Numerical and area comparison abilities in Down syndrome

Abreu-Mendoza, Roberto A.; Arias‐Trejo, Natalia

doi:10.1016/j.ridd.2015.05.008

Cited by 23 publications

(22 citation statements)

References 29 publications

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“…Taken together, these results suggest that all five dimensions showed ratio‐dependent performance, consistent with Weber's law, and that Area and Length accuracy was superior to Number accuracy, which in turn was significantly better than Time and Density accuracy. These results broadly replicate previous work (Abreu‐Mendoza & Arias‐Trejo, ; Droit‐Volet et al., ; Odic et al., ; Odic, Libertus, et al., ; Starr & Brannon, , ) and further add information about children's perception of density.…”

Section: Resultssupporting

confidence: 89%

“…Other studies have similarly focused on the development of number and one or two other dimensions, but usually over a narrow age range that does not capture the entire developmental trajectory for these dimensions (e.g. Abreu‐Mendoza & Arias‐Trejo, ; Brannon, Lutz, & Cordes, ; Dormal & Pesenti, ; Droit‐Volet & Wearden, ). Here, we report data on a broad age‐range of participants, namely 2‐ to 12‐year‐old children and college‐aged adults, and across five discrimination tasks: number, area, density, line length and time.…”

Section: Introductionmentioning

confidence: 99%

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Children's intuitive sense of number develops independently of their perception of area, density, length, and time

Odic

2017

Developmental Science

130

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Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS - indexed as the most difficult ratio of two numbers that children can reliably discriminate - is well known to improve with development: whereas infants require relatively large ratios to discriminate number, children can discriminate finer and finer changes in number between toddlerhood and early adulthood. Which factors drive the developmental improvements in ANS precision? Here, we investigate the influence of four non-numeric dimensions - area, density, line length, and time - on ANS development, exploring the degree to which the ANS develops independently from these other dimensions, from inhibitory control, and from domain-general factors such as attention and working memory that are shared between these tasks. A sample of 185 children between the ages of 2 and 12 years completed five discrimination tasks: approximate number, area, density, length, and time. We report three main findings. First, logistic growth models applied to both accuracy and Weber fractions (w; an index of ANS precision) across age reveal distinct developmental trajectories across the five dimensions: while area and length develop by adolescence, time and density do not develop fully until early adulthood, with ANS precision developing at an intermediate rate. Second, we find that ANS precision develops independently of the other four dimensions, which in turn develop independently of the ANS. Third, we find that ANS precision also develops independently from individual differences in inhibitory control (indexed as the difference in accuracy and w between Congruent and Incongruent ANS trials). Together, these results are the first to provide evidence for domain-specific improvements in ANS precision, and place children's maturing perception of number, space, and time into a broader developmental context.

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Section: Resultssupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Children's intuitive sense of number develops independently of their perception of area, density, length, and time

Odic

2017

Developmental Science

130

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“…This means it is impossible to control all the variables. This issue becomes critical in the context of recent arguments in which the case has been made that the effects of numerosity is actually mediated by perceptual variables (Abreu-Mendoza & Arias-Trejo, 2015;DeWind et al, 2015;DeWind & Brannon, 2012;Feigensen et al, 2002;Gebuis and Reynvoet, 2012a, 2012bHalberda, Mazzoco, & Feigenson, 2008;Im, Zhong, & Halberda, 2016;Leibovich et al, 2017). The solution that the ANS diffusion models provide is to jointly model the effects of both numerosity and perceptual variables on performance as in DeWind et al (2015).…”

Section: Chapter 6 Discussionmentioning

confidence: 99%

“…Most researchers agree that numerosity discrimination is not solely determined by the numerosity of the stimuli. There are many perceptual variables confounded in the stimuli and they affect numerosity judgment (Abreu-Mendoza & Arias-Trejo, 2015;DeWind et al, 2015;DeWind & Brannon, 2012;Feigensen et al, 2002;Gebuis and Reynvoet, 2012a, 2012bHalberda, Mazzoco, & Feigenson, 2008;Im, Zhong, & Halberda, 2016;Leibovich et al, 2017). For example, when we compare the number of dots in two side-byside arrays, we may overestimate the number in one array if it has larger dots and the dots are more widely dispersed than the dots in the other side.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

“…If the dots on the left side are more dispersed, and so cover more area (i.e., a larger field area) than dots on the right side, this will affect numerosity discrimination. In order to control for this confounding effect, the field area can be kept constant across two arrays (Abreu-Mendoza & Arias-Trejo, 2015). In a similar way, other perceptual variables can be kept constant across different groups of dots to control their effects.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

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Modeling the interaction of numerosity and perceptual variables with the diffusion model

Kang

Ratcliff

2020

Cognitive Psychology

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Eye-tracking methodology in mathematics education research: A systematic literature review

et al. 2020

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Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking.

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Numerical and area comparison abilities in Down syndrome

Cited by 23 publications

References 29 publications

Children's intuitive sense of number develops independently of their perception of area, density, length, and time

Children's intuitive sense of number develops independently of their perception of area, density, length, and time

Modeling the interaction of numerosity and perceptual variables with the diffusion model

Eye-tracking methodology in mathematics education research: A systematic literature review

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