scholarly journals Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects

2018 ◽  
Vol 9 ◽  
Author(s):  
Attila Krajcsi ◽  
Gábor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effects ◽  
Number System ◽  
Numerical Distance ◽  
Number Comparison ◽  
Symbolic Number

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 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.

Response-Selection-Related Parietal Activation during Number Comparison

2004 ◽  
Vol 16 (9) ◽  
pp. 1536-1551 ◽  
Author(s):  
Silke M. Göbel ◽  
Heidi Johansen-Berg ◽  
Tim Behrens ◽  
Matthew F. S. Rushworth
Keyword(s):  
Nonhuman Primates ◽  
Response Selection ◽  
Perceptual Task ◽  
Numerical Distance ◽  
Single Digit ◽  
Selection Processes ◽  
Number Comparison ◽  
Basic Stimulus ◽  
The Right ◽  
Double Digit

Neuroimaging studies of number comparison have consistently found activation in the intraparietal sulcus (IPS). Recently, it has been suggested that activations in the IPS vary with the distance between the numbers being compared. In number comparison, the smaller the distance between a number and the reference the longer the reaction time (RT). Activations in the right or left IPS, however, have also been related to attentional and intentional selection. It is possible, therefore, that activity in this region is a reflection of the more basic stimulus and response-selection processes associated with changes in RT. This fMRI experiment investigated the effect of numerical distance independently from RT. In addition, activations during number comparison of single-digit and double-digit stimuli were compared. During number comparison blocks, subjects had to indicate whether digits were greater or smaller than a reference (5 or 65). In control blocks, they were asked to perform a perceptual task (vertical line present/absent) on either numerical or nonnumerical stimuli. Number comparison versus rest yielded a large bilateral parietal-posterior frontal network. However, no areas showed more activation during number comparison than during the control tasks. Furthermore, no areas were more active during comparison of numbers separated by a small distance than comparisons of those separated by a large distance or vice versa. A left-lateralized parietal-posterior frontal network varied significantly with RT. Our findings suggest that magnitude and numerical-distance-related IPS activations might be difficult to separate from fundamental stimulus and response-selection processes associated with RT changes. As is the case with other parameters, such as space, magnitude may be represented in the context of response selection in the parietal cortex. In this respect, the representation of magnitude in the human IPS may be similar to the representation of magnitude in other nonhuman primates.

The Approximate Number System is not Predictive for Symbolic Number Processing in Kindergarteners

2014 ◽  
Vol 67 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Delphine Sasanguie ◽  
Emmy Defever ◽  
Bieke Maertens ◽  
Bert Reynvoet
Keyword(s):  
Number System ◽  
Number Processing ◽  
Approximate Number System ◽  
Symbolic Number

scholarly journals The relationship between non-verbal systems of number and counting development: a neural signatures approach

2017 ◽  
Author(s):  
Daniel C. Hyde ◽  
Ilaria Berteletti ◽  
Yi Mou
Keyword(s):  
Individual Differences ◽  
Event Related Potentials ◽  
Number System ◽  
Attentional Processing ◽  
Initial Development ◽  
Related Potentials ◽  
And Mathematics ◽  
Pi System ◽  
Symbolic Number ◽  
Neural Signatures

Two non-verbal cognitive systems, an approximate number system (ANS) for extracting thenumerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here we used an individual differences approach to test for a relationship between the spontaneously evoked brain signatures (using event-related potentials) of PI and the ANS and initial development of symbolic number concepts in preschool children as displayed by counting. We observed that individual differences in the neural signatures of the PI system, but not the ANS, explained a unique portion of variance in counting proficiency after extensively controlling for general cognitive factors. These results suggest that differences in early attentional processing of objects between children are related to higher-level symbolic number concept development.

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