Article

Arithmetic and the brain

Institut National de la Santé et de la Recherche Médicale unit 562 Cognitive neuroimaging, Service Hospitalier Frederic Joliot, Commissariat à l'énergie atomique/DRM/DSV, 4 Place du general Leclerc, 91401 Orsay cedex, France.
Current Opinion in Neurobiology (Impact Factor: 6.63). 05/2004; 14(2):218-24. DOI: 10.1016/j.conb.2004.03.008
Source: PubMed

ABSTRACT

Recent studies in human neuroimaging, primate neurophysiology, and developmental neuropsychology indicate that the human ability for arithmetic has a tangible cerebral substrate. The human intraparietal sulcus is systematically activated in all number tasks and could host a central amodal representation of quantity. Areas of the precentral and inferior prefrontal cortex also activate when subjects engage in mental calculation. A monkey analogue of these parieto-frontal regions has recently been identified, and a neuronal population code for number has been characterized. Finally, pathologies of this system, leading to acalculia in adults or to developmental dyscalculia in children, are beginning to be understood, thus paving the way for brain-oriented intervention studies.

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    • "In comparison, the neuronal basis for the visual identification of numerical symbols, including numerals, is less widely studied. Visual numeral representations were assumed to be localized in the ventral visual system , with direct connections to parietal and frontal areas involved in numerical cognition (Dehaene et al. 2004). Functional imaging and electrophysiological studies confirmed ventral temporal activation during tasks that involved visual processing of numerals or calculation (Allison et al. 1994; Park et al. 2012), for a review see Arsalidou and Taylor (2011). "
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    ABSTRACT: Recent evidence suggests that specific neuronal populations in the ventral temporal cortex show larger electrophysiological responses to visual numerals compared with morphologically similar stimuli. This study investigates how these responses change from simple reading of numerals to the active use of numerals in an arithmetic context. We recorded high-frequency broadband (HFB) signals, a reliable measure for local neuronal population activity, while 10 epilepsy patients implanted with subdural electrodes performed separate numeral reading and calculation tasks. We found that calculation increased activity in the posterior inferior temporal gyrus (ITG) with a factor of approximately 1.5 over the first 500 ms of calculation, whereas no such increase was noted for reading numerals without calculation or reading and judging memory statements. In a second experiment conducted in 2 of the same subjects, we show that HFB responses increase in a systematic manner when the single numerals were presented successively in a calculation context: The HFB response in the ITG, to the second and third numerals (i.e., b and c in a + b = c), was approximately 1.5 times larger than the responses to the first numeral (a). These results provide electrophysiological evidence for modulation of local neuronal population responses to visual stimuli based on increasing task demands.
    No preview · Article · Oct 2015 · Cerebral Cortex
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    • "Moreover, studies have consistently shown that children with math difficulties have an impaired ability to process these representations (Iuculano et al., 2008; Landerl et al., 2004; Landerl and Kölle, 2009; Mussolin Mejias and Noël, 2010; Rousselle and Noël, 2007). Parietal regions and, more specifically, the horizontal segment of the intraparietal sulcus, have been found to be active when processing both non-symbolic and symbolic numerical magnitudes (Dehaene et al., 2003, 2004). A neural distance effect has also been observed, denoted by greater activation when the quantities are closer together (Pinel et al., 2001). "
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    ABSTRACT: The ability to map between non-symbolic and symbolic magnitude representations is crucial in the development of mathematics and this map is disturbed in children with math difficulties. In addition, positive parietal ERPs have been found to be sensitive to the number distance effect and skills solving arithmetic problems. Therefore we aimed to contrast the behavioral and ERP responses in children with different levels of mathematical achievement: low (LA), average (AA) and high (HA), while comparing symbolic and non-symbolic magnitudes. The results showed that LA children repeatedly failed when comparing magnitudes, particularly the symbolic ones. In addition, a positive correlation between correct responses while analyzing symbolic quantities and WRAT-4 scores emerged. The amplitude of N200 was significantly larger during non-symbolic comparisons. In addition, P2P amplitude was consistently smaller in LA children while comparing both symbolic and non-symbolic quantities, and correlated positively with the WRAT-4 scores. The latency of P3 seemed to be sensitive to the type of numerical comparison. The results suggest that math difficulties might be related to a more general magnitude representation problem, and that ERP are useful to study its timecourse in children with different mathematical skills.
    Full-text · Article · Sep 2015 · Brain research
    • "To accomplish the second goal, the trials of the Add/Sub task were classified into four categories based on a 2 by 2 design, crossing 'Operation Type' (Addition vs. Subtraction) and 'Regrouping' (whether or not Carrying or Borrowing is needed). We hypothesized that Subtraction (compared to Addition) and Regrouping (compared to No-Regrouping) conditions would evoke more quantitative processing because it tends to be less practiced and less automatized (Ashkenazi et al. 2014;Dehaene et al. 2004;Duffau et al. 2002;van Harskamp and Cipolotti 2001). Thus, we expected to see stronger correlations between ANS acuity and calculations involving Subtraction (compared to Addition) and Regrouping (Carrying or Borrowing). "
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    ABSTRACT: Approximate number sense (ANS) acuity refers to the ability to non-symbolically recognize, estimate and operate upon large numerosities. ANS acuity has been reported to be correlated with math achievement in children and adolescents. However, reports of this relationship in adults have been inconsistent. The present study aimed to resolve the inconsistency in the relationship between adults’ ANS acuity and math achievement by contrasting between different kinds of mathematical problem solving. We hypothesized that the correlation between ANS acuity mathematical performance would be stronger when deep quantitative processing is required during problem solving. In Experiment 1, ANS acuity was correlated with Mathematical Reasoning but not Directed Calculation performance. In Experiment 2, ANS acuity was correlated with Two-digit Subtraction (but not Addition) performance only when Regrouping (i.e., borrowing) was required. The results from two experiments demonstrated that ANS acuity was correlated with mathematical performance only when problem solving involved effortful, quantitative processing that goes beyond automatized, routinized arithmetic. In addition, ANS acuity was distinguishable from Area acuity regarding its unique relationship with math achievement, which was unconfounded by the influence of demographic variables and fluid intelligence. Overall, the present results help resolve the inconsistency in previous reports of the correlation between ANS acuity and math achievement in adults.
    No preview · Article · Jul 2015
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