The Development of Procedural and Conceptual Knowledge in Computational Estimation

Children in Grades 4, 6, and 8 and adults estimated answers to multiplication problems. The problems varied in the number of digits: 1 x 2 (e.g., 8 x 18), 1 X 3 (e.g., 5 x 144), 2 x 2 (e.g., 22 x 91), and 2 x 3 (e.g., 45 x 164). Few children in Grade 4 could estimate. Most sixth and eighth graders provided reasonable estimates, however, even on difficult (e.g., 2 x 3) problems. Estimation performance improved with age, with adults producing more accurate estimates than children, but the most striking developmental changes were in the conceptual knowledge used to perform this estimation task. From Grade 6, students seemed to understand the role of the simplification principle in estimation. Children reduced complex problems through rounding and prior compensation to produce reasonable estimates. Only adults seemed to have a good grasp of the principle of proximity, however, understanding that it is important for the estimate to be reasonably close to the actual answer. Adults produced exact-answer solutions on simple problems and adjusted their preliminary estimates closer to the actual answer postcompensation). We propose a process model of estimation based on Siegler's model of strategy choice in simple arithmetic.