Non-symbolic Magnitude Comparison Research Articles

Extent of magnitude representation deficit and relationship with arithmetic skills in children with 22q11.2DS

BackgroundPrevious studies have produced conflicting results concerning the extent of magnitude representation deficit and its relationship with arithmetic achievement in children with 22q11.2 deletion syndrome. More specifically, it remains unclear whether deficits are restricted to visuospatial content or are more general and whether they could explain arithmetical impairment.MethodsFifteen 5- to 12-year-old children with 22q11.2 deletion syndrome and 23 age-matched healthy controls performed a non-symbolic magnitude comparison task. Depending on the trial, participants had to compare stimuli with high or low visuospatial load (visuospatial stimuli or temporal sequence of visual stimuli). The participants also completed a battery of arithmetic skills (ZAREKI-R) and a battery of global cognitive functioning (WISC-V or WPPSI-IV), from which working memory and visuospatial indices were derived.ResultsChildren with 22q11.2DS responded as fast as healthy controls did but received fewer correct responses, irrespective of visuospatial load. In addition, their performance in the non-symbolic magnitude comparison task did not correlate with the ZAREKI total score, while the working memory index did.ConclusionChildren with 22q11.2DS might suffer from a global magnitude representation deficit rather than a specific deficit due to visuospatial load. However, this deficit alone does not seem to be related to arithmetic achievement. Working memory might be a better concern of interest in favoring arithmetic skills in patients with 22q11.2 deletion syndrome.Trial registrationClinicaltrials, NCT04373226. Registered 16 September 2020.

Now you see it, now you don’t - Cognitive skills and their contributions to mathematics across early development

A broad variety of domain-specific (e.g., non-symbolic magnitude comparison and arithmetic) and domain-general (e.g., spatial skills and inhibition) skills have been identified as precursors to mathematics achievement. However, due to the increasing complexity of mathematics education with age and the associated increase in cognitive demands, it can be assumed that a divergent set of skills is predictive of mathematics achievement at different ages. This cross-sectional study in children aged 3, 5, and 7 years aims at identifying the differential contribution of domain-specific and domain-general contributors to mathematics and delineating their developmental dynamics. Our results reveal a consistent role for non-symbolic magnitude comparison across all age groups, non-symbolic arithmetic starting from the age of 5 years and visuospatial memory only in 5-year-olds. These findings support the notion that mathematics cannot be conceived as a unitary cognitive skill and provide a fine-grained analysis of the cognitive requirements of mathematical skills at different ages. On a more general note, they are in line with the idea that the ANS provides a critical scaffold for the development of mathematical skills but challenge the view that all ANS measures tap into the same underlying process.

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data.

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

Contributions of the psychology of mathematical cognition in early childhood education using apps.

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group (N = 49), high-performance group (N = 21), and control group (N = 123). The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages

Number writing involves transcoding from number words (e.g., “thirty-two”) to written digit strings (32) and is an important unique predictor of arithmetic. The existing longitudinal evidence about the relation between transcoding and arithmetic is mostly language specific. In languages with number word inversion (e.g., German), the order of tens and units is transposed in spoken number words compared with Arabic numbers. This makes transcoding more challenging than in languages without number word inversion (e.g., English). In the current study, we aimed to understand whether the contribution of number writing to the development of arithmetic is similar in languages with and without number word inversion. German-speaking children (n = 166) and English-speaking children (n = 201) were followed over the first 3 years of primary school. In a series of multiple linear regressions, we tested whether number writing of multi-digit numbers was a significant unique predictor of arithmetic after controlling for well-known non-numerical predictors (nonverbal reasoning and working memory) and numerical predictors (symbolic and nonsymbolic magnitude comparison). Number writing in Grade 1 predicted arithmetic in Grades 1, 2, and 3 over and above the other predictors. Crucially, number writing performance was of comparable importance for arithmetic development in German- and English-speaking children. Our findings extend previous evidence by showing that transcoding predicts the development of arithmetic skills during the first 3 years of primary school in languages with and without number word inversion.

