Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

Brankaer, Carmen; Ghesquière, Pol; Smedt, Bert De

doi:10.1371/journal.pone.0093565

Cited by 59 publications

(77 citation statements)

References 30 publications

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“…This suggests there is an additional cost to translating between the two formats. This result is broadly consistent with those found by Mundy andGilmore (2009) andBrankaer et al (2014). Mundy and Gilmore found in their second experiment that children roughly 7-8 years of age struggled with a mapping task (children judged which of two quantities matched the numerosity of a target, where the target was in a different format -symbolic or nonsymbolic -from that of the two options): Average accuracy was 62% (chance=50%).…”

Section: Evidence For the Sns→ams Viewsupporting

confidence: 89%

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Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Lyons

Bugden

Zheng³

et al. 2018

Developmental Psychology

111

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There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial debate and study of the relationship between approximate, nonverbal (approximate magnitude system, AMS) and exact, symbolic (symbolic number system, SNS) representations of number. Here we examined several hypotheses concerning whether, in the earliest stages of formal education, AMS abilities predict growth in SNS abilities, or the other way around. In addition to tasks involving symbolic (Arabic numerals) and non-symbolic (dot arrays) number comparisons, we also tested children's ability to translate between the two systems (i.e., mixed-format comparison). Our data included a sample of 539 Kindergarten children (mean=5.17yrs, SD=0.29yrs), with AMS, SNS and mixed comparison skills assessed at the beginning and end of the academic year. In this way, we provide, to the best of our knowledge, the most comprehensive test to date of the direction of influence between the AMS and SNS in early formal schooling. Results were more consistent with the view that SNS abilities at the beginning of Kindergarten lay the foundation for improvement in both AMS abilities and the ability to translate between the two systems. Importantly, we found no evidence to support the reverse. We conclude that, once one acquires a very basic grasp of exact number symbols, it is this understanding of exact number (and perhaps repeated practice therewith) that facilitates growth in the AMS. Though the precise mechanism remains to be understood, these data challenge the widely held view that the AMS scaffolds the acquisition of the SNS.

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Section: Evidence For the Sns→ams Viewsupporting

confidence: 89%

“…More recently, Brankaer et al (2014) found a highly similar result using similar matching and comparison tasks in children approximately 7 and 9 years old.…”

Section: Evidence For the Sns→ams Viewmentioning

confidence: 62%

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Lyons

Bugden

Zheng³

et al. 2018

Developmental Psychology

111

View full text Add to dashboard Cite

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“…Similarly Brankaer, Ghesquière, and De Smedt (2014) found that children's performance on a similar mapping task developed from age 6 to 8 and was related to performance on both timed and untimed mathematics tests, after controlling for magnitude comparison performance. These findings concur with data from Booth and Siegler (2008), which showed a relationship between children's ability to map symbolic Running head: PRESCHOOL MAGNITUDE REPRESENTATIONS 6 representations onto a number line and later arithmetical achievement.…”

Section: Magnitude Representations and Mathematicsmentioning

confidence: 79%

“…Similarly Brankaer, Ghesquière, and De Smedt (2014) found that children's performance on a similar mapping task developed from age 6 to 8 and was related to performance on both timed and untimed mathematics tests, after controlling for magnitude comparison performance. These findings concur with data from Booth and Siegler Alternatively, the symbolic system may be acquired independently of the nonsymbolic system and the mapping between nonsymbolic and symbolic representations might occur later, once children have acquired the symbolic system (e.g., Le Corre & Carey, 2007).…”

Section: Magnitude Representations and Mathematicsmentioning

confidence: 82%

Magnitude Representations and Counting Skills in Preschool Children

Batchelor

Keeble

Gilmore

2015

Mathematical Thinking and Learning

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When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this mapping only occurs once children have cardinality understanding. One difficulty with the current literature is that studies have employed tasks that only indirectly assess children's nonsymbolic-symbolic mappings. We introduce a task in which preschoolers made magnitude comparisons across representation formats (e.g., dot arrays vs. verbal number), allowing a direct assessment of mapping. We gave this task to 60 children aged 2;7 -4;10, together with counting and Give-a-Number tasks. We found that some children could map between nonsymbolic quantities and the number words they understood the cardinal meaning of, even if they had yet to grasp the general cardinality principle of counting.Keywords: counting, magnitude comparison, cardinality, preschool children, number Running head: PRESCHOOL MAGNITUDE REPRESENTATIONS 3 Magnitude Representations and Counting Skills in Preschool ChildrenWe know from more than a decade's worth of research that infants, children and adults can represent and manipulate numerical information nonsymbolically, without number words or digits. These nonsymbolic representations are robust across multiple modalities and set sizes. Children and adults can compare, add and subtract small and large quantities in visual arrays (Barth, Kanwisher, & Spelke, 2003;McCrink & Wynn, 2004), auditory sequences (Barth et al., 2003;Barth, La Mont, Lipton, & Spelke, 2005) and moving displays of actions (e.g., puppet jumps) (Wood & Spelke, 2005;Wynn, 1996;Wynn, Bloom, & Chiang, 2002).The nonsymbolic representations employed in these tasks are approximate and in an analogue format. They are inherently noisy and the variance associated with them increases with the absolute size of the magnitudes represented. As a result, success on these tasks depends on the ratio (or numerical distance) between the numerosities to be compared 1 . As the quantities get closer together, discrimination becomes more effortful and less precise.Importantly, the precision of these representations varies across individuals and increases over development. Infants can discriminate numerosities with ratios as small as 2:3, whilst preschool children show a ratio-limit of 3:4, and adults, 7:8 (Barth et al., 2003;Feigenson, Dehaene, & Spelke, 2004).When children begin to count they learn to use external symbols to represent number.These symbolic representations enable exact number comparison and manipulation. There is evidence that when children acquire this symbolic system, the preexisting nonsymbolic system is not overridden; rather, nonsymbolic representations become mapped onto the newly acquired symbolic representations. The evidence for this is at least threefold. Firstly, children...

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“…Indeed, children’s exact number abilities – especially those related to their emerging understanding of exact number symbols – have also been shown to be important for math achievement. For example, Holloway and Ansari (2009), Brankaer and colleagues (2014), and Sasanguie and colleagues (Sasanguie et al, 2012; Sasanguie, Defever, Maertens, & Reynvoet, 2013) found that children’s performance on a symbolic number comparison task (e.g., showing participants two Arabic numerals and asking them to quickly judge which is greater) correlated with math abilities. Similarly, Kolkman and colleagues (2013) found that kindergarteners’ performance on a symbolic number comparison task and a symbolic number line estimation task (but not on a non-symbolic number comparison task or a non-symbolic number line estimation task) predicted math performance in first grade.…”

Section: Introductionmentioning

confidence: 99%

The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

Libertus

Odic

Feigenson

et al. 2016

Journal of Experimental Child Psychology

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Children can represent number in at least two ways: by using their non-verbal, intuitive Approximate Number System (ANS), and by using words and symbols to count and represent numbers exactly. Further, by the time they are five years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children’s math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation – mapping accuracy and variability – might each relate to math performance. Here, we address these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities.

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Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

Cited by 59 publications

References 30 publications

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Magnitude Representations and Counting Skills in Preschool Children

The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

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