scholarly journals Individual differences in numerical comparison is independent of numerical precision

2019 ◽  
Vol 5 (2) ◽  
pp. 220-240
Author(s):  
Richard Prather
Keyword(s):  
Mathematical Model ◽  
Individual Variation ◽  
Numerical Comparison ◽  
Behavioral Experiments ◽  
Comparison Task ◽  
Free Response ◽  
Estimation Task ◽  
Decision Making Factors ◽  
Numerical Precision ◽  
Value Representation

Numeracy, as measured by performance on the non-symbolic numerical comparison task, is a key construct in numerical and mathematical cognition. The current study examines individual variation in performance on the numerical comparison task. We contrast the hypothesis that performance on the numerical comparison task is primarily due to more accurate representations of numbers with the hypothesis that performance dependent on decision-making factors. We present data from two behavioral experiments and a mathematical model. In both behavioral experiments we measure the precision of participant’s numerical value representation using a free response estimation task. Taken together, results suggest that individual variation in numerical comparison performance is not predicted by variation in the precision of participants’ numerical value representation.

scholarly journals Individual differences in children’s numerical comparison is independent of numerical precision

2017 ◽  
Author(s):  
Richard Prather
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Individual Differences ◽  
Individual Variation ◽  
Mathematical Cognition ◽  
Numerical Comparison ◽  
Behavioral Experiments ◽  
Comparison Task ◽  
Decision Making Factors ◽  
Numerical Precision

Numeracy, as measured by performance on the non-symbolic numerical comparison task, is a key construct in numerical and mathematical cognition. The current study examines individual variation in performance on the numerical comparison task. We contrast the hypothesis that performance on the numerical comparison task is primarily due to more accurate representations of numbers with the hypothesis that performance dependent on decision-making factors. We present data from two behavioral experiments and a mathematical model. Taken together, results suggest that individual variation in numerical comparison performance is not predicted by variation in the precision of participants’ numerical value representation.

Exploring the Boundaries of the Number–Temporal Order Association

2015 ◽  
Vol 62 (3) ◽  
pp. 198-205 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Embodied Cognition ◽  
Mental Representation ◽  
Temporal Order ◽  
Past Research ◽  
Numerical Comparison ◽  
Negative Number ◽  
Comparison Task ◽  
Negative Numbers ◽  
The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

scholarly journals Numerical Comparisons and Sex-Related Brain Connectivity

2021 ◽  
Vol 13 (2) ◽  
pp. 62
Author(s):  
Fabiola R. Gómez-Velázquez ◽  
Andrés A. González-Garrido ◽  
Ricardo A. Salido-Ruiz ◽  
Sulema Torres-Ramos ◽  
Aurora Espinoza-Valdez ◽  
...  
Keyword(s):  
Brain Connectivity ◽  
Cognitive Strategies ◽  
Numerical Comparison ◽  
Math Learning ◽  
Comparison Task ◽  
Behavioral Measures ◽  
Functional Brain ◽  
Progressive Development ◽  
Interhemispheric Connectivity ◽  
Number Comparison

Despite the recent literature on sex-related anatomic, maturational and functional brain differences, the study of significant individual developments in math learning and achievement has scarcely approached this perspective. We aimed to compare the influence of sex in functional brain connectivity and behavioral measures in a numerical comparison task. Therefore, a group of school children with ages from 8 to 11 years old was evaluated during a number comparison task. Even though the behavioral performance was similar across the sexes, males distinctly showed a significant correlation between their math WRAT-4 scores and the number of correct responses in the experimental task and working memory scores. Besides, the analysis of the concurrent EEG during task performance showed that males comparatively had a greater brain left intra-hemispheric connectivity, as well as greater interhemispheric connectivity, particularly in Theta and Alpha bands during task performing -as compared to resting-. In contrast, females showed a significantly different decrement of brain connectivity in the Alpha band from resting to task performing. Present results are interpreted as probably reflecting sex-related maturational dissimilarities in neurodevelopment, along with the progressive development of more efficient cognitive strategies, processes running not necessarily parallel in both sexes. 

scholarly journals Numerical cognition in action: Reaching behavior reveals numerical distance effects in 5- to 6-year-olds

2018 ◽  
Vol 4 (2) ◽  
pp. 286-296 ◽  
Author(s):  
Christopher D. Erb ◽  
Jeff Moher ◽  
Joo-Hyun Song ◽  
David M. Sobel
Keyword(s):  
Spatial Representation ◽  
Numerical Cognition ◽  
Spatial Information ◽  
Numerical Comparison ◽  
Digital Display ◽  
Numerical Distance ◽  
Tight Coupling ◽  
Comparison Task ◽  
The Right ◽  
Trial Participants

