The Number Sense: How the Mind Creates Mathematics.

Hersh, Reuben; Dehaene, Stanislas

doi:10.2307/2589308

Cited by 132 publications

(218 citation statements)

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“…fMR-A research using numerical stimuli has for the most part converged on the finding that the IPS shows a signal recovery effect that is dependent on numerical ratio (Holloway et al, 2013;Notebaert et al, 2010;Piazza, Pinel, Le Bihan, & Dehaene, 2007;Vogel et al, 2015;Vogel, Goffin, et al, 2017). This ratio-dependent neural rebound effect has been suggested to result from the mapping of the symbolic numerical system onto a noisy, analog system of magnitude representation, called the approximate number system (ANS; Dehaene, 1997). In this ANS account of number representation, number magnitudes are represented on a mental number line in an analog fashion, and symbolic numbers are mapped onto this noisy magnitude system (Dehaene, 1997).…”

Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

“…This ratio-dependent neural rebound effect has been suggested to result from the mapping of the symbolic numerical system onto a noisy, analog system of magnitude representation, called the approximate number system (ANS; Dehaene, 1997). In this ANS account of number representation, number magnitudes are represented on a mental number line in an analog fashion, and symbolic numbers are mapped onto this noisy magnitude system (Dehaene, 1997).…”

Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

“…Each numerical quantity on this number line is hypothesized to be associated with a distribution of representational uncertainty (e.g., the representation of four also includes that of three and two) around the precise location of the number quantity, resulting in an analog representation of numerical magnitude (Dehaene, 1997). When people are asked to compare two numbers, this analog system of representing number results in a characteristic behavioral signature: the numerical distance effect (NDE; Moyer & Landauer, 1967).…”

Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

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A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study

Goffin

Vogel

Slipenkyj

et al. 2019

Human Brain Mapping

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How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI‐A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio‐dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI‐A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance‐dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers > letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI‐A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain.

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Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

Section: Functional Magnetic Resonance Adaptation and Symbolic Numementioning

confidence: 99%

See 1 more Smart Citation

A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study

Goffin

Vogel

Slipenkyj

et al. 2019

Human Brain Mapping

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“…Dyscalculia is characterized by impaired non-symbolic and symbolic numerical processing, the ability to quickly estimate and manipulate numerical magnitudes and quickly perform mental operations without writing out procedures (63) or relying on verbally-based strategies such as counting (64,65). The most popular view of mathematical cognition, and consequently of math disabilities [i.e., Triple Code Model; (66,67)], entail that all development of symbolic number skills derive (through alternative format re-coding), and are ultimately grounded on the innate endowed ability of "number sense." Accordingly, humans would form mental representations of numerical quantities using a mental number line, an imaginary line of numbers ordered in an ascending series.…”

Section: The Cognitive Profile Of Mathematical Disability and Dyscalcmentioning

confidence: 99%

From Schools to Scans: A Neuroeducational Approach to Comorbid Math and Reading Disabilities

Grant

Siegel

2020

Front. Public Health

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We bridge two analogous concepts of comorbidity, dyslexia-dyscalculia and reading-mathematical disabilities, in neuroscience and education, respectively. We assessed the cognitive profiles of 360 individuals (mean age 25.79 ± 13.65) with disability in reading alone (RD group), mathematics alone (MD group) and both (comorbidity: MDRD group), with tests widely used in both psychoeducational and neuropsychological batteries. As expected, the MDRD group exhibited reading deficits like those shown by the RD group. The former group also exhibited deficits in quantitative reasoning like those shown by the MD group. However, other deficits related to verbal working memory and semantic memory were exclusive to the MDRD group. These findings were independent of gender, age, or socioeconomic and demographic factors. Through a systematic exhaustive review of clinical neuroimaging literature, we mapped the resulting cognitive profiles to correspondingly plausible neuroanatomical substrates of dyslexia and dyscalculia. In our resulting "probing" model, the complex set of domain-specific and domain-general impairments shown in the comorbidity of reading and mathematical disabilities are hypothesized as being related to atypical development of the left angular gyrus. The present neuroeducational approach bridges a long-standing transdisciplinary divide and contributes a step further toward improved early prediction, teaching and interventions for children and adults with combined reading and math disabilities.

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“…Performance with nonsymbolic quantities in terms of accuracy and reaction times is dependent on the ratio between the two quantities to be compared such that larger ratios (i.e., larger relative difference in magnitude) lead to faster and more accurate responses than smaller ratios (i.e., smaller relative difference in magnitude; e.g., Buckley & Gillman, 1974;Feigenson, Dehaene, & Spelke, 2004;Halberda & Feigenson, 2008;Pica, Lemer, Izard, & Dehaene, 2004; this is consistent with Weber's law, see e.g., Bar, Fischer, & Algom, 2019 for a recent discussion). Such performance has been suggested to reflect the operation of the so-called Approximate Number System (ANS) which is thought to be an evolutionary old system shared with other animals (Barth, Kanwisher, & Spelke, 2003;Dehaene, 1997;Feigenson et al, 2004;Gallistel & Gelman, 2000;Halberda & Feigenson, 2008). Numerical magnitude representations in ANS are thought to be continuous (or analog) distributions around a point (similar to a Gaussian distribution) which overlap with neighboring distributions.…”

Section: Generalized Analog Magnitude Representation Systemmentioning

confidence: 99%

Processing symbolic magnitude information conveyed by number words and by scalar adjectives

Kochari¹

2020

Preprint

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Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like ‘big’, ‘long’, ‘loud’, etc. which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalized magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N=150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N=149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning. In the size congruity paradigm we observed interference between the processing of the numerical value of number words and the meaning of scalar adjectives, on the one hand, and physical (font-) size, on the other had, when participants had to judge the number words or the adjectives (while ignoring physical size). No interference was obtained for the reverse situation, i.e. when participants judged the physical font size (while ignoring numerical value or meaning). The results of the same/different task for both number words and scalar adjectives strongly suggested that the interference that was observed in the size congruity paradigm was likely due to a response conflict at the decision stage of processing rather than due to the recruitment of GMS representations. Taken together, it can be concluded that the size congruity paradigm does not provide evidence in support the hypothesis that GMS representations are used in the processing of number words or scalar adjectives. Nonetheless, the hypothesis we put forward about scalar adjectives is still is a promising potential line of research. We make a number of suggestions for how this hypothesis can be explored in future studies.

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The Number Sense: How the Mind Creates Mathematics.

Cited by 132 publications

References 0 publications

A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study

A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study

From Schools to Scans: A Neuroeducational Approach to Comorbid Math and Reading Disabilities

Processing symbolic magnitude information conveyed by number words and by scalar adjectives

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