Cognitive processes of numerical estimation in children

Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks

“…The "flipped" direction of bias continues into adulthood ( Figure 5). This result is consistent with two previous reports, one with adults on the NP task (Cohen & BlancGoldhammer, 2011), and the other with children and adults on the PN task (Ashcraft & Moore, 2012).…”

“…Median estimates from each age group were best characterized by the inverse one-cycle model (R 2 =.980 for 8-year-olds, R 2 =.995 for 9-year-olds, and R 2 =.996 for 10-year-olds) (Figure 4). However, the β-value corresponding to the 8-year-olds' estimates was less than one (β=.663), while the β-values corresponding to the 9-and 10-year-olds' estimates are slightly greater than one (β=1.131 for 9-year-olds and β=1.254 for 10-year-olds).This rather unexpected result (also noted earlier in several individuals from the 6-and 7-year-old group) means that 9-and 10-year-olds, on average, are producing estimates that follow an over-thenunder pattern, rather than the inverse under-then-over pattern associated with PN performance in the younger children (also see Siegler & Opfer, 2003; but see Ashcraft & Moore, 2012).…”

“…Slusser et al, 2013) will generally be inverted for the PN task 3 . One previous study has applied proportion models to PN data (Ashcraft & Moore, 2012). Though results were arguably consistent with the proportion models' predictions, they were interpreted as supporting the logarithmic-tolinear shift hypothesis due, in part, to the use of inappropriate model comparison methods.…”

“…For example, children characterized as linear estimators do better on standardized math tests and other measures of mathematical ability (Ashcraft & Moore, 2012;Booth & Siegler, 2006) and children with mathematical learning disability (MLD) produce linear estimates later than comparison groups (Geary, Hoard, Nugent, & Byrd-Craven, 2008) -behaviors that have been attributed to differences in children's numerical magnitude representations. These findings have also led researchers to develop effective interventions to improve formal math performance (e.g.…”

“…Very few studies have used a "position to number" or PN task, in which participants are given a number line with a marked position and must produce a corresponding number (cf. Ashcraft & Moore, 2012;Iuculano & Butterworth, 2011;Siegler & Opfer, 2003). With their initial introduction of the representational shift account, Siegler and Opfer (2003) (Siegler & Opfer, 2003).…”