What Skills Could Distinguish Developmental Dyscalculia and Typically Developing Children: Evidence From a 2-Year Longitudinal Screening

Developmental dyscalculia (DD) is a mathematics learning disorder that affects approximately 5% to 7% of the population. This study aimed to detect the underlying domain-specific and domain-general differences between DD and typically developing (TD) children. We recruited 9-year-old primary school children to form the DD group via a 2-year longitudinal screening process. In total, 75 DD children were screened from 1,657 children after the one-time screening, and 13 DD children were screened from 1,317 children through a consecutive 2-year longitudinal screening. In total, 13 experimental tasks were administered to assess their cognitive abilities to test the domain-specific magnitude representation hypothesis (including symbolic and nonsymbolic magnitude comparisons) and four alternative domain-general hypotheses (including working memory, executive function, attention, and visuospatial processing). The DD group had worse performance than the TD group on the number sense task, finger sense task, shifting task, and one-back task after both one-time and two-time screening. Logistic regressions further indicated the differences on the shifting task and the nonsymbolic magnitude comparison task could distinguish DD and TD children. Our findings suggest that domain-specific nonsymbolic magnitude representation and domain-general executive function both contribute to DD. Thus, both domain-specific and domain-general abilities will be necessary to investigate and to intervene in DD groups in the future.

Understanding additive composition is important for symbolic numerical magnitude processing

The present study examined additive composition as a longitudinal predictor for symbolic numerical magnitude comparison. Two hundred and twenty-four Chinese kindergarteners (Mage= 63.76 months; 103 boys, 121 girls) participated in this study across three waves of cognitive assessments. Cross-lagged panel analyses showed that additive composition predicted symbolic numerical magnitude comparison longitudinally but not vice versa. The cross-lagged effects remained significant beyond the influence of general intelligence, working memory, nonsymbolic magnitude comparison, and counting abilities. Theoretically, this study suggests that additive composition is a key factor underlying the exact representational system of numbers. It also entails educational implications that understanding the quantitative relations between numbers should be the focus of learning and teaching in early childhood mathematics education.

Cognición numérica temprana en niños sordos y oyentes: ¿más cercana de lo esperado?

Deaf students show a significant delay in their understanding of numeracy and measurement concepts as well as verbal problem solving. There is still no consensus about the origin of this delay but several studies have shown that deaf people show differences in basic numerical skills and executive function (EF), which could underlie the differences in the way they learn and develop their cognitive abilities. Children have the innate ability to estimate and compare numerosities without using language or numerical symbols. The ability to discriminate large numerosities depends on the approximate number system (ANS), a cognitive system believed to be governed by a neural circuit within the intraparietal sulcus. Researchers hypothesize that the ANS underlies the development of arithmetic and there is data supporting the contribution of the ANS for math achievements. Little is known about the approximate number system of deaf children at early ages. Deaf and hearing preschool children were compared in terms of specific cognitive functions shown to be important for success in mathematics. Executive functions and symbolic and nonsymbolic magnitude comparison abilities of 7 deaf children and 14 hearing children aged 4–7 years (M = 69.90 months, SD = 11.42), were compared. To do so, neuropsychological assessments for school-aged children were adapted into Portuguese Sign Language. Significant group differences were found in abstract counting as well as in symbolic and nonsymbolic magnitude comparisons. These findings suggest that deaf children are less competent in these early numeracy skills than are their hearing peers. https://doi.org/10.16888/interd.2022.39.2.8

Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years.

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

Cognitive mediators of US-China differences in early symbolic arithmetic.

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

When one size does not fit all: A latent profile analysis of low-income preschoolers’ math skills

On average, preschoolers from lower-income households perform worse on symbolic numerical tasks than preschoolers from middle- and upper-income households. Although many recent studies have developed and tested mathematics interventions for low-income preschoolers, the variability within this population has received less attention. The goal of the current study was to describe the variability in low-income children’s math skills using a person-centered analysis. We conducted a latent profile analysis on six measures of preschoolers’ (N = 115, mean age = 4.6 years) numerical abilities (nonsymbolic magnitude comparison, verbal counting, object counting, cardinality, numeral identification, and symbolic magnitude comparison). The results showed different patterns of strengths and weaknesses and revealed four profiles of numerical skills: (a) poor math abilities on all numerical measures (n = 13), (b) strong math abilities on all numerical measures (n = 41), (c) moderate abilities on all numerical measures (n = 35), and (d) strong counting and numeral skills but poor magnitude skills (n = 26). Children’s age, working memory, and inhibitory control significantly predicted their profile membership. We found evidence of quantitative and qualitative differences between profiles, such that some profiles were higher performing across tasks than others, but the overall patterns of performance varied across the different numerical skills assessed.

