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Introduction to the Special Issue: Toward a Developmental Cognitive Neuroscience of Numerical and Mathematical Cognition Daniel Ansari

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Numerical Cognition Laboratory, Department of Psychology , The University of Western Ontario , London, Canada Published online: 15 Jul 2011.

To cite this article: Daniel Ansari (2011) Introduction to the Special Issue: Toward a Developmental Cognitive Neuroscience of Numerical and Mathematical Cognition, Developmental Neuropsychology, 36:6, 645-650, DOI: 10.1080/87565641.2011.587736 To link to this article: http://dx.doi.org/10.1080/87565641.2011.587736

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DEVELOPMENTAL NEUROPSYCHOLOGY, 36(6), 645–650 Copyright © 2011 Taylor & Francis Group, LLC ISSN: 8756-5641 print / 1532-6942 online DOI: 10.1080/87565641.2011.587736

Introduction to the Special Issue: Toward a Developmental Cognitive Neuroscience of Numerical and Mathematical Cognition Downloaded by [University of Western Ontario] at 18:18 15 March 2014

Daniel Ansari Numerical Cognition Laboratory, Department of Psychology, The University of Western Ontario, London, Canada

The first insights into the neural basis of numerical and mathematical cognition were gleaned at the beginning of the twentieth century through the study of brain-damaged patients (Henschen, 1919; Lewandowsky & Stadelmann, 1908), pointing to areas of the parietal cortex as critical for these processes. The structure-function mappings established through the study of such patients led to the formulations of models of the brain circuits underlying different aspects of numerical and mathematical cognition (Dehaene & Cohen, 1995; McCloskey, 1992). Such models, in turn, allowed for the testing of hypotheses concerning the association and dissociation between different aspects of processing numerical information engaged in the adult brain, such as the difference between approximate and exact calculation (Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999). With the advent of modern, functional neuroimaging methods, such as electroencephalography (EEG), functional magnetic resonance imaging (fMRI), and transcranial magnetic stimulation (TMS), further insights have been garnered into the brain mechanisms that subserve numerical and mathematical cognition. These studies have led to great advances in understanding how brain structure and function enable numerical and mathematical cognition. However, the majority of this research has been conducted with adults who suffered damage to fully developed areas of their brain or healthy adults. A survey of the literature suggests that even as recently as a decade ago there was almost no empirical evidence on how the brains of children process number and which brain mechanisms support mathematical thinking and problem solving, such as calculation. In 1998, Elise Temple and Michael Posner published a pioneering study that used EEG to measure the brain activation patterns underlying the processing of numerical magnitude in 5-year-olds and adults, revealing qualitatively similar patterns of brain activation during the comparison of both symbolic (Arabic numerals) and non-symbolic (arrays of dots) in the two groups (Temple & Posner, 1998). It was not until 2004 that fMRI was used to compare the brain activation patterns underlying arithmetic problem solving between children and adults. Specifically, Kawashima and colleagues compared the brain activation patterns of children and adults while they solved simple arithmetic problems (Kawashima et al., 2004). The data resulting from this study were suggestive of large overlaps in activation and little evidence for Correspondence should be addressed to Daniel Ansari, Numerical Cognition Laboratory, Department of Psychology, The University of Western Ontario, London, ON N6A 3K7, Canada. E-mail: [email protected]

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age-related differences in brain activation. Much progress has been made since these pioneering studies to better understand the relationships between brain development and children’s developing numerical and mathematical competencies and studies have looked at both children with and without mathematical difficulties (Developmental Dyscalculia). The present special issue of Developmental Neuropsychology is a reflection of just how much progress has been and continues to be made and how diversified the sets of questions that are being asked and the populations being tested have become. The empirical studies and theoretical review contained within this special issue reflect several frontiers in the emerging field of what might be referred to as the “Developmental Cognitive Neuroscience of Numerical Cognition.” My reading of the articles suggests at least three such separate, although not mutually exclusive, questions that are being addressed by the article presented in this issue. I will be discussing each of these in the context of the special issue contributions and then close by proposing some future directions.

