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One hundred twenty-eight children in Grades 1, 2, and 3 were given two multiplication and four division word problems that differed in semantic structure. The children's solution strategies were classified by degree of abstraction into direct representation, double counting, transitional counting, additive or subtractive, or recalled number fact. Strategies were also classified by use of physical objects: use as representations of individual elements, use as tallies or repeated references, or no use. Analyses of the solution strategies indicated the existence of a two-step intuitive model for multiplication, two common intuitive models for partitive division and measurement division each of which was related to an intuitive model for subtraction, and a third model for partitive division.
Vicky L. Kouba (Wed,) studied this question.