Spontaneous partitioning and proportion estimation in children’s numerical judgments

What Do Biased Estimates Tell Us about Cognitive Processing? Spatial Judgments as Proportion Estimation

“…If the mixed model is simply the reflection of a combination of different partitioning strategies, then it makes sense that a two-parameter version of the mixed model should account for the data: a weighting parameter would reflect the relative contributions of each component, and a single beta parameter would describe the bias associated with both components 5 . This is exactly what is observed when children carry out number line estimation tasks, indicating the proper location of a given numeral on a line with two marked endpoints (Zax et al, 2019). A two-parameter mixed model accounted for number line data, and parameter values changed exactly as predicted by previous theoretical applications of the proportion judgment framework to number line tasks (e.g., Slusser et al, 2013).…”

“…One question that specifically makes contact with the model fits in the present study concerns how we should interpret the mixed model. For both the present spatial reproduction task in children and adults (see also Barth et al, 2015) and the bounded number line estimation task in children (Zax et al, 2019), a mixed proportion estimation model ( Figure 1C) provided a good quantitative explanation of performance. This mixed model, as described earlier, is a weighted combination of the pure models (a one-cycle model, Figure 1A, and a two-cycle model, Figure 1B).…”

“…More specifically, task properties that would be predicted to support young children's partitioning of the number line (such as cues to the location of the midpoint) were associated with a larger contribution of the two-cycle component. A larger two-cycle contribution was also associated with increased age (Zax et al, 2019). For both components, resulting beta values were less than 1.…”

“…It has emerged as a powerful explanation of the bias that characterizes performance and developmental change in similarly structured abstract magnitude judgments such as bounded number line estimation (e.g., Barth & Paladino, 2011;Barth et al, 2016;Cohen & Blanc-Goldhammer, 2011;Cohen & Sarnecka, 2014;Dackermann et al, 2018;Link et al, 2014;Peeters et al, 2016;Peeters, et al, 2017;Rouder & Geary, 2014;Slusser et al, 2013;Slusser & Barth, 2017;Xing et al, under revision;Zax et al, 2019). This approach has led to novel predictions about the specific patterns of bias that should arise for number line judgments made under different task conditions and by different age groups over development, with these predictions supported by data (Zax et al, 2019). The appeal of this theoretical framework is increased by its demonstrated ability to account for a range of different quantity judgments.…”

“…A converging body of work shows that the systematic patterns of estimation bias predicted by these models are also observed in tasks that require proportion judgments of abstract quantities, such as number line estimation (e.g. Barth & Paladino, 2011;Barth et al, 2016;Cohen & Blanc-Goldhammer, 2011;Cohen & Sarnecka, 2014;Dackermann, Kroemer, Nuerk, Moeller, & Huber, 2018;Link, Huber, Nuerk, & Moeller, 2014;Peeters et al, 2016;Peeters, Verschaffel, & Luwel, 2017;Rouder & Geary, 2014;Slusser et al, 2013;Slusser & Barth, 2017;Xing et al, under revision;Zax, Slusser, & Barth, 2019).…”