This study investigates how children’s numerical cognition is reflected in their unfolding actions. Five- and 6-year-olds (N = 34) completed a numerical comparison task by reaching to touch one of three rectangles arranged horizontally on a digital display. A number from 1 to 9 appeared in the center rectangle on each trial. Participants were instructed to touch the left rectangle for numbers 1-4, the center rectangle for 5, and the right rectangle for 6-9. Reach trajectories were more curved toward the center rectangle for numbers closer to 5 (e.g., 4) than numbers further from 5 (e.g., 1). This finding indicates that a tight coupling exists between numerical and spatial information in children’s cognition and action as early as the preschool years. In addition to shedding new light on the spatial representation of numbers during childhood, our results highlight the promise of incorporating measures of manual dynamics into developmental research.

scholarly journals Increasing entropy reduces perceived numerosity throughout the lifespan

2021 ◽  
Author(s):  
Chuyan Qu ◽  
Nicholas K. DeWind ◽  
Elizabeth Brannon
Keyword(s):  
Information Processing ◽  
Developmental Trajectory ◽  
Numerical Comparison ◽  
Systematic Bias ◽  
Rational Model ◽  
Comparison Task ◽  
Information Theoretic ◽  
Entropy Effect ◽  
Numerosity Perception ◽  
Visual Number

Illusions that arise from systematic bias in perceiving numerosity serve as a powerful window into the mechanisms supporting our visual number sense. Recent research has shown that similarly oriented elements appear more numerous than randomly oriented elements in an array. However, this coherence illusion is not predicted by dominant models of numerosity perception. Here we examine whether the orientation coherence illusion is a more general byproduct of the effect of entropy on numerical information processing. Participants engaged in an ordinal numerical comparison task where the color entropy of arrays was manipulated. We found that homogenously colored arrays were perceived as more numerous than entropic colored arrays (Experiments 1 and 2), suggesting that the coherence illusion on numerosity perception is not specific to a particular visual property (e.g., orientation) but instead that the entropy of visual arrays more generally affects numerical processing. In Experiment 3, we explored the developmental trajectory of the color entropy effect in children aged 5 to 17 and found that the strength of the coherence illusion increases into adulthood, raising intriguing questions as to how perceptual experiences influence the progression of this numerosity illusion. We consider a recently proposed resource-rational model as a framework for understanding the entropy effect on numerosity perception under an information-theoretic perspective.

scholarly journals Quantitative and qualitative differences in the canonical and the reverse distance effect and their selective association with arithmetic and mathematical competencies

2021 ◽  
Author(s):  
Stephan Vogel ◽  
Thomas J. Faulkenberry ◽  
Roland H. Grabner
Keyword(s):  
Standardized Test ◽  
Reaction Times ◽  
Distance Effect ◽  
Numerical Magnitude ◽  
Numerical Comparison ◽  
Central Research ◽  
Comparison Task ◽  
Mathematical Competencies ◽  
Numerical Order ◽  
Underlying Mechanisms

Understanding the relationship between symbolic numerical abilities and individual differences in mathematical competencies has become a central research endeavor in the last years. Evidence on this foundational relationship is often based on two behavioral signatures of numerical magnitude and numerical order processing: the canonical and the reverse distance effect. The former indicates faster reaction times for the comparison of numerals that are far in distance (e.g., 2 8) compared to numerals that are close in distance (e.g., 2 3). The latter indicates faster reaction times for the ordinal judgment of numerals (i.e., are numerals in ascending/descending order) that are close in distance (e.g., 2 3 4) compared to numerals that are far in distance (e.g., 2 4 6). While a substantial body of literature has reported consistent associations between the canonical distance effect and arithmetic abilities, rather inconsistent findings have been found for the reverse distance effect. Here, we tested the hypothesis that estimates of the reverse distance effect show qualitative differences (i.e., not all participants show a reverse distance effect in the expected direction) rather than quantitative differences (i.e., all individuals show a reverse distance effect, but to a different degree), and that inconsistent findings might be a consequence of this variation. We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.e., are three numerals presented in order or not), a paper pencil test of arithmetic fluency, as well as a standardized test to assess more complex forms of mathematical competencies. We found discriminatory evidence for the two distance effects. While estimates of the canonical distance effect showed quantitative differences, estimates of the reverse distance effect showed qualitative differences. Comparisons between individuals who demonstrated an effect and individuals who demonstrated no reverse distance effect confirmed a significant moderation on the correlation with mathematical abilities. Significantly larger effects were found in the group who showed an effect. These findings confirm that estimates of the reverse distance effect are subject to qualitative differences and that we need to better characterize the underlying mechanisms/strategies that might lead to these qualitative differences.

scholarly journals Neural coding partially accounts for the relation between children’s number line estimation and numerical comparison performance

2018 ◽  
Author(s):  
Richard Prather
Keyword(s):  
Neural Coding ◽  
Standardized Test ◽  
Number System ◽  
Number Line ◽  
Standardized Test Scores ◽  
Numerical Comparison ◽  
Comparison Task ◽  
Mathematics Interventions ◽  
Number Line Estimation ◽  
Number Perception

