Symbolic Numerical Processing Research Articles

Pathways to word reading and calculation skills in young Chinese children: From biologically primary skills to biologically secondary skills.

Drawing on Geary’s (1995) evolution-based model of cognitive and academic development, this study investigated the relation between biologically primary skills (vocabulary, executive functions, and visual-spatial processing) and subsequent word reading and calculation. It also examined the extent to which these relations were mediated by biologically secondary skills (metalinguistic awareness and symbolic numerical processing). A total of 197 Chinese children (age at the first measurement point: M ± SD = 53.38 ± 3.32 months) were assessed three times over 18 months on their vocabulary, spatial perception, working memory (WM), short-term memory (STM), inhibitory control, metalinguistic awareness (i.e., phonological awareness, morphological awareness, and orthographic awareness), symbolic numerical skills (i.e., counting, number comparison, and number transcoding), Chinese word reading, and calculation competencies. The results showed that STM and spatial perception predicted subsequent calculation after baseline performance and background information were controlled for, and the contributions were fully mediated by counting and number transcoding. Inhibitory control had a direct effect on later calculation, which was not mediated by any secondary skills. With regards to word reading, although none of the biologically primary skills predicted later word reading after controlling for baseline performance and background information, vocabulary; spatial perception; STM, inhibitory control; and WM had indirect effects on word reading via phonological awareness, orthographic awareness, and number transcoding. Implications for theory and practice are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Identifying children with persistent low math achievement: The role of number-magnitude mapping and symbolic numerical processing

Although an increasing number of research studies have investigated the cognitive deficits related to difficulties in learning mathematics, little is known about whether these cognitive deficits longitudinally predict low mathematics achievement over time. The current 6-year longitudinal study was conducted to address this issue. A sample of 101 students was tested on various numerical and cognitive competencies when they were in kindergarten and in Grade 1. They were then followed until they were in Grade 6, and their mathematics achievement was assessed bi-annually. A group of persistent low mathematics achievers (PLA) who scored consistently below the 25th percentile was identified. This group of PLA showed difficulties in most of the numerical tasks as early as kindergarten. More importantly, three of the early predictors correctly identified 79% of the PLAs. The current findings provide valuable information concerning the core cognitive deficits underlying difficulties in learning mathematics as well as an important tool for educators for identifying children who are at risk of persistent math learning difficulties in the elementary school years.

Impairment of Arabic- and spoken-number processing in children with mathematical learning disability

The performance of 24 French-Quebec 8‒9-year-old children with Mathematical Learning Disability (MLD) in Arabic and spoken number recognition, comprehension and production tasks designed to assess symbolic number processing was compared to that of 37 typically developing children (TD). Children with MLD were less successful than TD children in every symbolic numerical task, including recognition of Arabic and spoken numbers. These results thus suggested that this deficit of symbolic number recognition could compromise symbolic number comprehension and production. Children with MLD also presented with general cognitive difficulties as reading difficulties. Taken together, our results clearly showed that children with MLD presented with a symbolic numerical processing deficit that could be largely attributed to their poorer written language skills.

Individual differences in nonverbal number skills predict math anxiety

Math anxiety (MA) involves negative affect and tension when solving mathematical problems, with potentially life-long consequences. MA has been hypothesized to be a consequence of negative learning experiences and cognitive predispositions. Recent research indicates genetic and neurophysiological links, suggesting that MA stems from a basic level deficiency in symbolic numerical processing. However, the contribution of evolutionary ancient purely nonverbal processes is not fully understood. Here we show that the roots of MA may go beyond symbolic numbers. We demonstrate that MA is correlated with precision of the Approximate Number System (ANS). Individuals high in MA have poorer ANS functioning than those low in MA. This correlation remains significant when controlling for other forms of anxiety and for cognitive variables. We show that MA mediates the documented correlation between ANS precision and math performance, both with ANS and with math performance as independent variable in the mediation model. In light of our results, we discuss the possibility that MA has deep roots, stemming from a non-verbal number processing deficiency. The findings provide new evidence advancing the theoretical understanding of the developmental etiology of MA.

Both non-symbolic and symbolic quantity processing are important for arithmetical computation but not for mathematical reasoning

ABSTRACTThis study investigated whether numerical processing was important for two types of mathematical competence: arithmetical computation and mathematical reasoning. Thousand eight hundred and fifty-seven Chinese primary school children in third through sixth grades took eight computerised tasks: numerical processing (numerosity comparison, digit comparison), arithmetical computation, number series completion, non-verbal matrix reasoning, mental rotation, choice reaction time, and word rhyming. Hierarchical regressions showed that both non-symbolic numerical processing (numerosity comparison) and symbolic numerical processing (digit comparison) were independent predictors of arithmetical computation but neither was a predictor of mathematical reasoning (assessed by number series completion). These findings suggest that the cognitive basis of mathematical performance varies depending on the type of mathematical competence measured.

