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

Slusser, Emily; Barth, Hilary

doi:10.1016/j.jecp.2017.04.010

Cited by 54 publications

(46 citation statements)

References 33 publications

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“…Considerable evidence against this view has emerged in recent years. Researchers using a variety of methods have shown that performance in these estimation tasks is shaped by multiple cognitive processes, strategies, and/or computations that must prevent direct access to the forms of our numerical magnitude representations (e.g., Barth & Paladino, ; Barth et al., ; Chesney & Mathews, ; Cohen & Blanc‐Goldhammer, ; Cohen & Quinlan, ; Cohen & Sarnecka, ; Friso‐van den Bos et al., ; Hurst, Monahan, Heller, & Cordes, ; Link, Huber, Nuerk, & Moeller, ; Peeters, Degrande, Ebersbach, Verschaffel, & Luwel, ; Reinert, Huber, Nuerk, & Moeller, ; Rips, ; Rouder & Geary, ; Slusser, Santiago, & Barth, ; Slusser & Barth, ; Sullivan & Barner, ; Sullivan, Juhasz, Slattery, & Barth, ; see also Cantlon, Cordes, Libertus, & Brannon, ). But despite disagreement about what cognitive and developmental theories should be built upon number line estimates, researchers in both groups described above have generally assumed that the overall numerical magnitudes of the presented targets do ultimately drive task performance (cf.…”

Section: Introductionmentioning

confidence: 99%

Digit identity influences numerical estimation in children and adults

Lai

Zax

Barth

2018

Developmental Science

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Learning the meanings of Arabic numerals involves mapping the number symbols to mental representations of their corresponding, approximate numerical quantities. It is often assumed that performance on numerical tasks, such as number line estimation (NLE), is primarily driven by translating from a presented numeral to a mental representation of its overall magnitude. Part of this assumption is that the overall numerical magnitude of the presented numeral, not the specific digits that comprise it, is what matters for task performance. Here we ask whether the magnitudes of the presented target numerals drive symbolic number line performance, or whether specific digits influence estimates. If the former is true, estimates of numerals with very similar magnitudes but different hundreds digits (such as 399 and 402) should be placed in similar locations. However, if the latter is true, these placements will differ significantly. In two studies (N = 262), children aged 7-11 and adults completed 0-1000 NLE tasks with target values drawn from a set of paired numerals that fell on either side of "Hundreds" boundaries (e.g., 698 and 701) and "Fifties" boundaries (e.g., 749 and 752). Study 1 used an atypical speeded NLE task, while Study 2 used a standard non-speeded NLE task. Under both speeded and non-speeded conditions, specific hundreds digits in the target numerals exerted a strong influence on estimates, with large effect sizes at all ages, showing that the magnitudes of target numerals are not the primary influence shaping children's or adults' placements. We discuss patterns of developmental change and individual difference revealed by planned and exploratory analyses.

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Section: Introductionmentioning

confidence: 99%

Digit identity influences numerical estimation in children and adults

Lai

Zax

Barth

2018

Developmental Science

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“…Recent empirical evidence suggests that number line estimation tasks entail judgments of proportions (Barth & Paladino, 2011;Slusser & Barth, 2017).…”

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The nature of the association between number line and mathematical performance: An international twin study

Tosto

Garon‐Carrier

Gross

et al. 2018

Brit J of Edu Psychol

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Background: The number line task assesses the ability to estimate numerical magnitudes. People vary greatly in this ability and this variability has been previously associated with mathematical skills. However, the sources of individual differences in number line estimation and its association with mathematics are not fully understood. Aims: This large scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of genes and environments on: (1) individual variation in number line estimation and (2) the co-variation of number line estimation with mathematics. Samples: We used over 3,000 8-16 years-old twins from US, Canada, UK, and Russia, and a sample of 1,456 8-18 years-old singleton Russian students. Methods: Twins were assessed on: (1) estimation of numerical magnitudes using a number line task and (2) two mathematics components: fluency and problem solving. Results: Results suggest that environments largely drive individual differences in number line estimation. Both genes and environments contribute to different extents to the number line estimation and mathematics correlation, depending on the sample and mathematics component. Conclusions: Taken together, the results suggest that in more heterogeneous school settings, environments may be more important in driving variation in number line estimation and its association with mathematics, whereas in more homogeneous school settings, genetic effects drive the covariation between number line estimation and mathematics. These results are discussed in light of development and educational settings.

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“…Estimation strategies tell us how students approach the number line task; students' accuracy on the number line task reveals whether those estimation strategies are successful. For example, when they are asked to place whole numbers on number lines, older students and adults rely on both implicit (e.g., the midpoint) and explicit reference points (e.g., labelled endpoints) to guide their number line estimates (Ashcraft & Moore, 2012;Barth & Paladino, 2011;Di Lonardo et al, 2019;Slusser & Barth, 2017). Notably, when students rely on implicit reference points they also use proportional reasoning skills (e.g., 45 is a little smaller than 50 so it should be placed just to the left of the midpoint on a 0-100 number line) (Ashcraft & Moore, 2012;Barth & Paladino, 2011;Newman & Berger, 1984;Peeters et al, 2016;Schneider et al, 2018).…”

Section: Number Line Estimation Strategiesmentioning

confidence: 99%

Fraction Symbols and their Relation to Conceptual Knowledge

Douglas¹

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

Cited by 54 publications

References 33 publications

Digit identity influences numerical estimation in children and adults

Digit identity influences numerical estimation in children and adults

The nature of the association between number line and mathematical performance: An international twin study

Fraction Symbols and their Relation to Conceptual Knowledge

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