Numerical comparison is a primary measure of the acuity of children’s approximate number system (ANS). ANS acuity is associated with key developmental outcomes such as symbolic number skill, standardized test scores and even employment outcomes(Halberda, Mazzocco, & Feigenson, 2008; Parsons & Bynner, 1997). We examine the relation between children’s performance on the numerical comparison task and the number line estimation task. It is important to characterize the relation between tasks in order to develop mathematics interventions that lead to transfer across tasks. We find that number line performance is significantly predicted by non-symbolic comparison performance for participants ranging in age from 5 to 8 years. We also evaluate, using a computational model, if the relation between the two tasks can be adequately explained based on known neural correlates of number perception. Data from humans and non-human primates characterizes neural activity corresponding to the perception of numerosities. Results of behavioral experimentation and computational modeling suggest that though neural coding of number predicts a correlation in participants’ performance on the two tasks, it cannot account for all of the variability in the human data. This is interpreted as consistent with accounts of number line estimation in which number line estimation does not rely solely on participants’ numerical perception.

scholarly journals Predicting Numerical Comparison using Neural Networks and Electrophysiological Data

2018 ◽  
Author(s):  
Richard Prather ◽  
Sara Heverly-Fitt
Keyword(s):  
Neural Networks ◽  
Numerical Comparison ◽  
Model Design ◽  
Comparison Task ◽  
Cognitive Interventions ◽  
Electrophysiological Data ◽  
Individual Trial ◽  
The Individual ◽  
Current Paradigm ◽  
Independent Model

The effectiveness of cognitive interventions is dependent on researchers’ ability to predict individual participants’ behavior. In this study we present a novel computational model design that uses both behavioral and electrophysiological input to predict participants’ behavior the numerical comparison task. We focus on the numerical comparison task as performance on this task is used for the Numeracy construct which predicts important mathematical outcomes. We model participants’ behavior using independent model instantiations that are optimized for each participant using an evolutionary algorithm. We demonstrate that the use of electrophysiological data, at the individual trial level, can significantly improve the model's accuracy. We discuss both the potential and limitations of the current paradigm in developing training regimens for children with early math difficulty.

scholarly journals Policies or knowledge: priors differ between a perceptual and sensorimotor task

2019 ◽  
Vol 121 (6) ◽  
pp. 2267-2275 ◽  
Author(s):  
Claire Chambers ◽  
Hugo Fernandes ◽  
Konrad Paul Kording
Keyword(s):  
Probability Distributions ◽  
Perceptual Task ◽  
Comparison Task ◽  
Estimation Task ◽  
Model And Simulation ◽  
Simulation Based ◽  
Central Tenet ◽  
Internal States ◽  
Perceptual Comparison ◽  
The Brain

If the brain abstractly represents probability distributions as knowledge, then the modality of a decision, e.g., movement vs. perception, should not matter. If, on the other hand, learned representations are policies, they may be specific to the task where learning takes place. Here, we test this by asking whether a learned spatial prior generalizes from a sensorimotor estimation task to a two-alternative-forced choice (2-Afc) perceptual comparison task. A model and simulation-based analysis revealed that while participants learn prior distribution in the sensorimotor estimation task, measured priors are consistently broader than sensorimotor priors in the 2-Afc task. That the prior does not fully generalize suggests that sensorimotor priors are more like policies than knowledge. In disagreement with standard Bayesian thought, the modality of the decision has a strong influence on the implied prior distributions. NEW & NOTEWORTHY We do not know whether the brain represents abstract and generalizable knowledge or task-specific policies that map internal states to actions. We find that learning in a sensorimotor task does not generalize strongly to a perceptual task, suggesting that humans learned policies and did not truly acquire knowledge. Priors differ across tasks, thus casting doubt on the central tenet of many Bayesian models, that the brain’s representation of the world is built on generalizable knowledge.

Numerical Processing and Executive Functioning in Early Versus Middle Childhood: A Japanese Sample

2018 ◽  
Vol 125 (6) ◽  
pp. 1029-1054
Author(s):  
Kazufumi Omura ◽  
Shinya Matsuta
Keyword(s):  
Executive Functioning ◽  
Middle Childhood ◽  
Sixth Graders ◽  
Second Graders ◽  
Numerical Comparison ◽  
Control Mechanisms ◽  
Numerical Distance ◽  
Comparison Task ◽  
Numerical Processing ◽  
Age Related

Many previous studies have investigated developmental differences in numerical processing by manipulating numerical distance and physical size in a number sequence. While it has been theorized that children's maturity level in executive functioning affects their numerical processing, the interaction between numerical processing and executive functioning through development remains unclear. We divided 60 Japanese school children, aged 8–12 years, into three age-related groups (second graders, fourth graders, and sixth graders) and had them perform physical and numerical comparison Stroop tasks. In the physical comparison task, the numerical Stroop effect (i.e., automatic numerical processing) was evident in each group, but, in the numerical comparison task, the numerical distance effect (i.e., intentional numerical processing) was evident in each group. Also, in the numerical comparison task, the size congruity effect (an index of the attentional and inhibitory control mechanisms of executive functioning) was more salient among second graders than among fourth or sixth graders. These results suggest that numerical processing matures and then plateaus just before primary school, while executive functioning continues to develop. Thus, these data provide evidence of a developmental dissociation between numerical processing and executive functioning.

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