A sense of proportion: commentary on Opfer, Siegler and Young

Barth, Hilary; Slusser, Emily; Cohen, Dale J.; Paladino, Annie M.

doi:10.1111/j.1467-7687.2011.01081.x

Cited by 35 publications

(35 citation statements)

References 9 publications

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“…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).…”

Section: For Reviews)mentioning

confidence: 99%

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

Slusser

Barth

2017

Journal of Experimental Child Psychology

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Section: For Reviews)mentioning

confidence: 99%

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

Slusser

Barth

2017

Journal of Experimental Child Psychology

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“…However, the conclusion of such a representational shift as drawn by Siegler and colleagues is currently discussed controversially with respect to both theoretical but also methodological issues (e.g., Barth and Paladino, 2011; Barth et al, 2011; Moeller and Nuerk, 2011; Slusser et al, 2013; see also Ebersbach et al, 2013 for an overview). From a theoretical point of view, there are alternative accounts to explain the developmental changes in number line performance.…”

Section: Introductionmentioning

confidence: 99%

Unbounding the mental number line—new evidence on children's spatial representation of numbers

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Huber²,

Nuerk

et al. 2014

Front. Psychol.

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Number line estimation (i.e., indicating the position of a given number on a physical line) is a standard assessment of children's spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children—at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.

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“…Our interpretation of the observed feedback effects is that post-feedback estimates change in part because of the use of additional reference points (see also Barth, Slusser, Cohen, & Paladino, 2011), rather than because of a shift to a linear mental number representation. A deep representational change need not be invoked -broad and rapid change should come about if feedback simply supplies children with additional reference points.…”

Section: Introductionmentioning

confidence: 99%

How feedback improves children’s numerical estimation

et al. 2015

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Developmental change in children's number-line estimation has been thought to reveal a categorical logarithmic-to-linear shift in mental representations of number. Some have claimed that the broad and rapid change in estimation patterns that occurs with corrective feedback provides strong evidence for this shift. However, quantitative models of proportion judgment may provide a better account of children's estimation patterns while also predicting broad and rapid change following feedback. Here we test the hypothesis that local corrective feedback provides children with additional reference points, rather than catalyzing a shift to a different mental representation of number. We tested 117 children from several second-grade classrooms in a number-line feedback study. Data indicate that the proportion-judgment framework accounts for individual differences in estimation patterns, and that the effects of feedback are consistent with the unique quantitative predictions of the framework. They do not provide evidence supporting the representational shift hypothesis or, more broadly, for the proposal that cognitive change can occur rapidly at the level of entire mental representations.

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A sense of proportion: commentary on Opfer, Siegler and Young

Cited by 35 publications

References 9 publications

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

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

Unbounding the mental number line—new evidence on children's spatial representation of numbers

How feedback improves children’s numerical estimation

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