Children's understanding of the relation between addition and subtraction: inversion, identity, and decomposition

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.