Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability

Tibber, Marc S.; Manasseh, Gemma S.L.; Clarke, Richard C.; Gagin, Galina; Swanbeck, Sonja N.; Butterworth, Brian; Lotto, R. Beau; Dakin, Steven C.

doi:10.1016/j.visres.2013.06.006

Cited by 44 publications

(44 citation statements)

References 61 publications

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“…In fact, w was not correlated with symbolic arithmetic performance. This finding is consistent with recent studies that report small or negligible correlation between performance in non-symbolic number comparison performance and math (Castronovo & Gobel, 2012; Fuhs & McNeil, 2013; Gobel et al, 2014; Holloway & Ansari, 2009; Inglis et al, 2011; Kolkman et al, 2013; Nosworthy et al, 2013; Price et al, 2012; Sasanguie et al, 2012; Sasanguie, Defever, et al, 2013; Sasanguie, Gobel, et al, 2013; Tibber et al, 2013; Wei et al, 2012). Moreover, many of the studies that show a reliable correlation between performance on a non-symbolic number comparison task and math did not adequately control for other non-numerical fluid processing performance measures (such as attention, memory, and executive function) that may be important for math ability (Anobile, Stievano, & Burr, 2013; Blair & Razza, 2007; Bull, Espy, & Wiebe, 2008; Clark, Pritchard, & Woodward, 2010; DeStefano & LeFevre, 2004; Geary, 2011; St Clair-Thompson & Gathercole, 2006).…”

Section: Discussionsupporting

confidence: 93%

“…This hypothesis has been supported by recent studies that show a correlation between individual precision of the ANS, as measured by w , and individual mathematical competence as measured by standardized math tests, often even after controlling for verbal ability and general intelligence measures (DeWind & Brannon, 2012; Gilmore, McCarthy, & Spelke, 2010; Halberda, Ly, Wilmer, Naiman, & Germine, 2012; Halberda, Mazzocco, & Feigenson, 2008; Libertus, Feigenson, & Halberda, 2011; Libertus, Odic, & Halberda, 2012; Mazzocco, Feigenson, & Halberda, 2011a, 2011b; Piazza et al, 2010). It should be noted, however, that many other studies now report negative findings (Castronovo & Gobel, 2012; Fuhs & McNeil, 2013; Gobel, Watson, Lervag, & Hulme, 2014; Holloway & Ansari, 2009; Inglis, Attridge, Batchelor, & Gilmore, 2011; Kolkman, Kroesbergen, & Leseman, 2013; Nosworthy, Bugden, Archibald, Evans, & Ansari, 2013; Price, Palmer, Battista, & Ansari, 2012; Sasanguie, De Smedt, Defever, & Reynvoet, 2012; Sasanguie, Defever, Maertens, & Reynvoet, 2013; Sasanguie, Gobel, Moll, Smets, & Reynvoet, 2013; Tibber et al, 2013; Wei, Yuan, Chen, & Zhou, 2012), creating a controversy over whether the ANS is causally related to symbolic math and if so exactly what mechanisms underlie this relationship.…”

Section: Introductionmentioning

confidence: 99%

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Improving arithmetic performance with number sense training: An investigation of underlying mechanism

2014

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A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should explore implications from this finding that training young children on approximate arithmetic tasks even before they solidify the symbolic number understanding may be fruitful for improving readiness for math education.

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Section: Discussionsupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Improving arithmetic performance with number sense training: An investigation of underlying mechanism

2014

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“…To provide an example, several studies have shown that precision of the visual sense of number predicts the level of mathematical achievements in school (Halberda et al, 2008). By contrast, a study by the author of this chapter suggests that this association is not unique-mathematical achievements are also associated with processing a variety of visual features (Tibber et al, 2013). Hypothetically, even showing that numerosity is a better predictor would not settle the argument, because "Leaky" accumulator comprising a circuit of two neurons with different activity timescales.…”

Section: Ams Accumulator or Ams Integrator?mentioning

confidence: 87%

What counts in estimation? The nature of the preverbal system

Karolis

Butterworth

2016

Progress in Brain Research

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“…These correlations, however, are relatively weak and only predict a small amount of variance in mathematical performance. Some researchers have also suggested that non-symbolic numerical abilities are part of a larger suite of visual-perceptual abilities that predict mathematics performance (Tibber et al, 2013). Others have argued that ANS acuity provides unique variance to predicting mathematical performance and that other similar perceptual tasks do not (Agrillo, Piffer, & Adriano, 2013), or that both ANS acuity and other perceptual tasks provide unique variance (Lourenco, Bonny, Fernandez, & Rao, 2012).…”

Section: Discussionmentioning

confidence: 99%

Modeling the approximate number system to quantify the contribution of visual stimulus features

et al. 2015

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The approximate number system (ANS) subserves estimation of the number of items in a set. Typically, ANS function is assessed by requiring participants to compare the number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant’s Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spacing of dots. Current models of numerosity comparison do not account for these effects and consequently lead to different estimates of w depending on the methods used to control for non-numerical features. Here we proffer a new model that teases apart the effects of ANS acuity from the effects of non-numerical stimulus features. The result is an estimate of w that is a more theoretically valid representation of numerical acuity and novel terms that denote the degree to which a participant’s perception of number is affected by non-numerical features. We tested this model in a sample of 20 adults and found that, by correctly attributing errors due to non-numerical stimulus features, the w obtained was more reliable across different stimulus conditions. We found that although non-numerical features biased numerosity discriminations in all participants, number was the primary feature driving discriminations in most of them. Our findings support the idea that, while numerosity is a distinct visual quantity, the internal representation of number is tightly bound to the representation of other magnitudes. This tool for identifying the different effects of the numerical and non-numerical features of a stimulus has important implications not only for the behavioral investigation of the ANS, but also for the collection and analyses of neural data sets associated with ANS function.

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Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability

Cited by 44 publications

References 61 publications

Improving arithmetic performance with number sense training: An investigation of underlying mechanism

Improving arithmetic performance with number sense training: An investigation of underlying mechanism

What counts in estimation? The nature of the preverbal system

Modeling the approximate number system to quantify the contribution of visual stimulus features

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