The Experts below are selected from a list of 2535 Experts worldwide ranked by ideXlab platform
Elizabeth M. Brannon - One of the best experts on this subject based on the ideXlab platform.
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The Acuity and Manipulability of the ANS Have Separable Influences on Preschoolers' Symbolic Math Achievement.
Frontiers in psychology, 2018Co-Authors: Ariel Starr, Rachel C. Tomlinson, Elizabeth M. BrannonAbstract:The approximate number system (ANS) is widely considered to be a foundation for the acquisition of uniquely human Symbolic numerical capabilities. However, the mechanism by which the ANS may support Symbolic number representations and Mathematical thought remains poorly understood. In the present study, we investigated two pathways by which the ANS may influence early Math abilities: variability in the acuity of the ANS representations and children’s’ ability to manipulate ANS representations. We assessed the relation between four-year-old children’s performance on a nonSymbolic numerical comparison task, a nonSymbolic approximate addition task, and a standardized Symbolic Math assessment. Our results indicate that ANS acuity and ANS manipulability each contribute unique variance to preschooler’s early Math achievement, and this result holds after controlling for both IQ and executive functions. These findings suggest that there are multiple routes by which the ANS influences Math achievement. Therefore, interventions that target both the precision and manipulability of the ANS may prove to be more beneficial for improving Symbolic Math skills compared to interventions that target only one of these factors.
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the contributions of numerical acuity and non numerical stimulus features to the development of the number sense and Symbolic Math achievement
Cognition, 2017Co-Authors: Ariel Starr, Nicholas K Dewind, Elizabeth M. BrannonAbstract:Numerical acuity, frequently measured by a Weber fraction derived from nonSymbolic numerical comparison judgments, has been shown to be predictive of Mathematical ability. However, recent findings suggest that stimulus controls in these tasks are often insufficiently implemented, and the proposal has been made that alternative visual features or inhibitory control capacities may actually explain this relation. Here, we use a novel Mathematical algorithm to parse the relative influence of numerosity from other visual features in nonSymbolic numerical discrimination and to examine the strength of the relations between each of these variables, including inhibitory control, and Mathematical ability. We examined these questions developmentally by testing 4-year-old children, 6-year-old children, and adults with a nonSymbolic numerical comparison task, a Symbolic Math assessment, and a test of inhibitory control. We found that the influence of non-numerical features decreased significantly over development but that numerosity was a primary determinate of decision making at all ages. In addition, numerical acuity was a stronger predictor of Math achievement than either non-numerical bias or inhibitory control in children. These results suggest that the ability to selectively attend to number contributes to the maturation of the number sense and that numerical acuity, independent of inhibitory control, contributes to Math achievement in early childhood.
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Neural connectivity patterns underlying Symbolic number processing indicate Mathematical achievement in children.
Developmental science, 2013Co-Authors: Joonkoo Park, Elizabeth M. BrannonAbstract:In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human Symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis to investigate the neural substrates for Symbolic number processing in young children. We hypothesized that, as children solidify the mapping between symbols and underlying magnitudes, important developmental changes occur in the neural communication between the right parietal region, important for the representation of non-Symbolic numerical magnitudes, and other brain regions known to be critical for processing numerical symbols. To test this hypothesis, we scanned children between 4 and 6 years of age while they performed a magnitude comparison task with Arabic numerals (numerical, Symbolic), dot arrays (numerical, non-Symbolic), and lines (non-numerical). We then identified the right parietal seed region that showed greater blood-oxygen-level-dependent signal in the numerical versus the non-numerical conditions. A psychophysiological interaction method was used to find patterns of effective connectivity arising from this parietal seed region specific to Symbolic compared to non-Symbolic number processing. Two brain regions, the left supramarginal gyrus and the right precentral gyrus, showed significant effective connectivity from the right parietal cortex. Moreover, the degree of this effective connectivity to the left supramarginal gyrus was correlated with age, and the degree of the connectivity to the right precentral gyrus predicted performance on a standardized Symbolic Math test. These findings suggest that effective connectivity underlying Symbolic number processing may be critical as children master the associations between numerical symbols and magnitudes, and that these connectivity patterns may serve as an important indicator of Mathematical achievement.
