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Young Children's Intuitive Models of Multiplication and Division

Joanne T. Mulligan, Michael C. Mitchelmore 

May 1997, Volume 28, Issue 3, Page 309

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.

Keywords:
Pre-K-2
Grades 3-5
Clinical Interviews
Curriculum Developer
Conceptual Development
Teacher
Skill and Fluency
Reasoning and Proof
Multiplication and Division