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<p>One way to understand how meaning is associated with mathematical concepts is through the didactic category of <i>Grundvorstellungen</i> (GV). In the field of functional thinking, a&#xa0;distinction is commonly made between three <i>Grundvorstellungen</i>: the mapping GV, the covariation GV and the object GV. These ideas can be applied to all classes of functions. In each class, however, these ideas are linked to characteristic contexts as well as ways of thinking and operating, which in turn can serve as the starting point for new, more refined GVs. This article presents a&#xa0;method that can be used to differentiate the general GV of functions and to derive specific GVs for each class of functions. The procedure is based on a&#xa0;didactically orientated subject analysis in conjunction with Freudenthal’s didactic phenomenology and aspects of the genesis of mathematical concepts. Finally, the method is applied to trigonometric functions, identifying six normative GV about sine.</p>

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Didaktisch orientierte Sachanalysen zur Ausdifferenzierung der allgemeinen Grundvorstellungen zum Funktionsbegriff – Exemplarisch durchgeführt an der Sinusfunktion

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  • 出版模式：

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  • 发表日期：

    2025年1月27日

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  • Valentin Katter

摘要

One way to understand how meaning is associated with mathematical concepts is through the didactic category of Grundvorstellungen (GV). In the field of functional thinking, a distinction is commonly made between three Grundvorstellungen: the mapping GV, the covariation GV and the object GV. These ideas can be applied to all classes of functions. In each class, however, these ideas are linked to characteristic contexts as well as ways of thinking and operating, which in turn can serve as the starting point for new, more refined GVs. This article presents a method that can be used to differentiate the general GV of functions and to derive specific GVs for each class of functions. The procedure is based on a didactically orientated subject analysis in conjunction with Freudenthal’s didactic phenomenology and aspects of the genesis of mathematical concepts. Finally, the method is applied to trigonometric functions, identifying six normative GV about sine.