Do They Know What They Are Doing? Children's Use of Economical Addition Strategies and Knowledge of Commutativity

Children's methods of solving addition problems progress towards strategies that reverse the order of addends. The role knowledge of commutativity plays in this development is not clear. Previous studies suggest some use the strategies without believing addend order is irrelevant to addition. The numbers of such children are very small and the tests of commutativity may be inaccurate. Two studies using new tasks compare strategy use and knowledge. In the first, 47/48 children between 6 and 10 years old predicted order of addends would not alter quantity in some contexts. They also predominantly used strategies that reversed addend order. In the second study, 5‐year‐olds (18/24) were more likely to know commutativity than to use a strategy that reversed addend order or to answer sums correctly. Knowing commutativity precedes using strategies that presuppose it and does not derive from doing sums. Representing the addends with objects induced more arithmetic errors. Children used less accurate strategies when they could see the objects.