THE DEVELOPMENT OF PROCEDURAL AND CONCEPTUAL KNOWLEDGE IN COMPUTATIONAL ESTIMATION

Children in Grades 4, 6, and 8 and adults estimated answers to multipl ication 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 dif ficult (e.g., 2 x 3) problems. Estimation performance improved with ag e, with adults producing more accurate estimates than children, but th e most striking developmental changes were in the conceptual knowledge used to perform this estimation task. From Grade 6, students seemed t o understand the role of the simplification principle in estimation. C hildren reduced complex problems through rounding and prior compensati on 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 answe r. Adults produced exact-answer solutions on simple problems and adjus ted their preliminary estimates closer to the actual answer (postcompe nsation). We propose a process model of estimation based on Siegler's model of strategy choice in simple arithmetic.