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 kno w about the relation between these two operations. We looked at this knowle dge in two studies. In one we asked whether 5- and 6-year-old children unde rstand 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 princ iple even when the addend and subtrahend are the same in quantity but invol ve different material In our second study we showed that 6- to 8-year-old c hildren also use the inversion in combination with decomposition to solve a + b - (b + 1) problems. In both studies, factor analyses suggested that th e children were using different strategies in the control problems, which r equire computation, than in the inversion problems, which do not We conclud e that young children understand the relations between addition and subtrac tion and that this understanding may not be based on their computational sk ills. (C) 1999 Academic Press.