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<p>In primary arithmetic lessons, manipulatives should be used to support the development of number concepts, number and task relationships, and concepts of operations. For this development of concepts to succeed, manipulatives must be specifically selected, introduced and supervised by the teacher. It is assumed, that teachers’ implicit beliefs, among other factors, guide their actions. This study focusses on the beliefs of primary school teachers regarding the use of manipulatives in primary arithmetic lessons. Episodic interviews were conducted with twelve primary school teachers and analysed using the documentary method to gain insights into explicit and implicit beliefs. Four sensegenetic typologies could be reconstructed, each with two types of beliefs, with one type having beliefs close to didactical standards and the other having beliefs (rather) far from didactical standards. We further found that inconsistencies arise between explicit and implicit beliefs. Four profiles of teachers were identified across the typologies: a&#xa0;didactically close and a&#xa0;didactically far profile as well as two mixed profiles. Overall, our findings point to a&#xa0;discrepancy between the findings of mathematics education research and teachers’ beliefs, from which conclusions can be drawn for the initial and further training of teachers.</p>

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Die Bedeutung von Anschauungsmitteln im Anfangsunterricht – Eine empirische Rekonstruktion von Lehrkräfteüberzeugungen

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  • 出版模式：

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  • 发表日期：

    2026年5月12日

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  • Clara Ries,
  • Stephanie Schuler,
  • Gerald Wittmann

摘要

In primary arithmetic lessons, manipulatives should be used to support the development of number concepts, number and task relationships, and concepts of operations. For this development of concepts to succeed, manipulatives must be specifically selected, introduced and supervised by the teacher. It is assumed, that teachers’ implicit beliefs, among other factors, guide their actions. This study focusses on the beliefs of primary school teachers regarding the use of manipulatives in primary arithmetic lessons. Episodic interviews were conducted with twelve primary school teachers and analysed using the documentary method to gain insights into explicit and implicit beliefs. Four sensegenetic typologies could be reconstructed, each with two types of beliefs, with one type having beliefs close to didactical standards and the other having beliefs (rather) far from didactical standards. We further found that inconsistencies arise between explicit and implicit beliefs. Four profiles of teachers were identified across the typologies: a didactically close and a didactically far profile as well as two mixed profiles. Overall, our findings point to a discrepancy between the findings of mathematics education research and teachers’ beliefs, from which conclusions can be drawn for the initial and further training of teachers.