Are exact calculation and computational estimation categorically different?

Abstract

This study examined, through the problem-size effect, whether exact calculation and computational estimation are categorically different. In Experiment 1, 26 teacher candidates, most of whom were female, Caucasian, and in their early 20s, estimated 27 randomly generated double-digit multiplication problems. In Experiment 2, 44 similar participants estimated and calculated a common set of double-digit multiplication problems. Analysis of reaction times and error rates indicates that the problem-size effect holds true for exact calculation but not for estimation. In estimation, as problem size increases, reaction times do not increase, nor does the rate of unreasonable estimates. Instead, the difference between a factor's unit digit and the nearest ten to be rounded to was a primary contributor to the variance of reaction times. It is concluded that exact calculation and computational estimation are computationally, cognitively, and structurally different processes. Furthermore, it is suggested that estimation skills be given separate, dedicated attention in schools. Copyright © 2013 John Wiley & Sons, Ltd.