Children's Understanding of the Relation between Addition and Subtraction: Inversion, Identity, and Decomposition

心理学 反演(地质) 减法 关系(数据库) 身份(音乐) 发展心理学 认知心理学 社会心理学 算术 数学 物理 声学 古生物学 数据库 构造盆地 计算机科学 生物
作者
Peter Bryant,Clare Christie,Alison Rendu
出处
期刊:Journal of Experimental Child Psychology [Elsevier BV]
卷期号:74 (3): 194-212 被引量:109
标识
DOI:10.1006/jecp.1999.2517
摘要

In order to understand addition and subtraction fully, children have to know about the relation between these two operations. We looked at this knowledge in two studies. In one we asked whether 5- and 6-year-old children understand that addition and subtraction cancel each other out and whether this understanding is based on the identity of the addend and subtrahend or on their quantity. We showed that children at this age use the inversion principle even when the addend and subtrahend are the same in quantity but involve different material. In our second study we showed that 6- to 8-year-old children also use the inversion in combination with decomposition to solve a + b − (b + 1) problems. In both studies, factor analyses suggested that the children were using different strategies in the control problems, which require computation, than in the inversion problems, which do not. We conclude that young children understand the relations between addition and subtraction and that this understanding may not be based on their computational skills.
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