CHANGE VERSUS CONTINUITY IN BRAIN MECHANISMS As mentioned above, the early studies comparing the neural correlates of numerical and mathematical processing between children and adults suggested largely similar activation patterns and, therefore, did not suggest that there existed age-related changes in brain activation during tasks measuring numerical and mathematical cognition. However, following these early studies, other evidence emerged to demonstrate age-related changes in both basic numerical magnitude processing (Ansari & Dhital, 2006; Ansari, Garcia, Lucas, Hamon, & Dhital, 2005; Cantlon et al., 2009; Kaufmann et al., 2006, 2008) and mental arithmetic (Rivera, Reiss, Eckert, & Menon, 2005). Thus, one of the important frontiers in the study of the developmental cognitive neuroscience of numerical cognition is the question of the extent to which there is change or continuity in underlying brain mechanisms. Two of the contributions in this special issue provide evidence to suggest continuity in brain mechanisms underlying numerical magnitude processing. Specifically, Libertus et al. (this issue), through the use of EEG, demonstrate that the oscillatory brain responses to the repetition of arrays of the same number of dots and change in the number of dots did not differ between seven-month-old infants and adults. Furthermore, Berger (this issue), through the re-analysis of a previously published study of arithmetic processing in infants (Berger, Tzur, & Posner, 2006), also using EEG, demonstrates that when infants view incorrect solutions to simple arithmetic equations (presented non-symbolically), they, like adults, exhibit activation of right parietal brain regions that is followed by activation of frontal brain regions thought to be sensitive to the detection of errors. Thus, the same time course of brain activation was observed in both young infants and adults, providing yet further support for the notion of ontogenetic continuity in brain processes underlying the processing of numerical and arithmetic information. These new data reported in the present special issue, together with neuroimaging evidence from other published studies with infants (Brannon, Libertus, Meck, & Woldorff, 2008; Hyde, Boas, Blair, & Carey; Izard, Dehaene-Lambertz, & Dehaene, 2008) and young children (Cantlon, Brannon, Carter, & Pelphrey, 2006), suggest a high degree of ontogenetic continuity. Given the data discussed earlier that suggests ontogenetic changes, it is important to consider what might explain these seemingly contradictory sources of evidence. I would like to suggest that

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the question should not be whether there is developmental discontinuity or continuity in the neurocognitive mechanisms underlying numerical and mathematical processing, but rather how data showing both continuity and discontinuity can be accommodated into a coherent theoretical framework? This is a major challenge for future research and theory in this emerging field. I would like to suggest that one way of better understanding these data is to view them as being reflective of different levels of neurocognitive processing, which are differentially affected by developmental changes. Most of the studies that have provided evidence for ontogenetic continuity have been ones in which participants viewed numerical stimuli passively, while those suggesting developmental changes required participants to actively engage with the numerical stimuli to make comparisons or solve arithmetic problems. Thus, it is possible that while a core set of basic representations of numerical magnitude exhibit ontogenetic continuity, it is the processes that are actively engaged (such as in the process of comparison and arithmetic) and are subject to developmental changes. Moreover, it is important to consider that the results of any investigation of continuity and change will depend critically on the age groups tested. Many developmental changes in numerical and mathematical processing may happen rapidly over a short period of time and thus, age group selection is crucial. Take, for example, the acquisition of the meaning of Arabic numerals (such as understanding that the numeral 5 represents a set of five objects). Over the first year of school, children receive massive exposure to numerical symbols and this might, therefore, be a period of much change in the brain mechanisms underlying symbolic number processing. However, after this period, the brain mechanisms may already be very adult-like. Most of the available evidence consists of very coarse comparison of groups of “children” and “adults.” A fuller characterization of continuity and change will require a more fine-grained analysis of age-related changes.

THE INFLUENCE OF NON-NUMERICAL FACTORS One of the key questions in the study of the development of numerical and mathematical cognition concerns the origins of numerical magnitude representations. Many researchers have argued that there are innate, domain-specific representations of numerical magnitude and, indeed, the articles by Libertus et al. (this issue) and Berger (this issue) provide evidence in support of this account and interpret their data as being consistent with the notion that there exists a domain-specific, innate system for the representation of numerical magnitude. However, others have contended that numerical magnitude representations are constructed from domain-general systems for the representation of both numerical and non-numerical magnitudes, such as time and space. In the present special issue, Simon provides a theoretical review in which he postulates that numerical magnitude representations are constructed, over the course of development, from spatial and temporal information processing in interaction with attention mechanisms. Simon goes on to hypothesize that impairments of these domain-general basic processing mechanisms may explain similar profiles of numerical processing in individuals with different genetic developmental disorders such as Williams, Turner, and chromosome 22q11.2 deletion syndrome. Domain general mechanisms are also drawn on by Kucian et al. (this issue) to explain the results of an fMRI investigation comparing the neural correlates of non-symbolic numerical magnitude processing between children with and without Developmental Dyscalculia (DD). Unlike

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other neuroimaging studies comparing brain activation patterns in children with and without DD (Kaufmann, Vogel, Kremser, Schocke, & Wood, 2009; Mussolin et al., 2009; Price, Holloway, Räsänen, Vesterinen, & Ansari, 2007), Kucian et al. did not find group differences in areas of the intraparietal sulcus (IPS). Instead, differences were observed in areas of the frontal cortex that are often associated with response selection, cognitive control, and working memory. These findings raise the possibility that impairments of numerical magnitude processing in children with DD may not be solely caused by domain-specific impairments of numerical magnitude representations in the IPS but could be partially explained by an interaction between weak magnitude representations and domain-general processing resources (see also Kaufmann et al., 2009). The findings by Kucian et al. imply that multiple brain processes are involved in explaining differences between children with and without DD as well as the interaction between domain-general and domain-specific processes in numerical magnitude processing and the potential role played by domain-general processes in compensating for domain-specific impairments. Related to these considerations, in the present special issue, Soltész et al. report data from an EEG study that examines the relationship between cognitive control and automatic symbolic magnitude processing in grade 1-3 children using a numerical Stroop paradigm. Their data suggest that brain processes of cognitive control and numerical magnitude processing are temporally dissociable from one another. How these processes interact in atypical development is an important avenue for future research.

