Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples’ ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults’ accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities

Electrophysiological evidence for notation independence in numerical processing

BACKGROUND: A dominant view in numerical cognition is that numerical comparisons operate on a notation independent representation (Dehaene, 1992). Although previous human neurophysiological studies using scalp-recorded event-related potentials (ERPs) on the numerical distance effect have been interpreted as supporting this idea, differences in the electrophysiological correlates of the numerical distance effect in symbolic notations (e.g. Arabic numerals) and non-symbolic notations (e.g. a set of visually presented dots of a certain number) are not entirely consistent with this view. METHODS AND RESULTS: Two experiments were conducted to resolve these discrepancies. In Experiment 1, participants performed a symbolic and a non-symbolic numerical comparison task ("smaller or larger than 5?") with numerical values 1–4 and 6–9 while ERPs were recorded. Consistent with a previous report (Temple & Posner, 1998), in the symbolic condition the amplitude of the P2p ERP component (210–250 ms post-stimulus) was larger for values near to the standard than for values far from the standard whereas this pattern was reversed in the non-symbolic condition. However, closer analysis indicated that the reversal in polarity was likely due to the presence of a confounding stimulus effect on the early sensory ERP components for small versus larger numerical values in the non-symbolic condition. In Experiment 2 exclusively large numerosities (8–30) were used, thereby rendering sensory differences negligible, and with this control in place the numerical distance effect in the non-symbolic condition mirrored the symbolic condition of Experiment 1. CONCLUSION: Collectively, the results support the claim of an abstract semantic processing stage for numerical comparisons that is independent of input notation

Is Approximate Number Precision a Stable Predictor

Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills

Is Approximate Number Precision a Stable Predictor

Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills

The General Movement Assessment Helps Us to Identify Preterm Infants at Risk for Cognitive Dysfunction

Apart from motor and behavioral dysfunctions, deficits in cognitive skills are among the well-documented sequelae of preterm birth. However, early identification of infants at risk for poor cognition is still a challenge, as no clear association between pathological findings based on neuroimaging scans and cognitive functions have been detected as yet. The Prechtl General Movement Assessment (GMA) has shown its merits for the evaluation of the integrity of the young nervous system. It is a reliable tool for identifying infants at risk for neuromotor deficits. Recent studies on preterm infants demonstrate that abnormal general movements also reflect impairments of brain areas involved in cognitive development. The aim of this systematic review was to discuss studies that included (i) the Prechtl GMA applied in preterm infants, and (ii) cognitive outcome measures in six data bases. Seven studies met the inclusion criteria and yielded the following results: (a) children born preterm with consistently abnormal general movements up to 8 weeks after term had lower intelligence quotients at school age than children with an early normalization of general movements; (b) from 3 to 5 months after term, several qualitative and quantitative aspects of the concurrent motor repertoire, including postural patterns, were predictive of intelligence at 7 to 10 years of age. These findings in 428 individuals born preterm suggest that normal general movements along with a normal motor repertoire during the first months after term are markers for normal cognitive development until at least age 10

Number word use in toddlerhood is associated with number recall performance at seven years of age

Previous studies have shown that verbal working memory and vocabulary acquisition are linked in early childhood. However, it is unclear whether acquisition of a narrow range of words during toddlerhood may be particularly related to recall of the same words later in life. Here we asked whether vocabulary acquisition of number words, location and quantifier terms over the first three years of life are associated with verbal and visuospatial working memory at seven years. Our results demonstrate that children who produced more number words between 20-26 months and started to produce the number words 1-10 earlier showed greater number recall at 7 years of age. This link was specific to numbers and neither extended to quantifier and location terms nor verbal and visuospatial working memory performance with other stimuli. These findings suggest a category-specific link between the mental lexicon of number words and working memory for numbers at an early age. © 2014 Libertus et al

Relations between Subdomains of Home Math Activities and Corresponding Math Skills in 4-Year-Old Children

Most studies on the subject have investigated relations between home math activities and child math skills, without paying much attention to the specific skills that such activities foster and their alignment with children’s math assessments. The present study examined specific relations between subdomains of home math activities and children’s corresponding math skills (e.g., home counting/cardinality activities related to children’s counting/cardinality skills). Participants were 78 mostly middle-income, White parents and their four-year-old children (M age = 53.19 months; 45% girls). Parents completed a 24-item survey about the frequency of home activities supporting five subdomains of math: counting/cardinality, set comparison, number identification, adding/subtracting, and patterning. Children’s skills in these same five subdomains were assessed using the Preschool Early Numeracy Scale (PENS) and the Early Patterning Assessment. Specific relations were observed in set comparison, adding/subtracting, and patterning, such that higher frequency of home activities in these subdomains related to advanced child math skills in the corresponding subdomains. No specific relations were found in counting/cardinality and number identification. Overall home math activities averaged across the five math subdomains positively related to children’s overall math skills. Findings highlight the importance of engagement in specific math activities in the home environment and their significance for corresponding child math development

When approximate number acuity predicts math performance: The moderating role of math anxiety

<div><p>Separate lines of research suggest that people who are better at estimating numerical quantities using the approximate number system (ANS) have better math performance, and that people with high levels of math anxiety have worse math performance. Only a handful of studies have examined both ANS acuity and math anxiety in the same participants and those studies report contradictory results. To address these inconsistencies, in the current study 87 undergraduate students completed assessments of ANS acuity, math anxiety, and three different measures of math. We considered moderation models to examine the interplay of ANS acuity and math anxiety on different aspects of math performance. Math anxiety and ANS acuity were both unique significant predictors of the ability to automatically recall basic number facts. ANS acuity was also a unique significant predictor of the ability to solve applied math problems, and this relation was further qualified by a significant interaction with math anxiety: the positive association between ANS acuity and applied problem solving was only present in students with high math anxiety. Our findings suggest that ANS acuity and math anxiety are differentially related to various aspects of math and should be considered together when examining their respective influences on math ability. Our findings also raise the possibility that good ANS acuity serves as a protective factor for highly math-anxious students on certain types of math assessments.</p></div