The Development of the Commutativity Principle and Economical Addition Strategies

• DOI: 10.1207/s1532690xci0103_3
• Publication Date: 2006-01-30T14:34:06Z
• Authors: Arthur J. Baroody; Kathleen E. Gannon
• Keywords: 05 social sciences; 0501 psychology and cognitive sciences

What is the relationship between principle of commutativity and development addition strategies that disregard addend order? It has been proposed assumption (Conjecture 1) or discovery 2) a necessary condition for invention such advanced strategies. A third hypothesis suggests children may invent labor-saving without necessarily appreciating principle. This study tested three conjectures by evaluating 36 kindergartners on two types tasks. Both tasks involved predicting whether commuted noncommuted pairs problems would produce same different answers. Commutativity was not naturally assumed (as Conjecture 1), but appeared to be discovered. However, contrary 2 consistent with 3, an understanding evident in all those who invented also confirmed counting-all starting larger addend-a mental strategy recently discovered case study-was uncommon device among young children.