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Justin Halberda - One of the best experts on this subject based on the ideXlab platform.
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Approximate Number System discrimination training for 7 8 year olds improves Approximate but not exact arithmetics and only in children with low pre training arithmetic scores
Journal of Numerical Cognition, 2020Co-Authors: Nuria Ferresforga, Justin HalberdaAbstract:We investigated whether training the Approximate Number System (ANS) would transfer to improved arithmetic performance in 7-8 year olds compared to a control group. All children participated in Pre- and Post-Training assessments of exact symbolic arithmetic (additions and subtractions) and Approximate symbolic arithmetic abilities (a novel test). During 3 weeks of training (Approximately 25 minutes per day, two days per week), we found that children in the ANS Training group had stable individual differences in ANS efficiency and increased in ANS efficiency, both within and across the training days. We also found that individual differences in ANS efficiency were related to symbolic arithmetic performance. Regarding arithmetic performance, both the ANS training group and the control group improved in all tests (exact and Approximate arithmetics tests). Thus, the ANS training did not show a specific effect on arithmetic performance. However, considering the initial arithmetic level of children, we found that the trained children showed a higher improvement on the novel Approximate arithmetic test compared to the control group, but only for those children with a low pre-training arithmetic score. Nevertheless, this difference within the low pre-training arithmetic score level was not observed in the exact arithmetic test. The limited benefits observed in these results suggest that this type of ANS discrimination training, through quantity comparison tasks, may not have an impact on symbolic arithmetics overall, although we cautiously propose that it could help with Approximate arithmetic abilities for children at this age with below-average arithmetic performance.
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Emergence of the Link Between the Approximate Number System and Symbolic Math Ability.
Child development, 2020Co-Authors: Jinjing Jenny Wang, Justin Halberda, Lisa FeigensonAbstract:Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay. Furthermore, our cross-sectional investigation revealed that children 4.5 years and older experienced a significant transfer effect of ANS manipulation on math performance, whereas younger children showed no such transfer, despite experiencing significant changes in ANS precision. These findings support the existence of a causal link between nonverbal numerical approximation and symbolic math performance that first emerges during the preschool years.
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Bidirectional, Longitudinal Associations Between Math Ability and Approximate Number System Precision in Childhood
Journal of Cognition and Development, 2018Co-Authors: Leanne Elliott, Justin Halberda, Lisa Feigenson, Melissa E. LibertusAbstract:Research suggests that individual differences in math abilities correlate with Approximate representations of quantity that are supported by a primitive Approximate Number System (ANS). However, re...
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Scale and the Evolutionarily Based Approximate Number System: An Exploratory Study.
International Journal of Science Education, 2017Co-Authors: Cesar Delgado, M. Gail Jones, Hye Sun You, Laura Robertson, Katherine Chesnutt, Justin HalberdaAbstract:ABSTRACTCrosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based Systems of Number such as the Approximate Number System (ANS), which processes Approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accurac...
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The precision of mapping between Number words and the Approximate Number System predicts children's formal math abilities.
Journal of experimental child psychology, 2016Co-Authors: Melissa E. Libertus, Lisa Feigenson, Darko Odic, Justin HalberdaAbstract:Children can represent Number in at least two ways: by using their non-verbal, intuitive Approximate Number System (ANS) and by using words and symbols to count and represent Numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and Number words, as evidenced by their ability to verbally estimate Numbers of items without counting. How does the quality of the mapping between Approximate and exact Numbers relate to children's math abilities? The role of the ANS-Number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation-mapping accuracy and variability-might each relate to math performance. Here, we addressed these gaps by measuring individual differences in ANS precision, verbal Number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities, even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-Number word mapping may be especially important for formal math abilities.
Lisa Feigenson - One of the best experts on this subject based on the ideXlab platform.
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Emergence of the Link Between the Approximate Number System and Symbolic Math Ability.
Child development, 2020Co-Authors: Jinjing Jenny Wang, Justin Halberda, Lisa FeigensonAbstract:Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay. Furthermore, our cross-sectional investigation revealed that children 4.5 years and older experienced a significant transfer effect of ANS manipulation on math performance, whereas younger children showed no such transfer, despite experiencing significant changes in ANS precision. These findings support the existence of a causal link between nonverbal numerical approximation and symbolic math performance that first emerges during the preschool years.
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Neural basis of Approximate Number System develops independent of visual experience
2019Co-Authors: Shipra Kanjlia, Lisa Feigenson, Marina BednyAbstract:Abstract Thinking about numerical quantities is an integral part of daily human life that is supported by the intraparietal sulcus (IPS). The IPS is recruited during mathematical calculation and neuronal populations within the IPS code for the quantity of items in a set. Is the developmental basis of IPS Number representations rooted in visual experience? We asked if the IPS possesses population codes for auditory quantities in sighted individuals and, critically, whether it does in the absence of any visual experience in congenitally blind individuals. We found that sequences of 4, 8, 16 and 32 tones each elicited unique patterns of fMRI activity in the IPS of both sighted and congenitally blind individuals, such that the quantity a participant heard on a given trial could be reliably predicted based on the pattern of observed IPS activity. This finding suggests that the IPS Number System is resilient to dramatic changes in sensory experience.
