First-Graders’ Development of Calculation Strategies: How Deriving Facts Helps Automatize Facts
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A longitudinal section study encompassing 139 children from Lower Austria was conducted to assess the strategies underlying children's solving of addition and subtraction problems at the beginning of grade one, and to examine the ways in which children develop these strategies over the school year. These strategies were related to the didactics and methodology of primary arithmetic education provided for these children, on the one hand, and their number knowledge at school entry, on the other. The qualitative-exploratory part of the study is devoted to a detailed analysis of children's strategy developments with special emphasis being placed on derived facts strategies. The study's quantitative part provides a statistical backup for significant effects of children's number knowledge at the beginning of grade one as well as gender on the share of tasks solved by fact-utilizing strategies (suggesting that children with a higher level of number knowledge as well as boys have an advantage). Moreover, it has been found that children who use derived facts strategies on a certain task by mid first grade will by the end of the first grade solve the same task significantly more frequently by fact retrieval than children who by mid first grade were relying on counting on. The study's findings are discussed in particular as to their implications concerning the conception of initial arithmetic education. In the examined classrooms no efforts were taken to work out derived facts strategies on a systematic basis.