Children’s number-line estimation shows development of measurement skills (not number representations).

Abstract

Children’s understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this has often been interpreted as evidence of a change in the child’s psychological representation of integer quantities. The present article presents theoretical and empirical evidence that the change in number-line performance actually reflects the development of measurement skills used in the task. We compare 2 versions of the number-line task: the bounded version used in the literature and a new, unbounded version. Results indicate that it is only children’s performance on the bounded task (which requires subtraction or division) that changes markedly with age. In contrast, children’s performance on the unbounded task (which requires only addition) remains fairly constant as they get older. Thus, developmental changes in performance on the traditional bounded number-line task likely reflect the growth of task-specific measurement skills rather than changes in the child’s understanding of numerical quantities.

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

“…Importantly, patterns of developmental change on the PN task are broadly consistent with those found in previous work on the NP task, and can be explained by the developmental progression described by Slusser et al (2013;see also Barth & Paladino, 2011;Cohen & Sarnecka, 2014;Rouder & Geary, 2014). When presented with the PN task, older children are more likely than younger children to produce two-cycle estimates (consistent with the strategic use of endpoints as well as an inferred midpoint as reference points), and with values of the model parameter β approaching one (showing less bias and improved accuracy).…”

“…Taken together, the present data (within subjects comparisons across NP and PN tasks) and previous findings (which address the tasks separately; Ashcraft & Moore, 2012;Cohen & Blanc-Goldhammer, 2011) suggest that the developmental "flip" in direction of bias is related to task-specific challenges inherent to bounded number-line estimation, not to fundamental changes in numerical representation or processing. This is evidenced by the fact that direction of bias changes over development in the typical bounded number-line task, but not in an unbounded version of the task (Cohen & Sarnecka, 2014) in which participants are given a length that corresponds to a single unit and must indicate the position of a target number on an unmarked, unbounded line. In fact, children (ages 4-8) perform like adults on the unbounded task, in that they too produce estimates with a pattern of positively accelerating bias (Cohen & Blanc-Goldhammer, 2011;Cohen & Sarnecka, 2014).…”

“…Recent research has shown that the proportion estimation model is an excellent predictor of typical numerical estimation patterns and even explains systematic patterns of bias in estimation data that cannot be accounted for by the log-to-linear shift hypothesis (see Slusser et al, 2013 for a detailed discussion). 1 The model is consistent with the use of more than one cognitive process to arrive at an estimate; it does not provide evidence for the use of any one specific process (Spence 1990; see also Cohen & Sarnecka, 2014).…”

“…Converging evidence from multiple research groups, however, has recently shown that a different theoretical explanation offers a better explanation of performance on cognitive tasks, including number-line estimation tasks, that are commonly used to assess learning and development in numerical thinking Barth, Slusser, Kanjlia, Garcia, Taggart, & Chase, 2016;Cohen & Blanc-Goldhammer, 2011;Cohen & Sarnecka, 2014;Rouder & Geary, 2014;Slusser et al, 2013;Sullivan, Juhasz, Slattery, & Barth, 2011;see also Chesney & Matthews, 2013;Hurst, Monahan, Heller, & Cordes, 2014). These and other findings have fostered an ongoing debate, calling into question the hypothesis that a shift from logarithmic to linear mental representations of number underlies developmental change in numerical estimation and, in turn, observed improvements in formal math (see Barth, Slusser, Cohen, & Paladino, 2011;Opfer, Siegler, & Young, 2011).…”

“…Most of the hundreds of published number-line estimation studies make use of a "number to position" or NP task, in which participants are given a target number and must place a 2 This performance pattern could result from a number of different procedural strategies (Slusser et al, 2013) and may arise when children approach the number-line as an essentially "unbounded" estimation task (Cohen & Sarnecka, 2014).…”