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Bidirectional, Longitudinal Associations Between Math Ability and Approximate Number System Precision in Childhood
Journal of Cognition and Development, 2018Co-Authors: Leanne Elliott, Justin Halberda, Lisa Feigenson, Melissa E. LibertusAbstract:Research suggests that individual differences in math abilities correlate with Approximate representations of quantity that are supported by a primitive Approximate Number System (ANS). However, re...
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The precision of mapping between Number words and the Approximate Number System predicts children's formal math abilities.
Journal of experimental child psychology, 2016Co-Authors: Melissa E. Libertus, Lisa Feigenson, Darko Odic, Justin HalberdaAbstract:Children can represent Number in at least two ways: by using their non-verbal, intuitive Approximate Number System (ANS) and by using words and symbols to count and represent Numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and Number words, as evidenced by their ability to verbally estimate Numbers of items without counting. How does the quality of the mapping between Approximate and exact Numbers relate to children's math abilities? The role of the ANS-Number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation-mapping accuracy and variability-might each relate to math performance. Here, we addressed these gaps by measuring individual differences in ANS precision, verbal Number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities, even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-Number word mapping may be especially important for formal math abilities.
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Changing the precision of preschoolers' Approximate Number System representations changes their symbolic math performance.
Journal of experimental child psychology, 2016Co-Authors: Jinjing Jenny Wang, Justin Halberda, Darko Odic, Lisa FeigensonAbstract:From early in life, humans have access to an Approximate Number System (ANS) that supports an intuitive sense of numerical quantity. Previous work in both children and adults suggests that individual differences in the precision of ANS representations correlate with symbolic math performance. However, this work has been almost entirely correlational in nature. Here we tested for a causal link between ANS precision and symbolic math performance by asking whether a temporary modulation of ANS precision changes symbolic math performance. First, we replicated a recent finding that 5-year-old children make more precise ANS discriminations when starting with easier trials and gradually progressing to harder ones, compared with the reverse. Next, we show that this brief modulation of ANS precision influenced children's performance on a subsequent symbolic math task but not a vocabulary task. In a supplemental experiment, we present evidence that children who performed ANS discriminations in a random trial order showed intermediate performance on both the ANS task and the symbolic math task, compared with children who made ordered discriminations. Thus, our results point to a specific causal link from the ANS to symbolic math performance.
Elizabeth M. Brannon - One of the best experts on this subject based on the ideXlab platform.
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Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics
Language learning and development : the official journal of the Society for Language Development, 2017Co-Authors: Emily Szkudlarek, Elizabeth M. BrannonAbstract:ABSTRACTIn this article we first review evidence for the Approximate Number System (ANS), an evolutionarily ancient and developmentally conservative cognitive mechanism for representing Number without language. We then critically review five different lines of support for the proposal that symbolic representations of Number build upon the ANS, and discuss potential causes of conflicting findings in the literature. Finally, we consider potential mechanisms that could drive a relationship between the ANS and symbolic math. We conclude that while there is considerable evidence the relationship between the ANS and symbolic math is meaningful, we are far from understanding the cognitive and neural mechanisms that underlie this relationship.
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Using cognitive training studies to unravel the mechanisms by which the Approximate Number System supports symbolic math ability
Current opinion in behavioral sciences, 2016Co-Authors: Stephanie Bugden, Nicholas K. Dewind, Elizabeth M. BrannonAbstract:A picture is emerging that preverbal nonsymbolic numerical representations derived from the Approximate Number System (ANS) play an important role in mathematical development and sustained mathematical thinking. Functional imaging studies are revealing developmental trends in how the brain represents Number. We propose that combining behavioral and neuroimaging techniques with cognitive training approaches will help identify the fundamental relationship between the ANS and symbolic mathematics. Understanding this relationship should ultimately benefit educators by providing ways to harness the ANS and hopefully improve math readiness in young children.
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Significant Inter-Test Reliability across Approximate Number System Assessments.
