## Doctoral Dissertations

#### Title

Children's solution of arithmetic word problems as a function of number size

January 1998

#### Keywords

Education, Mathematics|Education, Educational Psychology|Psychology, Developmental|Psychology, Cognitive

Ph.D.

#### Abstract

Based on evidence indicating that young children reason more maturely about smaller ($\leq$5) than larger numbers ($\geq$6), it was hypothesized that 5- and 6-year-old children's solving of simple arithmetic word problems would vary as a function of the size of the numbers involved. Smaller-number problems should be solved in a more advanced fashion than larger-number problems. The problems used were simple addition and subtraction problems of the sort termed "change" and "combine" problems in the literature. There were 6 different types of "change" problems and 2 different types of "combine" problems. These different problem types previously have been found to vary in difficulty. It was expected that performance would be at an overall higher level on smaller-number than on larger-number problems. It was also expected that the performance difference between smaller-number and larger-number problems would increase as problem difficulty increased.^ The results were partially congruent with expectations. The 5- and 6-year-old children solved smaller-number problems at a higher level than larger-number problems, and the difference between smaller-number and larger-number problems became relatively, but not absolutely, larger as problem difficulty increased. An analysis examined how number size influences the theoretically separate processes of (a) understanding a problem to the extent that the computation to be carried out is generated and (b) performing the generated computation correctly. The analysis indicated that larger numbers reduced problem understanding as well as the correct carrying out of computations. The relative reduction in understanding produced by larger numbers grew as problems became more difficult. It was suggested that the effect of number size on problem understanding occurs because (a) young children can immediately retrieve information about the relative sizes of the sets referenced by smaller-number words but have difficulty retrieving information about the relative sizes of sets referenced by larger-number words and (b) the availability of such information facilitates understanding. ^

COinS