Intergenerational Features of Math Skills: Symbolic and Non-Symbolic Magnitude Comparison and Written Calculation in Mothers and Children

ABSTRACT In this article, we analyze symbolic and non-symbolic numerical abilities of parents in order to understand whether these are predictors of children’s numerical skills, considering basic symbolic, non-symbolic, and formal math skills (i.e., written calculation). A battery of cognitive and math tasks was administered to a sample of 83 children with established formal school experience (i.e., fourth and fifth grade students), and to their mothers. Correlational and regression analyses were performed. The results evidenced significant relationships between children’s and mothers’ symbolic and math skills, but children’s symbolic comparison skills were the most significant predictor of their math skills. The study suggests that the intergenerational features of math skills play a significant role in children’s numerical development but that children’s math skills ultimately depend mainly on their own numerical processing. Within an educational perspective, the development of symbolic number skills in children is crucial and might allow the constraints of intergenerational transmission of math skills to be reduced.

Predictors of Children's Early Numeracy: Environmental Variables, Intergenerational Pathways, and Children's Cognitive, Linguistic, and Non-symbolic Number Skills.

Early numeracy skills in preschool years have been found to be related to a variety of different factors, including Approximate Number System (ANS) skills, children’s cognitive and linguistic skills, and environmental variables such as home numeracy activities. The present study aimed to analyze the differential role of environmental variables, intergenerational patterns, children’s cognitive and linguistic skills, and their ANS in supporting early math skills. The sample included 64 children in their last year of kindergarten and one parent of each child. Children were administered a battery of cognitive and linguistic tasks, and a non-symbolic comparison task as a measure of ANS. Parents were administered similar tasks assessing cognitive skills, math skills, and ANS skills (estimation and non-symbolic comparison), together with a questionnaire on home numeracy. Results showed that home numeracy predicted children’s early math skills better than a number of parent and child variables. Considering children’s skills, their ability in the non-symbolic magnitude comparison task was the strongest predictor of early math skills. Results reinforce the importance of the role of home numeracy activities and children’s ANS skills above that of parents’ math skills.

Variation in early number skills and mathematics achievement: Implications from cognitive profiles of children with or without Turner syndrome.

Individuals with Mathematics Learning Disabilities have persistent mathematics underperformance but vary with respect to their cognitive profiles. The present study examined mathematics ability and achievement, and associated mathematics-specific numerical skills and domain-general cognitive abilities, in young children with Turner syndrome compared to their matched peers. We utilized two independent peer groups so that group comparisons would account for verbal skills, a hypothesized strength of girls with Turner syndrome, and nonsymbolic magnitude comparison skills, a hypothesized difference of girls with Turner syndrome. This individual matching approach afforded characterization of mathematics profiles of girls with Turner syndrome and girls without Turner syndrome that share potential key features of the Turner syndrome phenotype. Results indicated differences in mathematics ability and nonsymbolic magnitude comparison tasks between girls with Turner syndrome and peers with similar levels of verbal skill. Mathematics ability and mathematics achievement scores of girls with Turner syndrome did not differ significantly from their peers with similar levels of accuracy on a nonsymbolic magnitude comparison task. Cognitive correlates of mathematics outcomes showed disparate patterns across groups. These quantitative and qualitative differences across profiles enhance our understanding of variation in mathematics ability in early childhood and inform how mathematics skills develop in young children with or without Turner syndrome.

How Good Is the Phoneme Elision Test in Assessing Reading, Spelling and Arithmetic-Related Abilities?

The aim of this study was to investigate the psychometric properties and diagnostic accuracy of phoneme elision task (PET). We assessed cross-sectionally 470 Brazilian children (54.3% girls) aged between 7 and 11years (mean age=8.83, sd=0.85), from the 2nd to 4th grades. Children were assessed in their phonemic awareness ability, as well as intelligence, general school achievement, both verbal and visuospatial working memory, single-word reading, and nonsymbolic magnitude comparison. Beyond the psychometric properties and diagnostic accuracy of PET, we also provided reference values. Our data suggest that PET is composed mainly of one single construct, with high item reliability and precision (KR-20 above 0.90). In general, items have acceptable discriminability, considering item-total correlations. Overall PET is generally a good screening tool for reading and spelling difficulties (SD), as well as to identify children with learning difficulties in the early grades. However, it is not a reliable measure for screening math learning difficulties. Finally, PET shows good convergent and divergent validity. We provide evidence about the psychometric properties and diagnostic accuracy of a PET. Results contribute to the assessment of phonemic awareness in Brazilian children, in both clinical and research contexts. The PET can be used as a screening tool for reading and SD, which could lead to early interventions.

