scholarly journals Symbolic number comparison is not processed by the analogue number system: different symbolic and nonsymbolic numerical distance and size effects

2017 ◽  
Author(s):  
Attila Krajcsi ◽  
Gabor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effects ◽  
Goodness Of Fit ◽  
Numerical Cognition ◽  
Reaction Times ◽  
Number System ◽  
Error Rates ◽  
Numerical Distance ◽  
Comparison Task ◽  
Number Comparison ◽  
Symbolic Number

Dominant numerical cognition models suppose that both symbolic and nonsymbolic numbers are processed by the Analogue Number System (ANS) working according to Weber’s law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and nonsymbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times and diffusion model drift rates were systematically analyzed in both nonsymbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model’s prediction is relatively good for the nonsymbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only nonsymbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia

2010 ◽  
Vol 22 (5) ◽  
pp. 860-874 ◽  
Author(s):  
Christophe Mussolin ◽  
Anne De Volder ◽  
Cécile Grandin ◽  
Xavier Schlögel ◽  
Marie-Cécile Nassogne ◽  
...  
Keyword(s):  
Number Processing ◽  
Numerical Distance ◽  
Comparison Task ◽  
Developmental Dyscalculia ◽  
Disability History ◽  
Magnitude Processing ◽  
Number Magnitude ◽  
Number Comparison ◽  
The Right ◽  
Symbolic Number

Developmental dyscalculia (DD) is a deficit in number processing and arithmetic that affects 3–6% of schoolchildren. The goal of the present study was to analyze cerebral bases of DD related to symbolic number processing. Children with DD aged 9–11 years and matched children with no learning disability history were investigated using fMRI. The two groups of children were controlled for general cognitive factors, such as working memory, reading abilities, or IQ. Brain activations were measured during a number comparison task on pairs of Arabic numerals and a color comparison task on pairs of nonnumerical symbols. In each task, pairs of stimuli that were close or far on the relevant dimension were constituted. Brain activation in bilateral intraparietal sulcus (IPS) was modulated by numerical distance in controls but not in children with DD. Moreover, although the right IPS responded to numerical distance only, the left IPS was influenced by both numerical and color distances in control children. Our findings suggest that dyscalculia is associated with impairment in areas involved in number magnitude processing and, to a lesser extent, in areas dedicated to domain-general magnitude processing.

scholarly journals Processing symbolic numbers: The example of distance and size effects

2020 ◽  
Author(s):  
Attila Krajcsi ◽  
Petia Kojouharova ◽  
Gabor Lengyel
Keyword(s):  
Size Effects ◽  
Alternative Model ◽  
Numerical Cognition ◽  
Number System ◽  
Approximate Number System ◽  
Comparison Task ◽  
Semantic System ◽  
Simple Representation

According to the dominant view in the literature, several numerical cognition phenomena are explained coherently and parsimoniously by the Approximate Number System (ANS) model, which model supposes an evolutionarily old, simple representation behind many numerical tasks. We offer an alternative model, the Discrete Semantic System (DSS) to explain the same phenomena in symbolic numerical tasks. Our alternative model supposes that symbolic numbers are stored in a network of nodes, similar to conceptual or linguistic networks. The benefit of the DSS model is demonstrated through the example of distance and size effects of comparison task.

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.

Mental Representations in Fraction Comparison

2011 ◽  
Vol 58 (6) ◽  
pp. 480-489 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Benton H. Pierce
Keyword(s):  
Mental Representations ◽  
Reaction Times ◽  
Cross Product ◽  
Numerical Distance ◽  
Regression Analyses ◽  
Problem Size ◽  
Comparison Task ◽  
Strategy Types ◽  
Problem Size Effect ◽  
Fraction Comparison

In this study, we investigated the mental representations used in a fraction comparison task. Adults were asked to quickly and accurately pick the larger of two fractions presented on a computer screen and provide trial-by-trial reports of the types of strategies they used. We found that adults used a variety of strategies to compare fractions, ranging among just knowing the answer, using holistic knowledge of fractions to determine the answer, and using component-based procedures such as cross multiplication. Across all strategy types, regression analyses identified that reaction times were significantly predicted by numerical distance between fractions, indicating that the participants used a magnitude-based representation to compare the fraction magnitudes. In addition, a variant of the problem-size effect (e.g., Ashcraft, 1992) appeared, whereby reaction times were significantly predicted by the average cross product of the two fractions. This effect was primarily found for component-based strategies, indicating a role for strategy choice in the formation of mental representations of fractions.

scholarly journals The Source of the Symbolic Numerical Distance and Size Effects

2016 ◽  
Author(s):  
Attila Krajcsi ◽  
Gábor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Mathematical Knowledge ◽  
Semantic Network ◽  
Number System ◽  
Numerical Distance ◽  
Alternative Account ◽  
Semantic System ◽  
Alternative Approach ◽  
Conceptual Network

Human number understanding is thought to rely on the analogue number system (ANS), working according to Weber’s law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect.

