Neural correlates of numbers and mathematical terms
Highlights
► We compare brain organization for mathematical terms and numbers. ► Processing of geometric terms is relatively category-specific in left IPS. ► Mathematical terms share similar brain organization with ordinary words. ► Mathematical terms have greater activation in left MTG and IFG than numbers.
Introduction
Several lines of research have shown that numerical processing is subserved by the bilateral intraparietal sulcus (IPS) (e.g., Arsalidou and Taylor, 2011, Butterworth, 1999, Dehaene et al., 1999, Eger et al., 2003, Kadosh et al., 2005, Kadosh et al., 2007 Piazza et al., 2007, Thioux et al., 2005; see reviews by Brannon, 2006, Dehaene et al., 2003). 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., 2001, Cappelletti et al., 2002, Cappelletti et al., 2005, Crutch and Warrington, 2002, Diesfeldt, 1993, Jefferies et al., 2004, Jefferies et al., 2005, Lemer 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 non-numerical 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., 2003, Molko et al., 2004, Rotzer et al., 2008).
Based on the neuropsychological and neuroimaging evidence, Dehaene et al. (2003) proposed a three parietal circuit model for numerical processing: That is, the bilateral intraparietal system is associated with quantity representation, the left angular gyrus with verbal processing of numbers, and the posterior superior parietal lobule with attentional processes. The brain regions around the bilateral intraparietal sulcus are relatively specific to the number-related processes, but the regions for verbal and attentional processes have more general functions. In addition to the parietal cortex, the prefrontal cortex has also been found to be critical for numerical processing (e.g., Arsalidou and Taylor, 2011, Fehr and Herrmann, 2007, Ischebeck et al., 2006, Kong et al., 2005), most likely because it serves the purpose of general information processing, such as the working memory (Arsalidou and Taylor, 2011).
Although the evidence is clear that numbers are specifically processed by the IPS, less is known about the neural substrates for the processing of knowledge about mathematical terms (e.g. “decimal”, “fraction”, “group”, “rectangle”). On the one hand, mathematical terms are verbal materials that are supposed to be processed in the language network. On the other hand, they are related to numbers and other aspects of mathematics (e.g., spatial relations in geometry) that are processed by the IPS. To our knowledge, only three neuropsychological studies (Delazer and Benke, 1997, Hittmair-Delazer et al., 1994, Warrington, 1982) and three neuroimaging studies (Andres et al., 2011, Prado et al., 2011, Zhou et al., 2007) have shown limited but relevant results. Warrington (1982) found that lesions in the left parietal cortex led to a loss of memory of arithmetic facts but had no effects on the conceptual knowledge of arithmetic (e.g., operations, commutativity, addition/subtraction inverse principle). These results were confirmed by Hittmair-Delazer et al. (1994). In contrast, Delazer and Benke (1997) found that a patient who suffered from a left parietal glioblastoma completely lost conceptual knowledge of arithmetic, but preserved some arithmetic facts (multiplications, some additions and subtractions). Using fMRI, Zhou et al. (2007) found that addition had more activation in the right superior and inferior parietal lobules than multiplication, whereas the latter had more activation in some of the language-related regions such as the left posterior and anterior superior temporal gyrus. Prado et al. (2011) found a similar disassociation between the analogical and language-based representations of numbers. Andres et al. (2011) used transcranial magnetic stimulation (TMS) to demonstrate that multiplication had greater activation in the bilateral middle and superior temporal gyri than subtraction, though both relied on the horizontal IPS.
These results suggest that the memory of conceptual knowledge of arithmetic may be subserved by the left parietal cortex or the language-related regions such as the left frontal cortex and left temporal cortex. The current fMRI study aimed to examine systematically the processing of two types of mathematical terms—geometric (e.g., “sphere”, “trapezoid”) and algebraic terms (e.g., “even number”, “fraction”). The processing of mathematical terms was compared with that of three types of materials: Arabic numbers, linguistic terms (e.g. “noun”, “poem”), and tool words. The tool words actually included both words for tools (e.g. “scissors”, “rake”) and those for other common objects (e.g., “piano”, “candle”), following the convention of previous studies (e.g., Cappa et al., 1998, Martin et al., 1996). The present study used the semantic distance judgment task (Mummery et al., 1998, Zannino et al., 2006). If mathematical terms involve only verbal processing, we would expect the activation patterns of geometric and algebraic terms to be similar to those of the two types of verbal materials (linguistic terms and tool words). On the other hand, we expected that algebraic terms would activate mental representations of numbers. For example, “odd number” would activate the numbers “1, 3, 5, 7, 9, …”, “fraction” would activate the numbers “, , , …”, and “negative number” would activate the numbers “− 1, − 2, − 3, …” . Therefore, we expected greater activation in the IPS for the algebraic terms than for linguistic terms and tool words. Similarly, we expected that geometric terms such as “radius”, “arch”, “trapezoid”, and “vertex angle” would activate mental images of the actual geometric shapes, and hence elicit greater activation in the inferior parietal lobule, which has been found to be involved in processing mental images (e.g. Alivisatos and Petrides, 1997, Carpenter et al., 1999, Gauthier et al., 2002, Jordan et al., 2001, Vingerhoets et al., 2001).
Section snippets
Subjects
Twenty right-handed (10 male; aged 18.8–22.5 years old, and mean age = 20.6 years old) undergraduates were recruited from Beijing Normal University. These subjects reported having no previous history of neurological disorders or head injury. Procedures of the experiment were fully explained to all subjects before they gave informed consent. This study was approved by the Institutional Review Board (IRB) of the Institute of Cognitive Neuroscience and Learning at Beijing Normal University.
Stimuli and materials
Stimulus
Behavioral results
The mean reaction times (RTs) were 1856 ms for Arabic numbers, 1901 ms for geometric terms, 1867 ms for algebraic terms, 1855 ms for linguistic terms and 1866 ms for tool words. The mean error rates were 14.80%, 9.95%, 11.30%, 10.30%, and 10.90%, respectively. RTs and accuracy rates were analyzed with a repeated measures analysis of variance (ANOVA) (five types of materials: algebraic terms, geometric terms, linguistic terms, tool words and Arabic numbers). The main effect of stimulus type was not
Discussion
The goal of the current study was to investigate the neural correlates of the processing of two types of mathematical terms (geometric and algebraic terms). Control materials were Arabic numbers, linguistic terms, and tool words. The main findings include: (1) Algebraic terms did not elicit greater activation than did linguistic terms and tool words in the horizontal intraparietal sulcus, but geometric terms elicited greater activation than did algebraic terms, linguistic terms and tool words
Acknowledgments
This research was supported by two grants from the Natural Science Foundation of China (project nos. 60931003 and 30870759), a grant from the program New Century Excellent Talents at Universities (NCET-07-0101), and a grant from the Fundamental Research Funds for the Central Universities (248-105565GK).
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