Children's solutions to multiplication and division word problems: A longitudinal study

Children's solution strategies to a variety of multiplication and division word problems were analysed at four interview stages in a 2-year longitudinal study. The study followed 70 children from Year 2 into Year 3, from the time where they had received no formal instruction in multiplication and division to the stage where they were being taught basic multiplication facts. Ten problem structures, five for multiplication and five for division, were classified on the basis of differences in semantic structure. The relationship between problem condition (i.e. small or large number combinations and use of physical objects or pictures), on performance and strategy use was also examined. The results indicated that 75% of the children were able to solve the problems using a wide variety of strategies even though they had not received formal instruction in multiplication or division for most of the 2 year period. Performance level generally increased for each interview stage, but few differences were found between multiplication and division problems except for Cartesian and Factor problems. Solution strategies were classified for both multiplication and division problems at three levels: (i) direct modelling with counting; (ii) no direct modelling, with counting, additive or subtractive strategies; (iii) use of known or derived facts (addition, multiplication). A wide range of counting strategies were classified as counting-all, skip counting and double counting. Analysis of intuitive models revealed preference for a repeated addition model for multiplication, and a 'building-up' model for division.