Training nonsymbolic proportional reasoning in children and its effects on their symbolic math abilities

Our understanding of proportions can be both symbolic, as when doing calculations in school mathematics, or intuitive, as when folding a bed sheet in half. While an understanding of symbolic proportions is crucial for school mathematics, the cognitive foundations of this ability remain unclear. Here we implemented a computerized training game to test a causal link from intuitive (nonsymbolic) to symbolic proportional reasoning and other math abilities in 4th grade children. An experimental group was trained in nonsymbolic proportional reasoning (PR) with continuous extents, and an active control group was trained on a remarkably similar nonsymbolic magnitude comparison. We found that the experimental group improved at nonsymbolic PR across training sessions, showed near transfer to a paper-and-pencil nonsymbolic PR test, transfer to symbolic proportions, and far transfer to geometry. The active control group showed only a predicted far transfer to geometry. In a second experiment, these results were replicated with an independent cohort of children. Overall this study extends previous correlational evidence, suggesting a functional link between nonsymbolic PR on one hand and symbolic PR and geometry on the other.

Learning correspondences between magnitudes, symbols and words: Evidence for a triple code model of arithmetic development

According to the Triple Code Model, early arithmetic development depends on learning the mappings between non-verbal representations of magnitude (quantity) and symbolic verbal (number words) and visual (Arabic numerals) representations of number. We examined this hypothesis in a sample of 166 4- to 7-year old children. Children completed 4 paired-associate learning tasks and a broad range of measures assessing early numerical (symbolic and non-symbolic magnitude comparison, digit writing, arithmetic) and reading skills (letter-sound knowledge, phoneme awareness, rapid automatized naming, word reading). A path model showed that paired-associate learning tasks involving mapping magnitudes onto verbal or visual stimuli predicted arithmetic performance over and above other well-established predictors. This relationship was specific to arithmetic and, consistent with the Triple Code Model, highlights that mapping between non-symbolic magnitude representations and the corresponding symbolic forms (verbal and visual) is important to the development of arithmetic skills.

Math and Memory in Bilingual Preschoolers: The Relations Between Bilingualism, Working Memory, and Numerical Knowledge

ABSTRACTBilingual children exhibit enhanced working memory (WM) skill relative to monolingual children, which could have implications for early mathematics development. Competency in mathematics is supported by conceptual and procedural mathematical knowledge, and numerical knowledge is in turn supported by underlying cognitive processes such as WM. Building on this evidence, we investigated whether bilingual preschoolers demonstrated, relative to monolingual peers, enhanced performance on WM and greater numerical knowledge. We examined the role of WM in numerical understanding for both monolingual and bilingual children. Participants were 4- and 5-year old children (74) recruited from preschools serving families from a range of socioeconomic, racial, and ethnic backgrounds. Participants completed a nonverbal WM task and a range of numerical-knowledge measures, specifically numeral identification, addition, symbolic magnitude comparison, and nonsymbolic magnitude comparison tasks. Results revealed that bilingual children outperformed monolingual peers on WM even after controlling for age and socioeconomic status (SES). Bilingual children also demonstrated greater performance on addition and numeral identification tasks. For all tasks except numeral identification, WM predicted children’s performance on numerical knowledge measures. We discuss results in terms of the possible unique cognitive and academic advantages bilingual children may have.

The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children's Mathematical Abilities?

Spatial representations of number, such as a left-to-right oriented mental number line, are well documented in Western culture. Yet, the functional significance of such a representation remains unclear. To test the prominent hypothesis that a mental number line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasks: a non-symbolic magnitude comparison task, and a symbolic “Where was the number?” (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional mental number line across numerical format. Although there were no significant correlations between children’s SNAs on the WTN task and math ability, children’s SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented mental number line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the mental number line to math performance. We conclude with a discussion of the different properties that characterize a mental number line and how these different properties may relate to mathematical ability.

Narrowing the Early Mathematics Gap: A Play-Based Intervention to Promote Low-Income Preschoolers' Number Skills.

Preschoolers from low-income households lag behind preschoolers from middle-income households on numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children's numerical knowledge. Experiment 2 randomly assigned low-income preschoolers (M age = 4.7 years) to play either a numerical magnitude comparison or a numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants' symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers' early numerical knowledge.