The Development of the Commutativity Principle and Economical Addition Strategies

Arthur J. Baroody, Kathleen E. Gannon

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)321-339
Number of pages19
JournalCognition and Instruction
Issue number3
StatePublished - Jun 1 1984
Externally publishedYes

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Education
  • Developmental and Educational Psychology
  • Psychology(all)


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