Neuronal Correlates of Non-verbal Numerical Competence in Primates

2014 ◽  
Author(s):  
Andreas Nieder
Keyword(s):  
Numerical Cognition ◽  
Numerical Distance ◽  
Numerical Competence ◽  
Tuning Curves ◽  
Set Size ◽  
The Past ◽  
Neuronal Mechanisms ◽  
Semantic Associations ◽  
The Brain ◽  
Symbolic Number

Non-verbal numerical competence, such as the estimation of set size, is rooted in biological primitives that can also be explored in animals. Over the past years, the anatomical substrates and neuronal mechanisms of numerical cognition in primates have been unravelled down to the level of single neurons. Studies with behaviourally-trained monkeys have identified a parietofrontal network of individual neurons selectively tuned to the number of items (cardinal aspect) or the rank of items in a sequence (ordinal aspect). The properties of these neurons’ numerosity tuning curves can explain fundamental psychophysical phenomena, such as the numerical distance and size effect. Functionally overlapping groups of parietal neurons represent not only numerable-discrete quantity (numerosity), but also innumerable-continuous quantity (extent) and relations between quantities (proportions), supporting the idea of a generalized magnitude system in the brain. Moreover, many neurons in the prefrontal cortex establish semantic associations between signs and abstract numerical categories, a neuronal precursor mechanisms that may ultimately give rise to symbolic number processing in humans. These studies establish putative homologies between the monkey and human brain, and demonstrate the suitability of non-human primates as model system to explore the neurobiological roots of the brain’s non-verbal quantification system, which may constitute the phylogenetic and ontogenetic foundation of all further, more elaborate numerical skills in humans.

The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method

1996 ◽  
Vol 8 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Stanislas Dehaene
Keyword(s):  
Cognitive Task ◽  
Reaction Times ◽  
Event Related Potentials ◽  
Normal Subjects ◽  
Imaging Data ◽  
Comparison Task ◽  
Cerebral Lateralization ◽  
Magnitude Comparison ◽  
Number Comparison ◽  
Related Potentials

Measuring reaction times (RTs) using the additive-factors method provides information about the sequence of processing stages in a cognitive task. Here, I describe how the simultaneous recording of event-related potentials (ERPs) in the same task can provide complementary information that cannot be obtained using RTs alone. Most notably, ERP data can reveal the absolute activation time and the coarse brain localization of processing stages. RTs and ERPs can also be used to cross-validate a serial-stage model. These notions were applied to a study of the temporal unfolding of brain activations in a number comparison task. ERPs were recorded from 64 scalp electrodes while normal subjects classified numbers as larger or smaller than 5. Specific scalp signatures and timing data were obtained for stages of word and digit identification, magnitude comparison, response programming, and error capture and correction. The observed localizations were compatible with previous neuropsychological and brain imaging data and provided new insights into the cerebral lateralization and timing of number processing.

scholarly journals Conducting Web-based experiments for numerical cognition research

2019 ◽  
Author(s):  
Arnold Kochari
Keyword(s):  
Data Collection ◽  
Numerical Cognition ◽  
Time Windows ◽  
Reaction Times ◽  
Distance Effect ◽  
Masked Priming ◽  
Error Rates ◽  
Web Browser ◽  
Web Based ◽  
Replication Studies

[This is a postprint/accepted version of the manuscript. The manuscript has been published in Journal of Cognition.] It is becoming increasingly popular and straightforward to collect data in cognitive psychology through web-based studies. In this paper, I review issues around web-based data collection for the purpose of numerical cognition research. Provided that the desired type of data can be collected through a web-browser, such online studies offer numerous advantages over traditional forms of physical lab-based data collection, such as gathering data from larger sample sizes in shorter time-windows and easier access to non-local populations. I then present results of two replication studies that employ classical paradigms in numerical cognition research: the number–size congruity paradigm and comparison to a given standard, which also included a masked priming manipulation. In both replications, reaction times and error rates were comparable to original, physical lab-based studies. Consistent with the results of original studies, a distance effect, a congruity effect, and a priming effect were observed. Data collected online thus offers a level of reliability comparable to data collected in a physical lab when it comes to questions in numerical cognition.

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