Statement of the Problem. In this exploratory study, computational estimation performance in four dimensions and its relationship to several mathematical variables were studied. Research questions focused on differences in students' performance of computational estimation related to attributes of the items and identification of mathemtical skills related to computational estimation. Methodology. An Estimation Test was developed to measure four types of computational estimation: open-ended, reasonable vs. unreasonable, reference number, and order of magnitude. The test was balanced in four dimensions: type, form, number, and operation. The items were presented on an overhead projector and individually timed. A Related Factors Test was developed to measure achievement in selecting operations, making comparisons, knowing number facts, operating with tens, operating with multiples of ten, knowing place value, rounding, and judging relative size. The Problem Solving Test of the Iowa Problem Solving Project measured getting to know the problem, solving the problem, and looking back. Other variables were general mathematics achievement and sex. Subjects were 309 eighth grade students in seven southeastern Michigan school districts. Analysis of variance and multiple regression were used to study the relationships among the variables. Conclusions. Students performed differently on three types of estimation. The order of difficulty from easiest to hardest was: order of magnitude, reference number, and open-ended. Decimal number items were harder than whole number items. Division was the hardest operation, multiplication the next most difficult, and subtraction and addition were equally least difficult. Boys did better than girls on total computational estimation and order of magnitude estimation. There were no statistically significant differences between the sexes in performance of open-ended or reference number estimation. In a stepwise multiple regression, total estimation was explained by operating with tens, making comparisons, and getting to know the problem. Open-ended estimation was explained by judging relative size and operating with multiples of ten. Order of magnitude estimation was explained by operating with tens, making comparisons, looking back, and sex.
