Non-symbolic Numerical Skills Research Articles

Children skilled in mental abacus show enhanced non-symbolic number sense

Mental abacus is mental arithmetic with the help of an imagined abacus. Children skilled in mental abacus have been shown to exhibit top-quality arithmetic abilities. The current study investigated whether children with high-level mental abacus ability could outperform untrained control children in non-symbolic number sense, which is considered to be fundamental for arithmetic development. One hundred and fifty children (75 children skilled in mental abacus and 75 controls) took part in this study. Children skilled in mental abacus completed a mental abacus level test. The two groups of children performed serial cognitive tasks, assessing non-symbolic number comparison, arithmetic, language, spatial processing, visual perception, attention, processing speed, working memory, and general intelligence. Results showed that children skilled in mental abacus had significantly better non-symbolic number sense than the other children after controlling for general intelligence. The significant difference in non-symbolic number sense remained after controlling for age, gender, all types of cognitive processing available, and arithmetic performance. A mediation model showed that non-symbolic number sense partially mediated the group difference in arithmetic development. These findings suggest that children skilled in mental abacus have enhanced non-symbolic number sense and raise the possibility that mental abacus training could directly improve children’s non-symbolic numerical skills.

Differential contributions of cognitive precursors to symbolic versus non-symbolic numeracy in young Chinese children

Based on a longitudinal sample of young Hong Kong Chinese children (N = 104; age at the first wave of assessment: M ± SD = 59.69 ± 3.65 months), this study examined visual-spatial skills, working memory, phonological short-term memory, and phonological awareness in relation to symbolic and non-symbolic numerical skills. Children were tested first in their second year in kindergarten (K2; Time 1 [T1]) and then 12 months later in their third year (K3; Time 2 [T2]). Symbolic numerical skills were assessed using verbal counting, number recognition, number comparison, and written arithmetic tasks, while non-symbolic numerical skills were assessed using dot comparison and non-symbolic calculation tasks. Results from structural equation modeling showed that visual-spatial skills significantly predicted later non-symbolic numerical skills, while phonological short-term memory predicted later symbolic numerical skills. These associations remained even after controlling for the child's age and vocabulary. The findings highlight different constellations of cognitive skills that may be required in the development of young children's symbolic and non-symbolic numerical abilities.

Individual differences in basic numerical skills: The role of executive functions and motor skills

The aim of the current study was to explore individual differences in basic numerical skills in a normative sample of 151 kindergarteners (mean age = 6.45 years). Whereas previous research claims a substantial link between executive functions and basic numerical skills, motor abilities have been put forward to explain variance in numerical skills. Regarding the current study, these two assumptions have been combined, revealing interesting results. Namely, executive functions (inhibition, switching, and visuospatial working memory) were found to relate to symbolic numerical skills, and motor skills (gross and fine motor skills) showed a significant correlation to nonsymbolic numerical skills. Suggesting that motor skills and executive functions are associated with basic numerical skills could lead to potential avenues for interventions in certain disorders or disabilities such as nonverbal learning disability, developmental dyscalculia, and developmental coordination disorder.

Children's Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability.

Most empirical evidence supports the view that non-symbolic and symbolic representations are foundations for advanced mathematical ability. However, the detailed development trajectories of these two types of representations in childhood are not very clear, nor are the different effects of non-symbolic and symbolic representations on the development of mathematical ability. We assessed 253 4- to 8-year-old children’s non-symbolic and symbolic numerical representations, mapping skills, and mathematical ability, aiming to investigate the developmental trajectories and associations between these skills. Our results showed non-symbolic numerical representation emerged earlier than the symbolic one. Four-year-olds were capable of non-symbolic comparisons but not symbolic comparisons; five-year-olds performed better at non-symbolic comparisons than symbolic comparisons. This performance difference disappeared at age 6. Children at age 6 or older were able to map between symbolic and non-symbolic quantities. However, as children learn more about the symbolic representation system, their advantage in non-symbolic representation disappeared. Path analyses revealed that a direct effect of children’s symbolic numerical skills on their math performance, and an indirect effect of non-symbolic numerical skills on math performance via symbolic skills. These results suggest that symbolic numerical skills are a predominant factor affecting math performance in early childhood. However, the influences of symbolic and non-symbolic numerical skills on mathematical performance both declines with age.

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.

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.