Young children's intuitive models of multiplication and division

Joanne T. Mulligan, Michael C. Mitchelmore

Research output: Contribution to journalArticle

79 Citations (Scopus)

Abstract

In this study, an intuitive model was defined as an internal mental structure corresponding to a class of calculation strategies. A sample of female students was observed 4 times during Grades 2 and 3 as they solved the same set of 24 word problems. From the correct responses, 12 distinct calculation strategies were identified and grouped into categories from which the children's intuitive models of multiplication and division were inferred. It was found that the students used 3 main intuitive models: direct counting, repeated addition, and multiplicative operation. A fourth model, repeated subtraction, only occurred in division problems. All the intuitive models were used with all semantic structures, their frequency varying as a complex interaction of age, size of numbers, language, and semantic structure. The results are interpreted as showing that children acquire an expanding repertoire of intuitive models and that the model they employ to solve any particular problem reflects the mathematical structure they impose on it.

Original languageEnglish
Pages (from-to)309-330
Number of pages22
JournalJournal for Research in Mathematics Education
Volume28
Issue number3
Publication statusPublished - May 1997

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