Developmental Differences in Understanding and Solving Simple Mathematics Word Problems

The hypothesis was tested that older chidren, fifth/sixth graders versus third graders, who are more accurate in word problem solution, would show evidence of problem differentiation consistent with schema theories of problem representation and solution. A mathematics word problem sorting task and an accuracy test were used to assess problem representation and accuracy of solution across 16 different problem types. Cluster analyses of sorting data revealed that older children demonstrated sorting patterns consistent with a refined schema theory. Younger children were both less accurate and less systematic in their sorting. Idealized sorting patterns representing schema theories as well as surface structure problem similarity were tested against actual sorting patterns. Regression analyses confirmed that the fifth/sixth graders' and third graders' sorting data were best fit by a schematic sort and by a surface structure sort, respectively. Additionally, an English versus Spanish language contrast showed no effect of language on either accuracy of solution or the sorting patterns of the math word problems.