METHODOLOGICAL CHALLENGES AND ADVANCES The comparison of adults and children comes with a host of methodological and analytical challenges. The present special issue contains a number of important advances in an effort to refine the developmental study of the neural correlates of numerical and mathematical development. One of the issues facing developmental researchers is that children and adults solve calculation problems at different rates and with different levels of accuracy, potentially confounding comparisons of underlying brain activation patterns. In their contribution to this special issue, Krinzinger et al. demonstrate that a self-paced paradigm represents a reliable and reproducible option to fixed duration paradigms. Several meta-analyses of adult neuroimaging studies of numerical and mathematical processing have been published and provide an important basis for hypothesis-driven research (Cohen Kadosh, Lammertyn, & Izard, 2008; Dehaene, Piazza, Pinel, & Cohen, 2003). However, for reasons articulated elsewhere (Ansari, 2009), these adult meta-analyses are only partially useful in the context of developmental studies. Thus far, only one meta-analysis of the brain regions engaged during numerical and mathematical processing in children is available in the published literature (Houde, Rossi, Lubin, & Joliot, 2010). In the present special issue, Kaufmann et al. report results from another meta-analysis that includes data from children with and without DD. Such summaries of data represent important resources in helping researchers to identify the most consistent patterns of activation and how these differ between typically and atypically developing children. The present special issue also features an eye-tracking study comparing eye-movements between children and adults during performance of a carry operation in mental addition. The findings from this investigation show that the measurement of eye-movements provides a level

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of analysis that cannot be gleaned from behavioral data alone. There are surprisingly few studies of eye-movements in the study of numerical and mathematical cognition and the findings reported by Moeller et al. (this issue) suggest that this cost-effective methodology may be able to provide an untapped tool to analyze developmental changes in numerical and mathematical processing. Taken together, the present special issue is a testament to the rapidly evolving study of the neurocognitive mechanisms underlying the development of numerical and mathematical skills. The contributions not only touch on current existing theoretical issues, raise novel questions and grounds for conceptual discussion, thereby drawing attention to many avenues for future research, but also addresses important methodological questions and provides summaries of the available evidence. By doing so, this special issue will become an important resource for Developmental Cognitive Neuroscientists interested in the ontogenesis of the mathematical brain. REFERENCES Ansari, D. (2009). Neurocognitive approaches to developmental disorders of numerical and mathematical cognition: The perils of neglecting the role of development. Learning and Individual Differences, 20(2), 123–129. Ansari, D., & Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience, 18(11), 1820–1828. Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. Neuroreport, 16(16), 1769–1773. Berger, A., Tzur, G., & Posner, M. I. (2006). Infant brains detect arithmetic errors. Proceedings of the National Academy of Sciences U S A, 103(33), 12649–12653. Brannon, E. M., Libertus, M. E., Meck, W. H., & Woldorff, M. G. (2008). Electrophysiological measures of time processing in infant and adult brains: Weber’s Law holds. Journal of Cognitive Neuroscience, 20(2), 193–203. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125. Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M., & Pelphrey, K. A. (2009). The neural development of an abstract concept of number. Journal of Cognitive Neuroscience, 21(11), 2217–2229. Cohen Kadosh, R., Lammertyn, J., & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84(2), 132–147. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3–6), 487–506. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284(5416), 970–974. Henschen, S. E. (1919). Uber sprach-, musik-, und rechenmechanismen und ihre lokalisationen im grobhirn. Zeitschrift fur die gesamte Neurologie und Psychiatrie, 52, 273–298. Houde, O., Rossi, S., Lubin, A., & Joliot, M. (2010). Mapping numerical processing, reading, and executive functions in the developing brain: An fMRI meta-analysis of 52 studies including 842 children. Developmental Science, 13(6), 876–885. Hyde, D. C., Boas, D. A., Blair, C., & Carey, S. (2010). Near-infrared spectroscopy shows right parietal specialization for number in pre-verbal infants. Neuroimage, 53(2), 647–652. Izard, V., Dehaene-Lambertz, G., & Dehaene, S. (2008). Distinct cerebral pathways for object identity and number in human infants. PLoS Biology, 6(2), e11. Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, . . . Ischebeck, A. (2006). Neural correlates of the number-size interference task in children. Neuroreport, 17(6), 587–591.

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