scholarly journals Developmental Continuity in the Link Between Sensitivity to Numerosity and Physical Size

2015 ◽  
Vol 1 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Ariel Starr ◽  
Elizabeth M. Brannon
Keyword(s):  
Individual Differences ◽  
Weber Fraction ◽  
Number Line ◽  
Line Length ◽  
Stimulus Dimension ◽  
Significant Relation ◽  
General Representation ◽  
Physical Size ◽  
Magnitude Comparison ◽  
Developmental Continuity

Converging evidence suggests that representations of number, space, and other dimensions depend on a general representation of magnitude. However, it is unclear whether there exists a privileged relation between certain magnitude dimensions or if all continuous magnitudes are equivalently related. Four-year-old children and adults were tested with three magnitude comparison tasks – nonsymbolic number, line length, and luminance – to determine whether individual differences in sensitivity are stable across dimensions. A Weber fraction (w) was calculated for each participant in each stimulus dimension. For both children and adults, accuracy and w values for number and line length comparison were significantly correlated, whereas neither accuracy nor w was correlated for number and luminance comparison. However, although line length and luminance comparison performance were not correlated in children, there was a significant relation in adults. These results suggest that there is a privileged relation between number and line length that emerges early in development and that relations between other magnitude dimensions may be later constructed over the course of development.

scholarly journals Numerosity representations in crows obey the Weber–Fechner law

2016 ◽  
Vol 283 (1827) ◽  
pp. 20160083 ◽  
Author(s):  
Helen M. Ditz ◽  
Andreas Nieder
Keyword(s):  
Weber Fraction ◽  
Discrimination Performance ◽  
Brain Structures ◽  
Number System ◽  
Number Line ◽  
Just Noticeable Difference ◽  
Match To Sample ◽  
Close Phylogenetic Relationship ◽  
The One ◽  
Numerical Representations

The ability to estimate number is widespread throughout the animal kingdom. Based on the relative close phylogenetic relationship (and thus equivalent brain structures), non-verbal numerical representations in human and non-human primates show almost identical behavioural signatures that obey the Weber–Fechner law. However, whether numerosity discriminations of vertebrates with a very different endbrain organization show the same behavioural signatures remains unknown. Therefore, we tested the numerical discrimination performance of two carrion crows ( Corvus corone ) to a broad range of numerosities from 1 to 30 in a delayed match-to-sample task similar to the one used previously with primates. The crows' discrimination was based on an analogue number system and showed the Weber-fraction signature (i.e. the ‘just noticeable difference’ between numerosity pairs increased in proportion to the numerical magnitudes). The detailed analysis of the performance indicates that numerosity representations in crows are scaled on a logarithmically compressed ‘number line’. Because the same psychophysical characteristics are found in primates, these findings suggest fundamentally similar number representations between primates and birds. This study helps to resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear, and not just in primates, but across vertebrates.

scholarly journals Cognitive mediators of US—China differences in early symbolic arithmetic

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255283
Author(s):  
John E. Opfer ◽  
Dan Kim ◽  
Lisa K. Fazio ◽  
Xinlin Zhou ◽  
Robert S. Siegler
Keyword(s):  
Standardized Tests ◽  
Number Line ◽  
Chinese Children ◽  
Numerical Magnitude ◽  
Magnitude Comparison ◽  
Cognitive Mediators ◽  
Number Line Estimation ◽  
Mathematics Knowledge ◽  
Us Children ◽  
Symbolic Number

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations

2019 ◽  
Vol 46 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Stephanie Morano ◽  
Paul J. Riccomini
Keyword(s):  
Middle School Students ◽  
Effective Area ◽  
Number Line ◽  
Students With Learning Disabilities ◽  
School Students ◽  
National Assessment ◽  
Circular Area ◽  
Magnitude Comparison ◽  
Number Line Estimation

The present study examines the features and quality of visual representations (VRs) created by middle school students with learning disabilities and difficulties in mathematics in response to a released fraction item from the National Assessment of Educational Progress (NAEP). Relations between VR quality and scores on other measures of fraction knowledge are also investigated. Results show that students used circular area models most frequently to represent the NAEP item, but used bar models most accurately. Based on results, bar models may be the most efficient and effective area model VRs for use in fractions instruction. Representation quality was associated with problem-solving accuracy, as well as with performance on fraction number line estimation and fraction magnitude comparison. Implications for practice are discussed.

A Common Representation for Semantic and Physical Properties

2006 ◽  
Vol 53 (2) ◽  
pp. 87-94 ◽  
Author(s):  
Roi Cohen Kadosh ◽  
Avishai Henik
Keyword(s):  
Brain Structure ◽  
Traditional Approach ◽  
Brain Area ◽  
Mutual Interference ◽  
Intraparietal Sulcus ◽  
Physical Size ◽  
Magnitude Comparison ◽  
Common Representation ◽  
Neurophysiological Studies ◽  
Physical Information

This is the first report of a mutual interference between luminance and numerical value in magnitude judgments. Instead of manipulating the physical size of compared numbers, which is the traditional approach in size congruity studies, luminance levels were manipulated. The results yielded the classical congruity effect. Participants took more time to process numerically larger numbers when they were brighter than when they were darker, and more time to process a darker number when its numerical value was smaller than when it was larger. On the basis of neurophysiological studies of magnitude comparison and interference between semantic and physical information, it is proposed that the processing of semantic and physical magnitude information is carried out by a shared brain structure. It is suggested that this brain area, the left intraparietal sulcus, subserves various comparison processes by representing various quantities on an amodal magnitude scale.

