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Recognising mathematical creativity in schoolchildren

Mathematische Kreativität bei Schulkindern erkennen

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Abstract

Examples of tasks designed to recognise creative thinking within mathematics, used with 11–12-year-old pupuls, are described. The first construct empoyed in the design of these tasks is the ability to overcome fixation. Sometimes pupils demonstrate content-universe fixation, by restricting their thinking about a problem to an insufficient or inappropriate range of elements. Other times they show algorithmic fixation by continuing to adhere to a routine procedure or stereotype response even when this becomes inefficient or inappropriate. The second construct employed is that of divergent production, indicated by flexibility and originality in mathematical tasks to which a large number of appropriate responses are possible. Examples of three categories of such tasks are described: (1) problem-solving, (2) problem-posing, and (3) redefinition. Examples of pupils’ responses to various tasks are used to argue that they do indeed reveal thinking that can justifiably be described as creative. The relationship to conventional mathematics attainment is discussed-mathematics attainment is seen to limit but not to determine mathematical creativity.

Kurzreferat

Es werden Beispielaufgaben beschrieben, die dem Erkennen kreativen Denkens in Mathematik bei 11–12 jährigen Schülern dienen sollen. Die erste: Aufgabengruppe dient der Fähigkeit, Fixierungen zu überwinden. Manche Schüler zeigen eine Fixierung in der Gesamtheit eines Inhaltsbereichs, die dazu führt, daß sie ihr problemdenken auf einen unzureichenden oder ungeeigneten Teibereich von Möglichkeiten beschränken. Andere Schüler wiederum zeigen eine algorithmische Fixierung, indem sie Routinemethoden oder stereotype Antworten auch dann noch verwenden, wenn sich diese als uneffizient oder ungeeignet herausstellen. Die zweite Aufgabengruppe soll divergentes. Denken fördern; sie ist gekennzeichnet durch Flexibilität und Originalität der mathematischen Aufgaben, zu denen es eine Vielzahl möglicher Ergebnisse gibt. Drei Kategorien solcher Aufgaben werden beispielhaft beschrieben: (1) Problemlösen, (2) Problemstellen und (3) Neudefinition. Beispielhafte Schülerantworten zu verschiedenen Aufgaben werden benutzt, um zu zeigen, daß sie tatsächlich ein Denken enthüllen, das kreativ genannt werden kann. Die Beziehung zu konventionellen mathematischen Leistungen wird diskutiert—diese scheinen mathematische Kreativität eher zu hemmen.

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Haylock, D. Recognising mathematical creativity in schoolchildren. Zentralblatt für Didaktik der Mathematik 29, 68–74 (1997) doi:10.1007/s11858-997-0002-y

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