Longitudinal relations between the approximate number system and symbolic number skills in preschool children

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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The relationship between children’s approximate number certainty and symbolic mathematics

Journal of Numerical Cognition ◽

10.5964/jnc.v6i1.220 ◽

2020 ◽

Vol 6 (1) ◽

pp. 50-65

Author(s):

Carolyn Baer ◽

Darko Odic

Keyword(s):

Large Body ◽

Number System ◽

Math Performance ◽

Approximate Number System ◽

Mathematical Skills ◽

Math Ability ◽

Positive Correlations ◽

Number Perception ◽

The Relationship ◽

Symbolic Number

Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.

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Mechanisms Underlying Transfer from Domain-Specific and Domain-General Cognitive Training to Children’s Math Skills

10.31234/osf.io/v6srz ◽

2021 ◽

Author(s):

Andrew David Ribner ◽

Melissa Libertus

Keyword(s):

Math Achievement ◽

Skill Training ◽

Later Life ◽

Number System ◽

Approximate Number System ◽

Life Outcomes ◽

Math Skills ◽

Domain Specific ◽

Number Representations ◽

Symbolic Number

Math achievement is one of the strongest predictors of later life outcomes, and much of what comprises later math is decided by the time children enter kindergarten. Individual differences in precision of approximate representations of number and mapping between non-symbolic and symbolic number representations predict math achievement and honing these representations improves math skills. The goal of this registered report is to disentangle potential mechanisms of transfer. Approximately 324 preschool-aged children will be assigned to one of three, 5-week computerized, teacher-facilitated training conditions to target their approximate number system, symbolic number skills, and executive function to better understand whether changes in approximate number system acuity, mapping between number representations, or attention to number underlie successful transfer of skill training.

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Ordinal structure of the symbolic number system mediates refinement of the approximate number system

10.31234/osf.io/qwhzm ◽

2020 ◽

Author(s):

Christian Peake ◽

Carolina Briones ◽

Cristina Rodríguez

Keyword(s):

Developmental Psychology ◽

Number System ◽

First Year ◽

Approximate Number System ◽

Parallel Development ◽

School Year ◽

System P ◽

Underlying Mechanisms ◽

The Relationship ◽

Symbolic Number

Interest in the relationship between the Approximate Number System (ANS, an early cognitive system to process non-symbolic quantities) and the Symbolic Number System (SNS, learned through instruction or intense exposure) is currently growing among researchers in developmental psychology. This research contrasted the two main hypotheses regarding the issue: the traditional mapping account, which states that the ANS underlies the learning of numerical symbols; and the parallel development account, which argues that the SNS develops independently from the ANS and, in fact, serves to refine it during mapping between them, as the ANS is approximate in nature. Moreover, this study focused on the underlying mechanisms that mediate the relationship between the ANS and the SNS. A sample of 200 children in first year of preschool (4 to 5 years old) were followed over the course of the school year. Symbolic and non-symbolic comparison tasks and estimation tasks where applied at the beginning (T1) and end (T2) of the school year. A cardinality task was administered at T1 and an ordinality task at T2. This allowed us to run two serial multiple mediator models to test both hypotheses with multiple longitudinal mediators. Results showed a bidirectional causal relationship between the ANS and the SNS that was interpreted as supporting the parallel development account. Importantly, ordinality mediated the relationship between the SNS at T1 and the ANS at T2, even when controlling for the development of translation skills from the SNS to the ANS and cardinality. This is the first evidence that knowledge of the relationship between number symbols, addressed in terms of their ordinal structure, is the cognitive mechanism that underlies the refinement of the ANS. As such, it supports the idea that the two systems develop independently, although they may impact each other at early stages of learning.

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Relationships between approximate number system acuity and early symbolic number abilities

Trends in Neuroscience and Education ◽

10.1016/j.tine.2012.09.003 ◽

2012 ◽

Vol 1 (1) ◽

pp. 21-31 ◽

Cited By ~ 35

Author(s):

Christophe Mussolin ◽

Julie Nys ◽

Jacqueline Leybaert ◽

Alain Content

Keyword(s):

Number System ◽

Approximate Number System ◽

Symbolic Number

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Non-Symbolic Numerosity and Symbolic Numbers are not Processed Intuitively in Children: Evidence From an Event-Related Potential Study

Frontiers in Education ◽

10.3389/feduc.2021.629053 ◽

2021 ◽

Vol 6 ◽

Author(s):

Anne H. van Hoogmoed ◽

Marije D. E. Huijsmans ◽

Evelyn H. Kroesbergen

Keyword(s):

Number System ◽

Number Processing ◽

Event Related Potential ◽

Visual Features ◽

Approximate Number System ◽

Match To Sample ◽

Potential Study ◽

Symbolic Number

The approximate number system (ANS) theory and the ANS mapping account have been the most prominent theories on non-symbolic numerosity processing and symbolic number processing respectively, over the last 20 years. Recently, there is a growing debate about these theories, mainly based on research in adults. However, whether the ANS theory and ANS mapping account explain the processing of non-symbolic numerosity and symbolic number in childhood has received little attention. In the current ERP study, we first examined whether non-symbolic numerosity processing in 9-to-12-year-old children (N = 34) is intuitive, as proposed by the ANS theory. Second, we examined whether symbolic number processing is rooted in non-symbolic numerosity processing, as proposed the ANS mapping account. ERPs were measured during four same-different match-to-sample tasks with non-symbolic numerosities, symbolic numbers, and combinations of both. We found no evidence for intuitive processing of non-symbolic numerosity. Instead, children processed the visual features of non-symbolic stimuli more automatically than the numerosity itself. Moreover, children do not seem to automatically activate non-symbolic numerosity when processing symbolic numbers. These results challenge the ANS theory and ANS mapping account in 9-to-12-year-old children.

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Number Representations and their Relation with Mathematical Ability

10.1093/oxfordhb/9780199642342.013.035 ◽

2014 ◽

Cited By ~ 2

Author(s):

Titia Gebuis ◽

Bert Reynvoet

Keyword(s):

Number System ◽

Neural Representation ◽

Approximate Number System ◽

Developmental Models ◽

Domain Specific ◽

Mathematical Abilities ◽

Number Representations ◽

The One ◽

Insight Into ◽

Symbolic Number

In this chapter we review research on the processes that underlie the development of mathematical abilities. It is proposed that numerical deficiencies might arise from domain specific problems. The approximate number system that supports reasoning with non-symbolic numbers, on the one hand, and the symbolic number system on the other hand were put forth as possible candidates. To gain insight into the two different systems, we will describe the development of non-symbolic and symbolic number processing and introduce the two main theories about numerical deficiencies: the approximate number system and the access deficit hypothesis. The paradigms used to study both accounts differ in several ways and are of importance for research on the relation between non-symbolic and symbolic number and mathematical abilities. Then, we will review how the studies investigating both accounts relate to two different sets of developmental models that describe the neural representation of number.

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