scholarly journals Modeling the latent structure of individual differences in the numerical size-congruity effect

2020 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Kristen Bowman
Keyword(s):  
Individual Differences ◽  
Numerical Cognition ◽  
Congruity Effect ◽  
Numerical Magnitude ◽  
Data Sets ◽  
Comparison Task ◽  
Physical Size ◽  
The Individual ◽  
Size Congruity Effect ◽  
Individual Size

When people are asked to choose the physically larger of a pair of numerals, they are often slower when relative physical size is incongruent with numerical magnitude. This size-congruity effect is usually assumed as evidence for automatic activation of numerical magnitude. In this paper, we apply the methods of Haaf and Rouder (2017) to look at the size-congruity effect through the lens of individual differences. Here, we simply ask whether everyone exhibits the effect. We develop a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual size- congruity effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. We then apply this modeling technique to three data sets. In all three data sets, the winning model was one in which the size-congruity effect was constrained to be positive. This indicates that, at least in a physical comparison task with numerals, everyone exhibits a positive size-congruity effect. We discuss these results in the context of measurement fidelity and theory-building in numerical cognition.

Techniques for Assessing Standardization in Artifact Assemblages: Can We Scale Material Variability?

2001 ◽  
Vol 66 (3) ◽  
pp. 493-504 ◽  
Author(s):  
Jelmer W. Eerkens ◽  
Robert L. Bettinger
Keyword(s):  
Coefficient Of Variation ◽  
Visual Inspection ◽  
Weber Fraction ◽  
Line Length ◽  
Statistical Technique ◽  
Random Data ◽  
Length Estimation

The study of artifact standardization is an important line of archaeological inquiry that continues to be plagued by the lack of an independent scale that would indicate what a highly variable or highly standardized assemblage should look like. Related to this problem is the absence of a robust statistical technique for comparing variation between different kinds of assemblages. This paper addresses these issues. The Weber fraction for line-length estimation describes the minimum difference that humans can perceive through unaided visual inspection. This value is used to derive a constant for the coefficient of variation (CV = 1.7 percent) that represents the highest degree of standardization attainable through manual human production of artifacts. Random data are used to define a second constant for the coefficient of variation that represents variation expected when production is random (CV = 57.7 percent). These two constants can be used to assess the degree of standardization in artifact assemblages regardless of kind. Our analysis further demonstrates that CV is an excellent measure of standardization and provides a robust statistical technique for comparing standardization in samples of artifacts.

scholarly journals How the Abstract Becomes Concrete: Irrational Numbers are Understood Relative to Natural Numbers and Perfect Squares

2018 ◽  
Author(s):  
Purav Patel
Keyword(s):  
Teaching And Learning ◽  
Number System ◽  
Number Line ◽  
Natural Numbers ◽  
Comparison Task ◽  
Irrational Numbers ◽  
Magnitude Comparison ◽  
Number Systems ◽  
Number Line Estimation ◽  
Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root of 2, is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers – specifically, the radicands of radical expressions – as natural numbers. Strategy self-reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task-specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.

scholarly journals Occipitotemporal Representations Reflect Individual Differences in Conceptual Knowledge

2018 ◽  
Author(s):  
K. Braunlich ◽  
B. C. Love
Keyword(s):  
Decision Making ◽  
Individual Differences ◽  
Conceptual Knowledge ◽  
Irrelevant Stimulus ◽  
Stimulus Dimension ◽  
Association Cortex ◽  
Categorization Theory ◽  
Representational Space ◽  
Stimulus Features ◽  
Attentional Weight

AbstractThrough selective attention, decision-makers can learn to ignore behaviorally-irrelevant stimulus dimensions. This can improve learning and increase the perceptual discriminability of relevant stimulus information. To account for this effect, popular contemporary cognitive models of categorization typically include of attentional parameters, which provide information about the importance of each stimulus dimension in decision-making. The effect of these parameters on psychological representation is often described geometrically, such that perceptual differences over relevant psychological dimensions are accentuated (or stretched), and differences over irrelevant dimensions are down-weighted (or compressed). In sensory and association cortex, representations of stimulus features are known to covary with their behavioral relevance. Although this implies that neural representational space might closely resemble that hypothesized by formal categorization theory, to date, attentional effects in the brain have been demonstrated through powerful experimental manipulations (e.g., contrasts between relevant and irrelevant features). This approach sidesteps the role of idiosyncratic conceptual knowledge in guiding attention to useful information sources. To bridge this divide, we used formal categorization models, which were fit to behavioral data, to make inferences about the concepts and strategies used by individual participants during decision-making. We found that when greater attentional weight was devoted to a particular visual feature (e.g., “color”), its value (e.g., “red”) was more accurately decoded from occipitotemporal cortex. We additionally found that this effect was sufficiently sensitive to reflect individual differences in conceptual knowledge. The results indicate that occipitotemporal stimulus representations are embedded within a space closely resembling that proposed by classic categorization models.

Sign in / Sign up

Export Citation Format

Share Document