Frontiers in psychology, 2016Co-Authors: Nicholas K. Dewind, Elizabeth M. BrannonAbstract:The Approximate Number System (ANS) is the hypothesized cognitive mechanism that allows adults, infants, and animals to enumerate large sets of items Approximately. Researchers usually assess the ANS by having subjects compare two sets and indicate which is larger. Accuracy or Weber fraction is taken as an index of the acuity of the System. However, as Clayton et al., (2015) have highlighted, the stimulus parameters used when assessing the ANS vary widely. In particular, the numerical ratio between the pairs, and the way in which non-numerical features are varied often differ radically between studies. Recently, Clayton et al. (2015) found that accuracy measures derived from two commonly used stimulus sets are not significantly correlated. They argue that a lack of inter-test reliability threatens the validity of the ANS construct. Here we apply a recently developed modeling technique to the same data set. The model, by explicitly accounting for the effect of numerical ratio and non-numerical features, produces dependent measures that are less perturbed by stimulus protocol. Contrary to their conclusion we find a significant correlation in Weber fraction across the two stimulus sets. Nevertheless, in agreement with Clayton et al., we find that different protocols do indeed induce differences in numerical acuity and the degree of influence of non-numerical stimulus features. These findings highlight the need for a Systematic investigation of how protocol idiosyncrasies affect ANS assessments.
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Modeling the Approximate Number System to quantify the contribution of visual stimulus features.
Cognition, 2015Co-Authors: Nicholas K. Dewind, Geoffrey K. Adams, Michael L. Platt, Elizabeth M. BrannonAbstract:The Approximate Number System (ANS) subserves estimation of the Number of items in a set. Typically, ANS function is assessed by requiring participants to compare the Number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant’s Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spacing of dots. Current models of numerosity comparison do not account for these effects and consequently lead to different estimates of w depending on the methods used to control for non-numerical features. Here we proffer a new model that teases apart the effects of ANS acuity from the effects of non-numerical stimulus features. The result is an estimate of w that is a more theoretically valid representation of numerical acuity and novel terms that denote the degree to which a participant’s perception of Number is affected by non-numerical features. We tested this model in a sample of 20 adults and found that, by correctly attributing errors due to non-numerical stimulus features, the w obtained was more reliable across different stimulus conditions. We found that although non-numerical features biased numerosity discriminations in all participants, Number was the primary feature driving discriminations in most of them. Our findings support the idea that, while numerosity is a distinct visual quantity, the internal representation of Number is tightly bound to the representation of other magnitudes. This tool for identifying the different effects of the numerical and non-numerical features of a stimulus has important implications not only for the behavioral investigation of the ANS, but also for the collection and analyses of neural data sets associated with ANS function.
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Electrophysiological evidence for the involvement of the Approximate Number System in preschoolers' processing of spoken Number words
Journal of cognitive neuroscience, 2014Co-Authors: Michal Pinhas, Sarah E. Donohue, Marty G. Woldorff, Elizabeth M. BrannonAbstract:Little is known about the neural underpinnings of Number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3-to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory Number word was incongruent with the Number of visual objects on half the trials and congruent on the other half. Children's Number word comprehension predicted their ERP incongruency effects. Specifically, children with the least Number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high Number word knowledge showed an enhanced, negative polarity incongruency response (Ninc) over centroparietal sites from 200 to 500 msec after the Number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (Pinc) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most Number word knowledge showed ratio dependence in the Pinc (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the Pinc from 700 to 800 msec was found in children with intermediate Number word knowledge. These results provide the first neural correlates of spoken Number word comprehension in preschoolers and are consistent with the view that children map Number words onto Approximate Number representations before they fully master the verbal count list.
Melissa E. Libertus - One of the best experts on this subject based on the ideXlab platform.
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Understanding the Link Between the Approximate Number System and Math Abilities
Cognitive Foundations for Improving Mathematical Learning, 2019Co-Authors: Melissa E. LibertusAbstract:Abstract Previous correlational studies have suggested that the Approximate Number System (ANS) may be foundational to the acquisition of formal math abilities. In this chapter, I review evidence from training studies that provide support for a causal link between the ANS and math. However, the extant findings can neither be fully explained by the shared reliance on similar mental operations between the ANS and math nor by the notion that symbolic Number representations rely at least to some extent on ANS representations. Thus I propose that individual differences in the ANS may instead lead to differences in an individual's attention to and engagement with math-related information, which in turn affects math ability. Preliminary support for this hypothesis comes from recent studies showing that parents’ ANS acuity correlates with the amount of math talk they engage in while playing with their child and children's math abilities.
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Bidirectional, Longitudinal Associations Between Math Ability and Approximate Number System Precision in Childhood
Journal of Cognition and Development, 2018Co-Authors: Leanne Elliott, Justin Halberda, Lisa Feigenson, Melissa E. LibertusAbstract:Research suggests that individual differences in math abilities correlate with Approximate representations of quantity that are supported by a primitive Approximate Number System (ANS). However, re...
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Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics.
Frontiers in psychology, 2018Co-Authors: Emily J. Braham, Leanne Elliott, Melissa E. LibertusAbstract: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.
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Intergenerational associations of the Approximate Number System in toddlers and their parents.
