Children's understanding of the relationship between addition and subtraction

@article{citeulike:2750629, abstract = {In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields 12. Here, we investigate whether preschool children's approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.}, author = {Gilmore, Camilla K. and Spelke, Elizabeth S. }, citeulike-article-id = {2750629}, doi = {10.1016/j.cognition.2007.12.007}, journal = {Cognition}, keywords = {development, mathematics}, month = {June}, number = {3}, pages = {932--945}, posted-at = {2008-05-03 21:36:57}, priority = {2}, title = {Children's understanding of the relationship between addition and subtraction}, url = {http://dx.doi.org/10.1016/j.cognition.2007.12.007}, volume = {107}, year = {2008} }

TY - JOUR ID - citeulike:2750629 L3 - citeulike-article-id:2750629 TI - Children's understanding of the relationship between addition and subtraction JF - Cognition VL - 107 IS - 3 SP - 932 EP - 945 N2 - In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields 12. Here, we investigate whether preschool children's approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding. KW - development KW - mathematics AU - Gilmore, Camilla AU - Spelke, Elizabeth PY - 2008/06// UR - http://dx.doi.org/10.1016/j.cognition.2007.12.007 ER -