Children's Use of Mathematical Structure.

This study examined the use of the commutativity, addition-subtraction complement, and N + 1 progression principles in a numerical task by capable first, second, and third graders. Fifty-four children were interviewed individually. A series of number combinations was given as a game in which one had to compute in solving some items but could avoid computation in others by using one of the principles. Commutativity was used extensively by children at each grade. Use of the addition-subtraction complement principle to solve subtraction items varied across grades and depended on how efficiently the preceding addition counterpart had been solved. The N + 1 pattern was seldom used at any grade.