of several characteristics (cf. Sect. 2.5). However, for a widespread uptake of modelling in mathematics education, a comprehensive and systematic cl
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