A study of preservice teachers' selection of computational methods based on the characteristics of the mathematics test items

The objectives of the study were to determine: (1) if the type of computational methods preservice elementary teachers select to use to solve a series of arithmetic items are correlated with item and subject characteristics; (2) if there is a relationship between computational methods selected by an expert and the preservice teacher selections; and, (3) if the underlying thought processes related to number sense that subjects use to select a computational method differ between the high and low mental arithmetic subjects.;Sixty-six preservice elementary teachers and a mathematics expert were administered a Computational Methods Test (CMT), an attitude toward mathematics instrument, and an attitude toward calculator instrument. Twelve subjects were selected for interviews which provided insight into the thought processes used to select computational methods.;After analysis of the responses, it was found that subjects tended to solve problems involving: (1) "nice numbers" with mental arithmetic; (2) "near nice numbers" using a calculator; (3) fractions using paper-and-pencil. Overall, it appeared that the subject characteristics (gender, age, CMT score, attitude toward calculators, attitude toward mathematics, Math 105 grade) did not constitute a reasonable set of variables to predict computational method. Twenty-four dichotomus item characteristics such as nice numbers, fractions, and near nice numbers proved more useful in predicting the computational method selected by preservice subjects. The expert and the preservice teachers agreed in their selection of computational methods 62.4% of the cases. The largest percentage of agreements occurred when the expert selected calculator and the preservice teachers chose calculators. The largest percentage of disagreements occurred when the expert selected paper-and-pencil and the subjects chose calculators. During the interviews subjects in the high mental arithmetic group used more numbers sense strategies and showed more confidence than the subjects in the low mental arithmetic group.;Programmatic recommendations for teacher preparation courses include: (1) providing a strong foundation in historical and current thinking on mathematics educations; (2) learning mathematics as they will be expected to teach it; (3) developing number sense ideas; (4) using the CMT; and (5) incorporating the interview process.