Spontaneous focusing on numerosity and the arithmetic advantage

Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4–5 years (N = 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number.

Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing.

Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the number sense, is not well-known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18–25) and 25 older adults (60–77) participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly [RTs, accuracy and Weber fractions (w)]. All participants showed decreased non-symbolic acuity (accuracy and w) in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive, and embedded number sense.

Count on dopamine: influences of COMT polymorphisms on numerical cognition

Catechol-O-methyltransferase (COMT) is an enzyme that is particularly important for the metabolism of dopamine. Functional polymorphisms of COMT have been implicated in working memory and numerical cognition. This is an exploratory study that aims at investigating associations between COMT polymorphisms, working memory, and numerical cognition. Elementary school children from 2th to 6th grades were divided into two groups according to their COMT val158met polymorphism [homozygous for valine allele (n = 61) vs. heterozygous plus methionine homozygous children or met+ group (n = 94)]. Both groups were matched for age and intelligence. Working memory was assessed through digit span and Corsi blocks. Symbolic numerical processing was assessed through transcoding and single-digit word problem tasks. Non-symbolic magnitude comparison and estimation tasks were used to assess number sense. Between-group differences were found in symbolic and non-symbolic numerical tasks, but not in working memory tasks. Children in the met+ group showed better performance in all numerical tasks while val homozygous children presented slower development of non-symbolic magnitude representations. These results suggest COMT-related dopaminergic modulation may be related not only to working memory, as found in previous studies, but also to the development of magnitude processing and magnitude representations.

Individual differences in nonverbal number discrimination correlate with event-related potentials and measures of probabilistic reasoning

The current study investigated the neural activity patterns associated with numerical sensitivity in adults. Event-related potentials (ERPs) were recorded while adults observed sequentially presented display arrays (S1 and S2) of non-symbolic numerical stimuli (dots) and made same/different judgments of these stimuli by pressing a button only when numerosities were the same (target trials). The main goals were to contrast the effects of numerical distance (close, medium, and far) and change direction (increasing, decreasing) between S1 and S2, both in terms of behavior and brain activity, and to examine the influence of individual differences in numeracy on the effects of these manipulations. Neural effects of distance were found to be significant between 360 and 600ms after the onset of S2 (greater negativity-wave activity for closer numerical distances), while direction effects were found between 320 and 440ms (greater negativity for decreasing direction). ERP change direction effects did not interact with numerical distance, suggesting that the two types of information are processed independently. Importantly, subjects’ behavioral Weber fractions (w) for the same/different discrimination task correlated with distance-related ERP-activity amplitudes. Moreover, w also correlated with a separate objective measure of mathematical ability. Results thus draw a clear link between brain and behavior measures of number discrimination, while also providing support for the relationship between nonverbal magnitude discrimination and symbolic numerical processing.

Functional Imaging of Numerical Processing in Adults and 4-y-Old Children

Adult humans, infants, pre-school children, and non-human animals appear to share a system of approximate numerical processing for non-symbolic stimuli such as arrays of dots or sequences of tones. Behavioral studies of adult humans implicate a link between these non-symbolic numerical abilities and symbolic numerical processing (e.g., similar distance effects in accuracy and reaction-time for arrays of dots and Arabic numerals). However, neuroimaging studies have remained inconclusive on the neural basis of this link. The intraparietal sulcus (IPS) is known to respond selectively to symbolic numerical stimuli such as Arabic numerals. Recent studies, however, have arrived at conflicting conclusions regarding the role of the IPS in processing non-symbolic, numerosity arrays in adulthood, and very little is known about the brain basis of numerical processing early in development. Addressing the question of whether there is an early-developing neural basis for abstract numerical processing is essential for understanding the cognitive origins of our uniquely human capacity for math and science. Using functional magnetic resonance imaging (fMRI) at 4-Tesla and an event-related fMRI adaptation paradigm, we found that adults showed a greater IPS response to visual arrays that deviated from standard stimuli in their number of elements, than to stimuli that deviated in local element shape. These results support previous claims that there is a neurophysiological link between non-symbolic and symbolic numerical processing in adulthood. In parallel, we tested 4-y-old children with the same fMRI adaptation paradigm as adults to determine whether the neural locus of non-symbolic numerical activity in adults shows continuity in function over development. We found that the IPS responded to numerical deviants similarly in 4-y-old children and adults. To our knowledge, this is the first evidence that the neural locus of adult numerical cognition takes form early in development, prior to sophisticated symbolic numerical experience. More broadly, this is also, to our knowledge, the first cognitive fMRI study to test healthy children as young as 4 y, providing new insights into the neurophysiology of human cognitive development.