Symbolic numerical magnitude processing is as important to arithmetic as phonological awareness is to reading

In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties

Cross-domain associations of key cognitive correlates of early reading and early arithmetic in 5-year-olds

Disabilities in reading and arithmetic often co-occur, but (dis)abilities in reading and arithmetic have mostly been studied in isolation from each other. This study explicitly focused on the co-development of early reading and early arithmetic before primary education. The Multiple Deficit Model was used as theoretical framework (Pennington, 2006). According to this model, the overlap between early reading and early arithmetic is due to a constellation of shared and unique cognitive correlates. Therefore, we investigated whether key cognitive correlates of one academic ability also correlate with the other. Participants were 188 five-year-old kindergartners who had not yet been formally instructed in reading and arithmetic. Phonological awareness was selected as reading-specific cognitive correlate and (non)symbolic numerical magnitude processing and numeral recognition were considered as arithmetic-specific cognitive correlates. We administered a productive letter knowledge task as a proxy of early reading. Early arithmetic was assessed with simple problems such as 2 + 3 =? . Regression analyses and Bayesian hypothesis testing revealed significant correlations between early reading and early arithmetic before children start primary education. Phonological awareness predicted not only early reading but also, early arithmetic, even when controlling for early reading and arithmetic-specific cognitive correlates. Likewise, numeral recognition predicted not only early arithmetic, but also early reading, even when controlling for early arithmetic and phonological awareness. Phonological awareness and numeral recognition can be considered shared cognitive correlates of both academic domains. In contrast, non-symbolic and symbolic numerical magnitude processing skills were specifically correlated to early arithmetic, and not to early reading, indicating that they are unique to only one academic domain. In line with the Multiple Deficit Model, our data suggest that early reading and early arithmetic have a shared as well as unique underlying cognitive basis. Further unravelling what these academic abilities have in common can be of high value for detecting children at risk already before their transition to formal primary education

Mathematics anxiety: An intergenerational approach.

This study investigated mathematics anxiety from an intergenerational perspective, by investigating data on 172 primary-school children and both their biological parents. This family dataset (n = 516) allowed us to not only replicate previous findings per generation but also, importantly, explore intergenerational correlations. We found a significant negative association between sixth graders’ arithmetical performance and their mathematics anxiety. Gender differences occurred in each generation: females were more anxious than males about mathematics. Interestingly, these gender differences were not found in actual arithmetical performance. Analyses of our intergenerational data revealed that children’s mathematics anxiety was significantly associated with their mothers’ mathematics anxiety and both their mothers’ and fathers’ educational level. Regression analyses revealed that the significance level of mothers’ mathematics anxiety became borderline when considering mathematics anxiety and educational level of both parents simultaneously. Interestingly, mathematics anxiety as well as educational level of both biological parents was associated, suggesting that mathematics anxiety results from a complex entanglement of nature and nurture. Current intergenerational data suggest a complex familial basis of mathematics anxiety and indicate that the investigation of parental levels of education and mathematics anxiety contributes to the understanding of individual differences in children’s arithmetic performance.status: publishe

Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use

Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between these numerical magnitude representations and children’s strategy use during single-digit arithmetic. Our findings reveal that children’s symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits, retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming and general mathematics achievement were additionally controlled for. This all indicates that particularly the access to numerical meaning from Arabic symbols is key for children’s arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent.status: publishe

Arithmetic strategy development and its domain-specific and domain-general cognitive correlates

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Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: A longitudinal study in children with persistent mathematical learning difficulties

Deficits in arithmetic fact retrieval constitute the hallmark of children with mathematical learning difficulties (MLD). It remains, however, unclear which cognitive deficits underpin these difficulties in arithmetic fact retrieval. Many prior studies defined MLD by considering low achievement criteria and not by additionally taking the persistence of the MLD into account. Therefore, the present longitudinal study contrasted children with persistent MLD (MLD-p; mean age: 9 years 2 months) and typically developing (TD) children (mean age: 9 years 6 months) at three time points, to explore whether differences in arithmetic strategy development were associated with differences in numerical magnitude processing, working memory and phonological processing. Our longitudinal data revealed that children with MLD-p had persistent arithmetic fact retrieval deficits at each time point. Children with MLD-p showed persistent impairments in symbolic, but not in nonsymbolic, magnitude processing at each time point. The two groups differed in phonological processing, but not in working memory. Our data indicate that both domain-specific and domain-general cognitive abilities contribute to individual differences in children's arithmetic strategy development, and that the symbolic processing of numerical magnitudes might be a particular risk factor for children with MLD-p.publisher: Elsevier articletitle: Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: A longitudinal study in children with persistent mathematical learning difficulties journaltitle: Research in Developmental Disabilities articlelink: http://dx.doi.org/10.1016/j.ridd.2014.06.023 content_type: article copyright: Copyright © 2014 Elsevier Ltd. All rights reserved.status: publishe

Is the Long-Term Association Between Symbolic Numerical Magnitude Processing and Arithmetic Bi-Directional?

By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits.status: publishe

Is the Long-Term Association Between Symbolic Numerical Magnitude Processing and Arithmetic Bi-Directional?

By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits

Profiles of children's arithmetic fact development: A model-based clustering approach

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Does numerical processing uniquely predict first graders' future development of single-digit arithmetic?

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