Measuring the approximate number system in children: Exploring the relationships among different tasks

Gilmore, Camilla; Attridge, Nina; Smedt, Bert De; Inglis, Matthew

doi:10.1016/j.lindif.2013.10.004

Cited by 48 publications

(50 citation statements)

References 48 publications

(65 reference statements)

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“…However recent studies have found promising relationships between multiple non-symbolic quantity processing tasks (e.g. Gilmore, Attridge, De Smedt, & Inglis, 2014;Xenidou-Dervou, De Smedt, van der Schoot, & van Lieshout, 2013). Replicating the present findings using composite measures for both approximate and small discrimination would further strengthen the conclusions.…”

Section: Limitations Future Directions and Implicationssupporting

confidence: 84%

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Soto-Calvo

Simmons

Willis

et al. 2015

Journal of Experimental Child Psychology

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The extent that phonological, visual-spatial STM and non-symbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4:8. Phonological awareness, visual-spatial STM and non-symbolic approximate discrimination predicted growth in early calculation skills. These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small non-symbolic quantity discrimination task (where the presented quantities were always within the subitising range) predicted growth in cardinal counting skills.These results suggest that the development of counting and calculation are supported by different cognitive abilities.

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Section: Limitations Future Directions and Implicationssupporting

confidence: 84%

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Soto-Calvo

Simmons

Willis

et al. 2015

Journal of Experimental Child Psychology

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“…Indeed, the relations may change developmentally, with the ANS important in preschool and early elementary school in supporting learning of symbolic arithmetic, but later overshadowed in importance by knowledge of the symbolic system. Findings that symbolic and nonsymbolic systems are correlated in younger children but not older children or adults provide support for this view …”

Section: Developing Understanding Of Discrete and Continuous Numbermentioning

confidence: 86%

Thinking about quantity: the intertwined development of spatial and numerical cognition

Newcombe

Levine

Mix

2015

WIRES Cognitive Science

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There are many continuous quantitative dimensions in the physical world. Philosophical, psychological, and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time and mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, and density) and number can be conceptualized discretely or continuously (i.e., natural vs real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability, and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions.

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“…This effect has been consistently demonstrated in both nonsymbolic and symbolic approximate tasks (e.g., De Smedt, Verschaffel, & Ghesquière, 2009;Holloway & Ansari, 2008Sasanguie et al, 2011). Even though performance on approximate magnitude 4 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014 XENIDOU-DERVOU, VAN DER SCHOOT, VAN LIESHOUT measures has received a lot of research attention with respect to its role in children's mathematical achievement, very little is known so far about the underlying cognitive mechanisms of nonsymbolic and symbolic approximate number processing (De Smedt, Noël, Gilmore, & Ansari, 2013;Gilmore, Attridge, De Smedt, & Inglis, 2014;Gilmore, Attridge, & Inglis, 2011). In Sasanguie et al's (2011) study, the single-digit approximate measures did not correlate with their number line measures.…”

Section: The Role Of Mental Number Line Estimationsmentioning

confidence: 99%

Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic

Xenidou-Dervou¹,

Schoot²,

Lieshout³

2015

Quarterly Journal of Experimental Psychology

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How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.

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Measuring the approximate number system in children: Exploring the relationships among different tasks

Cited by 48 publications

References 48 publications

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Thinking about quantity: the intertwined development of spatial and numerical cognition

Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic

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