The British journal of developmental psychology, 2018Co-Authors: Monica G. Navarro, Emily J. Braham, Melissa E. LibertusAbstract:From birth, humans are able to discriminate quantities using the Approximate Number System (ANS). However, previous methods have only been suitable to examine ANS functioning in infancy and older children. The goals of this study were twofold: first, to modify an existing method of assessing ANS functioning for toddlerhood; and second, to investigate individual differences in toddlers' ANS performance by examining correlations with their parents' ANS acuity. Using a preferential looking paradigm, we found that 1- to 3-year-olds (N = 46) looked significantly longer to numerically changing images compared to numerically constant ones suggesting that the paradigm is a suitable measure of ANS functioning in toddlerhood. Furthermore, we found a positive relation between toddlers' ANS performance and that of their parents (assessed using a non-symbolic Number comparison task) independent of children's vocabulary or parents' perceived math ability or preference for math. These findings are consistent with a specific intergenerational transmission of the ANS. Statement of contribution What is already known on this subject? Past methods used to examine ANS functioning were only suitable for infants and older children. Little research has examined sources underlying individual difference in ANS acuity. What does this study add? We developed a preferential looking task to assess ANS functioning in toddlerhood. Individual differences in toddlers' ANS functioning are correlated with their parents' ANS acuity.
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Deficits in Approximate Number System Acuity and Mathematical Abilities in 6.5-Year-Old Children Born Extremely Preterm
Frontiers in psychology, 2017Co-Authors: Melissa E. Libertus, Ulrika Ådén, Lea Forsman, Kerstin HellgrenAbstract:Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of Number that relies on an unlearned, Approximate Number System (ANS) and whether there is a link between preterm children’s ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., < 27 weeks gestation, n=82) and term-born children (n=89) completed a non-symbolic Number comparison (ANS acuity) task and a standardized math test. We found that extremely preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.
Jacqueline Leybaert - One of the best experts on this subject based on the ideXlab platform.
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Symbolic Number Abilities Predict Later Approximate Number System Acuity in Preschool Children
PloS one, 2014Co-Authors: Christophe Mussolin, Julie Nys, Jacqueline LeybaertAbstract:An ongoing debate in research on numerical cognition concerns the extent to which the Approximate Number System and symbolic Number knowledge influence each other during development. The current study aims at establishing the direction of the developmental association between these two kinds of abilities at an early age. Fifty-seven children of 3–4 years performed two assessments at 7 months interval. In each assessment, children's precision in discriminating numerosities as well as their capacity to manipulate Number words and Arabic digits was measured. By comparing relationships between pairs of measures across the two time points, we were able to assess the predictive direction of the link. Our data indicate that both cardinality proficiency and symbolic Number knowledge predict later accuracy in numerosity comparison whereas the reverse links are not significant. The present findings are the first to provide longitudinal evidence that the early acquisition of symbolic Numbers is an important precursor in the developmental refinement of the Approximate Number representation System.
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does math education modify the Approximate Number System a comparison of schooled and unschooled adults
Trends in Neuroscience and Education, 2013Co-Authors: Paulo Ventura, Luis Querido, Tânia Fernandes, Jacqueline LeybaertAbstract:Does math education contribute to refine the phylogenetically inherited capacity to Approximately process large Numbers? The question was examined in Western adults with different levels of math education. Unschooled adults who never received math education were compared to unschooled-instructed adults who did not attend regular school but received math education in adulthood, and to schooled adults who attended regular school in childhood. In the Number-comparison task (Exp. 1), the unschooled group was slower and made more errors than the other groups both when numerical symbols and nonsymbolic dot collections were presented. In the forced-choice mapping task (Exp. 2), the unschooled group experienced more difficulty than the others in linking large nonsymbolic and symbolic quantities, as well as in matching purely nonsymbolic quantities. These results suggest that Western adults who did not receive math education have less precise Approximate Number skills than adults who acquired exact Number competences through math education.
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Relationships between Approximate Number System acuity and early symbolic Number abilities
Trends in Neuroscience and Education, 2012Co-Authors: Christophe Mussolin, Julie Nys, Jacqueline LeybaertAbstract:Abstract The present study assessed the relationships between Approximate and exact Number abilities in children with little formal instruction to ask (1) whether individual differences in acuity of the Approximate System are related to basic abilities with symbolic Numbers; and (2) whether the link between non-symbolic and symbolic Number performance changes over the development. To address these questions, four different age groups of 3- to 6-year-old children were asked to compare pairs of train wagons varying on numerical ratio, as well as to complete exact tasks including Number words or Arabic Numbers. When correlation analyses were conducted across age groups, results indicated that performance in numerosity comparison was associated with mastery of symbolic Numbers, even when short-term memory, IQ and age were controlled for. Separate analyses by age group revealed that the precision in numerosity discrimination was related to both Number word and Arabic Number knowledge but differently across the development.