Valters Gatis - One of the best experts on this subject based on the ideXlab platform.
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Initial Version of Matlab/Simulink Based Tool for VHDL Code Generation and FPGA Implementation of Elementary Generalized Unitary Rotation
IEEE, 2024Co-Authors: Valters GatisAbstract:This paper describes a Matlab/Simulink GUI based tool for automated FPGA implementation of complex Jacobi-like Elementary Generalized Unitary rotation (EGU-rotation). The present work is targeted on multiplier-adder based rotation algorithm. The developed tool supports a large number of EGU-rotation matrix (EGURM) faces. The Symbolic Math Toolbox is used for operations with formulas. An intensive text processing has been used to get elementary expressions suitable for HDL coding. The tool uses Simulink HDL coder to generate implementable VHDL code. Three kinds of tests and a comparison of results are used. Estimation of rotation quality is based on the mean square error. An interaction between Matlab/Simulink and Altera Quartus II/ModelSim involves the using of scripts
Soohyun Cho - One of the best experts on this subject based on the ideXlab platform.
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testing the efficacy of training basic numerical cognition and transfer effects to improvement in children s Math ability
Frontiers in Psychology, 2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named ‘123 Bakery’ which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post- training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested.
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Data_Sheet_1_Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children’s Math Ability.pdf
2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named “123 Bakery” which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested.
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Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children’s Math Ability
'Frontiers Media SA', 2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named “123 Bakery” which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested
Selim Jang - One of the best experts on this subject based on the ideXlab platform.
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testing the efficacy of training basic numerical cognition and transfer effects to improvement in children s Math ability
Frontiers in Psychology, 2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named ‘123 Bakery’ which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post- training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested.
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Data_Sheet_1_Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children’s Math Ability.pdf
2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named “123 Bakery” which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested.
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Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children’s Math Ability
'Frontiers Media SA', 2018Co-Authors: Narae Kim, Selim Jang, Soohyun ChoAbstract:The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children’s Math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named “123 Bakery” which includes four training modules; non-Symbolic numerosity comparison, non-Symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, Symbolic/non-Symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall Math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in Symbolic, exact calculation, or any other Math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to Symbolic Math ability remains to be further tested
Stella F. Lourenco - One of the best experts on this subject based on the ideXlab platform.
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spatial processing in infancy predicts both spatial and Mathematical aptitude in childhood
Psychological Science, 2016Co-Authors: Jillian E Lauer, Stella F. LourencoAbstract:Despite considerable interest in the role of spatial intelligence in science, technology, engineering, and Mathematics (STEM) achievement, little is known about the ontogenetic origins of individual differences in spatial aptitude or their relation to later accomplishments in STEM disciplines. The current study provides evidence that spatial processes present in infancy predict interindividual variation in both spatial and Mathematical competence later in development. Using a longitudinal design, we found that children’s performance on a brief visuospatial change-detection task administered between 6 and 13 months of age was related to their spatial aptitude (i.e., mental-transformation skill) and mastery of Symbolic-Math concepts at 4 years of age, even when we controlled for general cognitive abilities and spatial memory. These results suggest that nascent spatial processes present in the first year of life not only act as precursors to later spatial intelligence but also predict Math achievement during...
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The approximate number system and its relation to early Math achievement: Evidence from the preschool years
Journal of experimental child psychology, 2012Co-Authors: Justin W. Bonny, Stella F. LourencoAbstract:Humans rely on two main systems of quantification; one is nonSymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is Symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to Symbolic Math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal Mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early Math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and Math competence was stronger for children with lower Math scores than for children with higher Math scores. Taken together, our findings suggest that early-developing connections between the ANS and Mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.
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nonSymbolic number and cumulative area representations contribute shared and unique variance to Symbolic Math competence
Proceedings of the National Academy of Sciences of the United States of America, 2012Co-Authors: Stella F. Lourenco, Justin W. Bonny, Edmund P FernandezAbstract:Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of Symbolic Mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with Mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized Math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in Math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonSymbolic number and cumulative area representations to formally taught Mathematics. More broadly, they suggest that uniquely human branches of Mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude.
