Development of Numerical Estimation in Young Children

Abstract

Two experiments examined kindergartners', first graders', and second graders' numerical estimation, the internal representations that gave rise to the estimates, and the general hypothesis that developmental sequences within a domain tend to repeat themselves in new contexts. Development of estimation in this age range on 0-to-100 number lines followed the pattern observed previously with older children on 0-to-1,000 lines. Between kindergarten and second grade (6 and 8 years), patterns of estimates progressed from consistently logarithmic to a mixture of logarithmic and linear to a primarily linear pattern. Individual differences in number-line estimation correlated strongly with math achievement test scores, improved estimation accuracy proved attributable to increased linearity of estimates, and exposure to relevant experience tended to improve estimation accuracy.

Development of numerical estimation in Chinese preschool children

“…Within each task, the number cards were presented in a random order. The instructions were the same as those used by Siegler and colleagues (e.g., Siegler & Booth, 2004). Specifically, the experimenter began the test by saying, ''Today we're going to play a game with number lines.…”

“…This task was the same as Siegler's number line estimation task (e.g., Siegler & Booth, 2004). A 23-cm line was printed across the middle, with 0 at the left end and 100 at the right end.…”

“…First, we hypothesized that with age Chinese children's number representations would show a systematic improvement in line estimation (i.e., a decrease in errors and an increase in linearity). This developmental trend was a downward extrapolation based on the early findings from older samples in the United States (e.g., Siegler & Booth, 2004). Second, we hypothesized that children's performance would be better on the number lines using dots and objects than on the symbolic number line because of children's familiarity with the concrete materials over the symbolic numbers (Dehaene et al, 2008).…”

“…This law is believed to describe representations of numerical as well as physical magnitudes (Bank & Hill, 1974;Dehaene, 1997). One of the widely used tasks to examine how the human mind represents numbers is the number line estimation task, in which participants are asked to place a given number on a straight line anchored with numbers at the two ends (e.g., 0 on the left end and 10 or 100 on the right end; Dehaene, Izard, Spelke, & Pica, 2008;Ebersbach, Luwel, Frick, Onghena, & Verschaffel, 2008;Geary, Hoard, Nugent, & Byrd-Craven, 2008;Moeller, Pixner, Kaufmann, & Nuerk, 2009;Muldoon, Simms, Towse, Menzies, & Yue, 2011;Opfer, Siegler, & Young, 2011;Siegler & Booth, 2004;Siegler & Opfer, 2003;Slusser, Santiago, & Barth, 2013;Whyte & Bull, 2008;.…”

“…The strongest support for the logarithmic-to-linear shift hypothesis came from a large number of developmental studies carried out by Siegler and his colleagues (Booth & Siegler, 2006Laski & Siegler, 2007;Opfer & Siegler, 2007;Opfer & Thompson, 2008;Opfer et al, 2011;Siegler & Booth, 2004;Siegler & Mu, 2008;Siegler & Opfer, 2003;. They identified different ages at which American children move away from logarithmic representations and develop linear representations of different ranges of numbers.…”