<p>Learning difficulties with respect to division have been documented and discussed during the last three decades in the German as well as in the international literature. There have been several proposals for changing traditional teaching approaches. At the same time various international studies indicate that young children successfully solve context-related partitive and quotitive division problems even before they start school. However, frequently these studies were conducted many years ago and/or have various limitations. The study presented in this paper seeks to examine the early division skills of a&#xa0;total of 537 first and second graders working on paper-pencil tests with quotitive (n<sub>A</sub> = 291) and partitive (n<sub>V</sub> = 246) division problems with and without remainder before division was formally introduced in their classrooms. The tasks were set in familiar contexts for young children and presented as drawings combined with verbal instructions. The results demonstrate that the children who took part in the study were highly successful in solving the tasks irrespective of the underlying basic concept, i.e. quotioning or partitioning. However, children’s drawings turned out to be rather diverse and they differ significantly in terms of quotioning and partitioning. Implications for classroom practice and further research are discussed in conclusion.</p>

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Frühes Divisionsverständnis von Erst- und Zweitklässler*innen vor der unterrichtlichen Einführung der Division

  • Luca Wiggelinghoff,
  • Julia Streit-Lehmann,
  • Andrea Peter-Koop

摘要

Learning difficulties with respect to division have been documented and discussed during the last three decades in the German as well as in the international literature. There have been several proposals for changing traditional teaching approaches. At the same time various international studies indicate that young children successfully solve context-related partitive and quotitive division problems even before they start school. However, frequently these studies were conducted many years ago and/or have various limitations. The study presented in this paper seeks to examine the early division skills of a total of 537 first and second graders working on paper-pencil tests with quotitive (nA = 291) and partitive (nV = 246) division problems with and without remainder before division was formally introduced in their classrooms. The tasks were set in familiar contexts for young children and presented as drawings combined with verbal instructions. The results demonstrate that the children who took part in the study were highly successful in solving the tasks irrespective of the underlying basic concept, i.e. quotioning or partitioning. However, children’s drawings turned out to be rather diverse and they differ significantly in terms of quotioning and partitioning. Implications for classroom practice and further research are discussed in conclusion.