Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

Kadosh, Roi Cohen; Lammertyn, Jan; Izard, Véronique

doi:10.1016/j.pneurobio.2007.11.001

Cited by 339 publications

(353 citation statements)

References 153 publications

(182 reference statements)

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“…Current theories of dyscalculia include specific deficits of the ANS, that is, imprecise representations of nonsymbolic number (18), or specific deficits in mapping symbols to nonsymbolic number representations (68). These and other theories (17) have been silent about how nonsymbolic magnitudes other than number are represented in the brains of children and adults, and by extension, how a system of general magnitude representation, which includes nonnumerical magnitudes such as spatial extent and duration (69)(70)(71), might interface with learning and competence across different types of mathematical problem solving. Dyscalculia and other math-related disorders such as acalculia are heterogeneous in their symptomatology (15,72).…”

Section: Discussionmentioning

confidence: 99%

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

Lourenco

Bonny

Fernandez

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

186

163

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Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude.analog magnitude | Weber's law | estimation | nonsymbolic magnitude precision | mathematical cognition H ow do humans come to understand mathematics? A common view is that the mental capacity for formal mathwhich includes access to symbolic notations of number, knowledge of quantitative concepts, and the implementation of computational operations-builds on a set of core abilities such as an intuitive, nonverbal sense of numerosity (1-5). Also known as the approximate number system (ANS), this nonsymbolic sense of numerical magnitude is shared with nonhuman animals (6) and is widespread across cultures (7). Unlike the acquisition of symbolic number (e.g., Arabic digits) and formal math concepts, which are learned via explicit instruction and allow for exact quantification, the ANS may be innate (8) and is characteristically "noisy," with variance increasing linearly as a function of the absolute numerical value (9). This imprecision can be modeled as overlapping Gaussian distributions along an internal continuum (10) and is captured by Weber's law, which holds that subjective differences in intensity are proportional to the objective ratios between values. When people compare numerical values under conditions that prevent counting or that do not...

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Section: Discussionmentioning

confidence: 99%

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

Lourenco

Bonny

Fernandez

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

186

163

View full text Add to dashboard Cite

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“…Indeed, functional neuroimaging reveals that representations of these dimensions engage overlapping or neighboring regions of posterior parietal cortex (Cohen Kadosh et al, 2005, 2007; V. Dormal, Dormal, Joassin, & Pesenti, 2011;Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003). These findings provide mechanistic support for the many studies that have documented behavioral and neurological links between representations of space, time, and number (Allman, Pelphrey, & Meck, 2012;Cantlon et al, 2009;Cohen Kadosh, Lammertyn, & Izard, 2008;Feigenson, 2007;Hubbard et al, 2005;Walsh, 2003). However, implicit in ATOM is the idea that the links between different dimensions should be symmetrical.…”

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confidence: 93%

Visuospatial working memory influences the interaction between space and time

Starr

Brannon

2016

Psychon Bull Rev

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How do representations of space inform our perception of time? In language, spatial vocabulary is frequently used to describe temporal concepts, and spatial information biases temporal perception even in non-verbal tasks. In contrast, temporal information typically exerts little, if any, influence on the perception of spatial extent. Here, we used spatial and temporal reproduction tasks, both with and without verbal and spatial dual tasks, to investigate the mechanism underlying the asymmetric relation between space and time. Specifically, we tested whether the asymmetric interference between spatial and temporal stimulus attributes arises from interference in verbal or visuospatial working memory. We found that loading visuospatial working memory, but not verbal working memory, eliminated the asymmetric pattern of interference. This suggests that the interference between spatial and temporal representations arises due to processing constraints in visuospatial working memory. These findings are discussed in terms of the load theory of attention and the relative automaticity with which spatial and temporal information is processed.

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“…First, patients with parietal lesions consistently show selective impairments in numerical skills (e.g., Dehaene and Cohen, 1997;Denes and Signorini, 2001;Grafman et al, 1982;Takayama et al, 1994;Warrington, 1982;Zorzi et al, 2002), whereas patients with lesions to other brain regions showed preservation of numerical skills (e.g., Butterworth et al, 2001;Cappelletti et al, 2001Cappelletti et al, , 2002Cappelletti et al, , 2005Crutch and Warrington, 2002;Diesfeldt, 1993;Jefferies et al, 2004Jefferies et al, , 2005Lemer et al, 2003;Zamarian et al, 2006). Second, functional MRI studies have systematically shown that numerical processing elicits greater activation in the parietal lobule than does nonnumerical processing (e.g., Ansari et al, 2006;Cappelletti et al, 2010;Eger et al, 2003;Knops et al, 2006;Le Clec'H et al, 2000;Piazza et al, 2004;Thioux et al, 2005;Zago et al, 2008; but see Göbel et al, 2004;Kadosh et al, 2008;Shuman and Kanwisher, 2004). Third, developmental dyscalculia has also been showed to be associated with structural abnormalities in the IPS regions (e.g., Isaacs et al, 2001;Kucian et al, 2006;Molko et al, 2003Molko et al, , 2004Rotzer et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Neural correlates of numbers and mathematical terms

2012

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Numerical processing has been demonstrated to be subserved typically by the brain regions around the bilateral intraparietal sulcus (IPS). The goal of the current study was to investigate whether the processing of mathematical terms shared the same brain regions with numerical processing. Healthy adult participants performed semantic distance judgment tasks on five types of materials, including geometric terms, algebraic terms, linguistic terms, words for tools and other common objects, and Arabic numbers. Brain activation was measured with functional magnetic resonance imaging (fMRI). The results showed that geometric terms had greater activation than algebraic terms, linguistic terms and tool words in the horizontal IPS, but algebraic terms did not have greater activation than linguistic terms and tool words in this region. Arabic numbers showed greater activation than non-number materials (including geometric terms, algebraic terms, linguistic terms and tool words) in the bilateral IPS, right inferior frontal gyrus and bilateral middle frontal gyrus, but the non-number materials showed stronger activation in the left inferior frontal gyrus and left middle temporal gyrus. These results suggest that the brain area for the processing of numbers (the left IPS) seems to be involved in semantic processing of geometric terms, but not that of other mathematical terms such as algebraic terms. Both algebraic and geometric terms share similar brain organization with basic semantic processing in the left temporal and frontal regions.

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Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

Cited by 339 publications

References 153 publications

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

Visuospatial working memory influences the interaction between space and time

Neural correlates of numbers and mathematical terms

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