How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior

doi:10.1016/j.tine.2013.06.001

Trends in Neuroscience and Education

Volume 2, Issue 2, June 2013, Pages 48-55

https://doi.org/10.1016/j.tine.2013.06.001 Get rights and content

Abstract

Many studies tested the association between numerical magnitude processing and mathematics achievement, but results differ depending on the number format used. For symbolic numbers (digits), data are consistent and robust across studies and populations: weak performance correlates with low math achievement and dyscalculia. For non-symbolic formats (dots), many conflicting findings have been reported. These inconsistencies might be explained by methodological issues. Alternatively, it might be that the processes measured by non-symbolic tasks are not critical for school-relevant mathematics. A few neuroimaging studies revealed that brain activation during number comparison correlates with children's mathematics achievement level, but the consistency of such relationships for symbolic and non-symbolic processing is unclear. These neurocognitive data provided ground for educational interventions, which seem to have positive effects on children's numerical development in (a)typical populations.

Introduction

One important way in which cognitive neuroscience has made successful connections to educational research is by drawing attention to the importance of numerical magnitude processing as a foundation for higher-level numerical and mathematical skills (e.g., [10], [19]). Over the last decade, this has fueled research aimed at investigating the relationship between individual differences in numerical magnitude processing skills and arithmetic achievement in typically developing children as well as studies probing whether children with atypical mathematical development or developmental dyscalculia (DD) are impaired in their abilities to process numerical magnitudes. Such research is beginning to lay the foundations for the design and evaluation of educational interventions that foster numerical magnitude processing.

One of the outstanding questions in this emerging body of research is whether processing magnitudes in either symbolic (digits) or non-symbolic (dots) formats or both is crucial for successful mathematics achievement. Such research can pinpoint more precisely the mathematical content that should be included in specific interventions.

Beyond educational applications, establishing whether symbolic or non-symbolic numerical magnitude processing skills, or both, are predictive of children's mathematics achievement is of theoretical importance too. While non-symbolic representations of numerical magnitudes are thought to be shared across species and can already be measured in early infancy [13], symbolic representations are uniquely human and relatively recent cultural inventions to provide abstract representations of numerical magnitude. Thus, by investigating the relationship between, on the one hand symbolic and non-symbolic numerical magnitude processing and, on the other, children's mathematical achievement, larger questions concerning the role of evolutionary ancient skills for the acquisition of uniquely human number skills and representations can also be constrained. In this contribution, we provide an integrative review of the existing body of data that has dealt with this question.

Section snippets

Development of non-symbolic number processing

The nature and role of typically developing children's magnitude representations have been commonly explored with magnitude comparison tasks (Box 1). Nonsymbolic (dot) comparison tasks are frequently thought to index the precision or acuity of representations within the approximate number system (ANS), a system which allows individuals to represent and process numerical magnitude information. Representations within the ANS are noisy and become increasingly imprecise with increasing magnitude.

Symbolic processing development

The development of symbolic number processing has been typically investigated by means of magnitude comparison tasks that involve Arabic digits (Box 1). Performance on this task improves with age [33], [70] and is also characterized by an effect of distance or ratio. Scores on this task are not straightforward to interpret, as they might reflect the nature of underlying ANS representations, or the mapping between symbols and the ANS representations, or alternatively the nature of symbolic

Atypical numerical development: developmental dyscalculia

Developmental dyscalculia (DD) is a persistent and specific disorder of numerical development and mathematical learning despite normal intelligence and scholastic opportunities. Several authors have proposed that DD arises from a fundamental impairment in the representation of numerical magnitudes (e.g., [8], [9], [81]). This hypothesis has been tested with numerical magnitude comparison tasks (see Table 3). Data on symbolic comparison tasks has led to very consistent results showing weaker

Brain imaging data

There have been a growing number of efforts to uncover which brain regions might underlie the associations between numerical magnitude processing and mathematics achievement. In studies with both children and adults, the left and the right intraparietal sulci (IPS) have been found to be important neural correlates of numerical magnitude processing (see Refs. [2], [17], [21]; see Ref. [36] for a meta-analysis in children), with evidence suggesting that there is increasing specialization of the

Educational interventions

Various attempts have been made to design educational interventions to foster the development of numerical magnitude processing. These types of interventions have been embedded in larger-scale kindergarten programs for children from low-income communities [24], [29] and children at-risk for DD [74]. These programs comprised a wide variety of numerical activities, including number recognition, counting, comparing sets, playing board games, etc., and have been shown to have significant effects on

Summary and conclusions

One of the most robust findings in the literature that sought to uncover the association between numerical magnitude processing and mathematics achievement is that children who are better in determining which of two symbolic numbers is the largest have higher achievement in mathematics. Relatedly, children with DD show significant deficits in their ability to compare symbolic numbers. These data may suggest that children with low mathematics achievement or DD have difficulties in mapping

Acknowledgments

Bert De Smedt is funded by grant GOA 2012/010 of the Research Fund KULeuven, Belgium. Marie-Pascale Noël is supported by the National Research Fund of Belgium. Camilla Gilmore is funded by a British Academy Fellowship. Daniel Ansari is funded by the Natural Sciences and Engineering Council of Canada (NSERC), the Canadian Institutes of Health Research (CIHR) and the Canada Research Chairs Program (CRC).

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Research in PerspectiveHow do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior

Abstract

Introduction

Section snippets

Development of non-symbolic number processing

Symbolic processing development

Atypical numerical development: developmental dyscalculia

Brain imaging data

Educational interventions

Summary and conclusions

Acknowledgments

Journal of Experimental Child Psychology

Cognition

Developmental Cognitive Neuroscience

Progress in Neurobiology

Journal of Experimental Child Psychology

Educational Research Review

Journal of Experimental Child Psychology

Journal of Experimental Child Psychology

Developmental Cognitive Neuroscience

Early Childhood Research Quarterly

Journal of Experimental Child Psychology

Learning and Instruction

Journal of Experimental Child Psychology

Cognition

Journal of Experimental Child Psychology

Learning and Individual Differences

Acta Psychologica

Journal of Neurolinguistics

Cognition

Journal of Experimental Child Psychology

Cognition

Learning and Instruction

Cognition

Current Biology

Acta Psychologica

Journal of Applied Developmental Psychology

Cognitive Development

Cognition

Journal of Experimental Child Psychology

Research in Developmental Disabilities

Pratiques Psychologiques

Lingua

Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities

Learning and Individual Differences

Effects of development and enculturation on number representation in the brain

Nature Reviews Neuroscience

Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study

Journal of Cognitive Neuroscience

Neural correlates of symbolic number processing in children and adults

Neuroreport

The mathematical brain

Developmental dyscalculia

Dyscalculia: from brain to education

Science

The neural development of an abstract concept of number

Journal of Cognitive Neuroscience

Neural activity during natural viewing of Sesame Street statistically predicts test scores in early childhood

PLOS Biology

Research in Perspective
How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior