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Numerical representation in the parietal lobes: Abstract or not abstract?

  • Roi Cohen Kadosh (a1) and Vincent Walsh (a2)
Abstract

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

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Ansari, D. (2007) Does the parietal cortex distinguish between “10,” “Ten,” and ten dots? Neuron 53:165–67.
Ansari, D. (2008) Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 9(4):278–91.
Ansari, D. & Dhital, B. (2006) Age-related changes in the activation of the intraparietal sulcus during non-symbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience 18:1820–28.
Ansari, D., Dhital, B. & Siong, S. C. (2006a) Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes. Brain Research 1067:181–88.
Ansari, D., Fugelsang, J. A., Dhital, B., Venkatraman, V. (2006b) Dissociating response conflict from numerical magnitude processing in the brain: An event-related fMRI study. NeuroImage 32:799805.
Ansari, D., Garcia, N., Lucas, E., Hamon, K. & Dhital, B. (2005) Neural correlates of symbolic number processing in children and adults. NeuroReport 16(16):1769–73.
Ansari, D. & Karmiloff-Smith, A. (2002) Atypical trajectories of number development: A neuroconstructivist perspective. Trends in Cognitive Sciences 6:511–16.
Ashkenazi, S., Henik, A., Ifergane, G. & Shelef, I. (2008) Basic numerical processing in left intraparietal sulcus (IPS) acalculia. Cortex 44:439–48.
Bächtold, D., Baumuller, M. & Brugger, P. (1998) Stimulus-response compatibility in representational space. Neuropsychologia 36:731–35.
Banks, W. P., Fujii, M. & Kayra-Stuart, F. (1976) Semantic congruity effects in comparative judgments of magnitudes of digits. Journal of Experimental Psychology: Human Perception and Performance 2:435–47.
Barge, J. A. (1992) The ecology of automaticity: Towards establishing the conditions needed to produce automatic processing effect. American Journal of Psychology 105:181–99.
Barsalou, L. W. (1999) Perceptual symbol systems. Behavioral and Brain Sciences 22:577660.
Barsalou, L. W. (2003) Abstraction in perceptual symbol systems. Philosophical Transactions of the Royal Society B: Biological Sciences 358:1177–87.
Barsalou, L. W., Santos, A., Simmons, W. K. & Wilson, C. D. (2008) Language and simulation in conceptual processing. In: Symbols, embodiment, and meaning, ed. De Vega, M., Glenberg, A. M. & Graesser, A. C., pp. 245–83. Oxford University Press.
Barth, H., Kanwisher, N. & Spelke, E. (2003) The construction of large number representations in adults. Cognition 86:201–21.
Brannon, E. M. (2006) The representation of numerical magnitude. Current Opinion in Neurobiology 16:222–29.
Butterworth, B. (1999) The mathematical brain. Macmillan.
Butterworth, B. (2004) Developmental dyscalculia. In: Handbook of mathematical cognition, ed. Campbell, J. I. D.. Psychology Press.
Butterworth, B. (2005) The development of arithmetical abilities. Journal of Child Psychology and Psychiatry 46:318.
Calabrese, R. L. (2007) Motor networks: Shifting coalitions. Current Biology 17:R139R141.
Campbell, J. I. D. (1994) Architectures for numerical cognition. Cognition 53(1):144.
Campbell, J. I. D. & Clark, J. M. (1988) An encoding complex view of cognitive number processing: Comment on McCloskey, Sokol, & Goodman (1986). Journal of Experimental Psychology: General 117:204–14.
Campbell, J. I. D. & Epp, L. J. (2004) An encoding-complex approach to numerical cognition in Chinese-English bilinguals. Canadian Journal of Experimental Psychology (Revue Canadienne De Psychologie Experimentale) 58(4):229–44.
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:e125.
Cantlon, J. F., Platt, M. L. & Brannon, E. M. (2009) Beyond the number domain. Trends in Cognitive Sciences 13:8391.
Carr, T. H. (1992) Automaticity and cognitive anatomy: Is word recognition “automatic”? American Journal of Psychology 105:201–37.
Castelli, F., Glaser, D. E. & Butterworth, B. (2006) Discrete and analogue quantity processing in the parietal lobe: A functional MRI study. Proceedings of the National Academy of Science USA 103:4693–98.
Cipolotti, L. & Butterworth, B. (1995) Toward a multiroute model of number processing: Impaired number transcoding with preserved calculation skills. Journal of Experimental Psychology: General 124:375–90.
Cohen, L., Dehaene, S., Naccache, L., Lehéricy, S., Dehaene-Lambertz, G., Henaff, M.-A. & Michel, F. (2000) The visual word form area: Spatial and temporal characterization of an initial stage of reading in normal subjects and posterior split-brain patients. Brain 123:291307.
Cohen Kadosh, K., Henson, R. N. A., Cohen Kadosh, R., Johnson, M. H. & Dick, F. (in press) Strategy-dependent activation of face-sensitive cortex: An fMRI adaptation study. Journal of Cognitive Neuroscience.
Cohen Kadosh, K. & Johnson, M. H. (2007) Developing a cortex specialized for face perception. Trends in Cognitive Sciences 11:367–69.
Cohen Kadosh, R., (2008a) Numerical representation: Abstract or non-abstract? Quarterly Journal of Experimental Psychology 61(8):1160–68.
Cohen Kadosh, R., (2008b) The laterality effect: Myth or truth? Consciousness and Cognition 17:350–54.
Cohen Kadosh, R., Brodsky, W., Levin, M. & Henik, A. (2008b) Mental representation: What can pitch tell us about the distance effect? Cortex 44:470–77.
Cohen Kadosh, R., Cohen Kadosh, K. & Henik, A. (2007a) The neuronal correlate of bi-directional synaesthesia: A combined ERP and fMRI study. Journal of Cognitive Neuroscience 19:2050–59.
Cohen Kadosh, R., Cohen Kadosh, K. & Henik, A. (2008c) When brightness counts: The neuronal correlate of numerical-luminance interference. Cerebral Cortex 18:337–43.
Cohen Kadosh, R., Cohen Kadosh, K., Henik, A. & Linden, D. E. J. (2008d) Processing conflicting information: Facilitation, interference, and functional connectivity. Neuropsychologia 46:2872–79.
Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A. & Goebel, R. (2007b) Notation-dependent and -independent representations of numbers in the parietal lobes. Neuron 53(2):307–14.
Cohen Kadosh, R., Cohen, Kadosh, K., Linden, D. E. J., Gevers, W., Berger, A. & Henik, A. (2007c) The brain locus of interaction between number and size: A combined functional magnetic resonance imaging and event-related potential study. Journal of Cognitive Neuroscience 19:957–70.
Cohen Kadosh, R. & Henik, A. (2006) A common representation for semantic and physical properties: A cognitive-anatomical approach. Experimental Psychology 53:8794.
Cohen Kadosh, R., Henik, A. & Rubinsten, O. (2008e) Are Arabic and verbal numbers processed in different ways? Journal of Experimental Psychology: Learning, Memory and Cognition 34(6):1377–91.
Cohen Kadosh, R., Henik, A., Rubinsten, O., Mohr, H., Dori, H., Van de Ven, V., Zorzi, M., Hendler, T., Goebel, R. & Linden, D. E. J. (2005) Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia 43:1238–48.
Cohen Kadosh, R., Lammertyn, J. & Izard, V. (2008f) Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology 84:132–47.
Cohen Kadosh, R., Muggleton, N., Slivanto, J. & Walsh, V. (submitted b) Modulating number-specific neurons in the human parietal cortex.
Cohen Kadosh, R., Tzelgov, J. & Henik, A. (2008g) A synesthetic walk on the mental number line: The size effect. Cognition 106:548–57.
Cohen Kadosh, R. & Walsh, V. (2007) Dyscalculia. Current Biology 17:R946R947.
Cohen Kadosh, R. & Walsh, V. (2008) From magnitude to natural numbers: A developmental neurocognitive perspective. Behavioral and Brain Sciences 31:647–48.
Corbetta, M., Akbudak, E., Conturo, T. E., Snyder, A. Z., Ollinger, J. M., Drury, H. A., Linenweber, M. R., Petersen, S. E., Raichle, M. E., Van Essen, D. C. & Shulman, G. L. (1998) A common network of functional areas for attention and eye movements. Neuron 21(4):761–73.
Dehaene, S. (1992) Varieties of numerical abilities. Cognition 44:142.
Dehaene, S. (1996) The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience 8:4768.
Dehaene, S. & Akhavein, R. (1995) Attention, automaticity, and levels of representation in number processing. Journal of Experimental Psychology: Learning, Memory, and Cognition 21(2):314–26.
Dehaene, S., Bossini, S. & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 122:371–96.
Dehaene, S. & Cohen, L. (1997) Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33:219–50.
Dehaene, S., Dehaene-Lambertz, G. & Cohen, L. (1998a) Abstract representations of numbers in the animal and human brain. Trends in Neurosciences 21:355–61.
Dehaene, S., Dupoux, E. & Mehler, J. (1990) Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance 16:626–41.
Dehaene, S., Izard, V., Spelke, E. & Pica, P. (2008) Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 320(5880):1217–20.
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2003) Three parietal circuits for number processing. Cognitive Neuropsychology 20(3–6):487506.
Delazer, M. & Benke, T. (1997) Arithmetic facts without meaning. Cortex 33:697710.
Delazer, M., Karner, E., Zamarian, L., Donnemiller, E. & Benke, T. (2006) Number processing in posterior cortical atrophy – a neuropsycholgical case study. Neuropsychologia 44:3651.
Diester, I. & Nieder, A. (2007) Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biology 5 (11):e294; 2684–95.
Doricchi, F., Guariglia, P., Gasparini, M. & Tomaiuolo, F. (2005) Dissociation between physical and mental number line bisection in right hemisphere brain damage. Nature Neuroscience 8:1663–65.
Dormal, V., Seron, X. & Pesenti, M. (2006) Numerosity-duration interference: A Stroop experiment. Acta Psychologica 121:109124.
Droit-Volet, S., Clement, A. & Fayol, M. (2008) Time, number and length: Similarities and differences in discrimination in adults and children. Quarterly Journal of Experimental Psychology 61(12):1827–46.
Duncan, J. (2001) An adaptive coding model of neural function in prefrontal cortex. Nature Reviews Neuroscience 2:820–29.
Eger, E., Sterzer, P., Russ, M. O., Giraud, A.-L. & Kleinschmidt, A. (2003) A supramodal number representation in human intraparietal cortex. Neuron 37:719–25.
Fias, W. (2001) Two routes for the processing of verbal numbers: Evidence from the SNARC effect. Psychological Research – Psychologische Forschung 65(4):242–49.
Fias, W., Brysbaert, M., Geypens, F. & d'Ydewalle, G. (1996) The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Mathematical Cognition 2(1):95110.
Fias, W. & Fischer, M. H. (2004) Spatial representation of numbers. In: Handbook of mathematical cognition, ed. Campbell, J. I. D.. Psychology Press.
Fias, W., Lammertyn, J., Caessens, B. & Orban, G. A. (2007) Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. Journal of Neuroscience 27:8952–56.
Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P. & Orban, G. A. (2003) Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience 15:111.
Fias, W., Lauwereyns, J. & Lammertyn, J. (2001a) Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. Cognitive Brain Research 12:415–23.
Fias, W., Reynvoet, B. & Brysbaert, M. (2001b) Are arabic numerals processed as pictures in a Stroop inteference task? Psychological Research 65:242–49.
Fischer, M. H. & Rottmann, J. (2005) Do negative numbers have a place on the mental number line? Psychology Science 47(1):2232.
Gallistel, C. R. & Gelman, R. (1992) Preverbal and verbal counting and computation. Cognition 44:4374.
Ganor-Stern, D. & Tzelgov, J. (2008) Across-notation automatic numerical processing. Journal of Experimental Psychology: Learning, Memory and Cognition 34(2):430–37.
Gathers, A. D., Bhatt, R., Corbly, C. R., Farley, A. B. & Joseph, J. E. (2004) Developmental shifts in cortical loci for face and object recognition. NeuroReport 15:1549–53.
Gebuis, T., Cohen Kadosh, R., de Haan, E. & Henik, A. (2009) Automatic quantity processing in 5-year-olds and adults. Cognitive Processing 10:133–42.
Gertner, L., Henik, A. & Cohen Kadosh, R., (2009) When 9 is not on the right: Implications from number-form synaesthesia. Consciousness and Cognition 18:366–74.
Gevers, W. & Lammertyn, J. (2005) The hunt for SNARC. Psychology Science 47:1021.
Gevers, W., Lammertyn, J., Notebaert, W., Verguts, T. & Fias, W. (2006a) Automatic response activation of implicit spatial information: Evidence from the SNARC effect. Acta Psychologica 122:221–33.
Gevers, W., Ratinckx, E., De Baene, W. & Fias, W. (2006b) Further evidence that the SNARC effect is processed along a dual-route architecture: Evidence from the lateralized readiness potential. Experimental Psychology 53:5868.
Gilbert, S. J. & Burgess, P. W. (2008) Executive function. Current Biology 19:R110R114.
Girelli, L., Lucangeli, D. & Butterworth, B. (2000) The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology 76(2): 104–22.
Glaser, W. R. (1992) Picture naming. Cognition 42:61105.
Glickstein, M. (2007) What does the cerebellum really do? Current Biology 17:R824–27.
Göbel, S. M., Johansen-Berg, H., Behrens, T. & Rushworth, M. F. S. (2004) Response-selection-related parietal activation during number comparison. Journal of Cognitive Neuroscience 16:1536–51.
Grill-Spector, K., Henson, R. & Martin, A. (2006a) Repetition and the brain: Neural models of stimulus-specific effects. Trends in Cognitive Sciences 10:1423.
Grill-Spector, K., Sayres, R. & Ress, D. (2006b) High-resolution imaging reveals highly selective nonface clusters in the fusiform face area. Nature Neuroscience 9:1177–85.
Hasher, L. & Zacks, R. T. (1979) Automatic and effortful processes in memory. Journal of Experimental Psychology: General 108:356–88.
Haxby, J. V., Hoffman, E. A. & Gobbini, M. I. (2000) The distributed human neural system for face perception. Trends in Cognitive Sciences 4:223–33.
Henik, A. & Tzelgov, J. (1982) Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory and Cognition 10:389–95.
Holloway, I. D. & Ansari, D. (2008) Domain-specific and domain-general changes in children's development of number comparison. Developmental Science 11:644–49.
Holloway, I. D. & Ansari, D. (2009) Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology 103(1):1729.
Hung, Y.-H., Hung, D. L., Tzeng, O. J.-L. & Wu, D. H. (2008) Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition 106(3):1441–50.
Ischebeck, A. (2003) Differences between digit naming and number word reading in a flanker task. Memory and Cognition 31:529–37.
Ito, Y. & Hatta, T. (2003) Semantic processing of Arabic, Kanji, and Kana numbers: Evidence from interference in physical and numerical size judgments. Memory and Cognition 31(3):360–68.
Ito, Y. & Hatta, T. (2004) Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect. Memory and Cognition 32(4):662–73.
Izard, V. & Dehaene, S. (2008) Calibrating the mental number line. Cognition 106:1221–47.
Izard, V., Dehaene-Lambertz, G. & Dehaene, S. (2008) Distinct cerebral pathways for object identity and number in human infants. PLoS Biology 6:e11.
Johnson, M. H. (2001) Functional brain development in humans. Nature Reviews Neuroscience 2(7):475–83.
Johnson, M. H., Grossman, T. & Cohen Kadosh, K., (2009) Mapping functional brain development: Building a social brain through interactive specialization. Developmental Psychology 45:151–59.
Johnson, M. H. & Munakata, Y. (2005) Processes of change in brain and cognitive development. Trends in Cognitive Sciences 9:152–58.
Kanwisher, N., McDermott, J. & Chun, M. M. (1997) The fusiform face area: A module in human extrastriate cortex specialized for face perception. Journal of Neuroscience 17:4302–11.
Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg, P., Golaszewski, S., Felber, S. & Ischebeck, A. (2005) Neural correlates of distance and congruity effects in a numerical Stroop task: An event-related fMRI study. NeuroImage 25:888–98.
Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L.-B., Felber, S. & Ischebeck, A. (2006) Neural correlates of the number-size interference task in children. NeuroReport 17:587–91.
Koechlin, E., Naccache, L., Block, E. & Dehaene, S. (1999) Primed numbers: Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance 25(6):1882–905.
Lammertyn, J., Fias, W. & Lauwereyns, J. (2002) Semantic influences on feature-based attention due to overlap of neural circuits. Cortex 38:878–82.
Lemer, C., Dehaene, S., Spelke, E. & Cohen, L. (2003) Approximate quantities and exact number words: Dissociable systems. Neuropsychologia 41:1942–58.
Lewis, P. A. & Miall, R. C. (2003) Distinct systems for automatic and cognitively controlled time measurement: Evidence from neuroimaging. Current Opinion in Neurobiology 13:250–55.
Libertus, M. E., Woldorff, M. G. & Brannon, E. M. (2007) Electrophysiological evidence for notation independence in numerical processing. Behavioral Brain Function 3(1). (Online journal).
Lindemann, O., Abolafia, J. M., Pratt, J. & Bekkering, H. (2008) Coding strategies in number space: Memory requirements influence spatial–numerical associations. Quarterly Journal of Experimental Psychology 61:515–24.
Link, S. (1990) Modeling imageless thought: The relative judgment theory of numerical comparisons. Journal of Mathematical Psychology 34:241.
Logan, G. D. (1985) Skill and automaticity: Relations, implications, and future directions. Canadian Journal of Psychology 39:367–86.
Lueck, C. J., Zeki, S., Friston, K. J., Deiber, M.-P., Cope, P., Cunningham, V. J., Lammertsma, A. A., Kennard, C. & Frackowiac, R. S. J. (1989) The colour centre in the cerebral cortex of man. Nature 340:386–89.
Macaruso, P., McCloskey, M. & Aliminosa, D. (1993) The functional architecture of the cognitive numerical-processing system: Evidence from a patient with multiple impairments. Cognitive Neuropsychology 10:341–76.
Mapelli, D., Rusconi, E. & Umilta, C. (2003) The SNARC effect: An instance of the Simon effect? Cognition 88:B1B10.
Markman, A. B. & Dietrich, E. (2000) Extending the classical view of representation. Trends in Cognitive Sciences 4:470–75.
McCandliss, B. D., Cohen, L. & Dehaene, S. (2003) The visual word form area: Expertise for reading in the fusiform gyrus. Trends in Cognitive Sciences 7:293–99.
McCloskey, M. (1992) Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition 44:107–57.
McCloskey, M., Caramazza, A. & Basili, A. (1985) Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. Brain and Cognition 4:171–96.
Merigan, W. H. (1996) Basic visual capacities and shape discrimination after lesions of extrastriate area V4 in macaques. Visual Neuroscience 13:5160.
Miller, E. K. & Cohen, J. D. (2001) An integrative theory of prefrontal cortex function. Annual Review of Neuroscience 24:167202.
Moyer, R. S. & Landauer, T. K. (1967) Time required for judgment of numerical inequality. Nature 215:1519–20.
Mussolin, C. & Noel, M.-P. (2007) The nonintentional processing of Arabic numbers in children. Journal of Clinical and Experimental Neuropsychology 29:225–34.
Naccache, L. & Dehaene, S. (2001a) The priming method: Imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobes. Cerebral Cortex 11(10):966–74.
Naccache, L. & Dehaene, S. (2001b) Unconscious semantic priming extends to novel unseen stimuli. Cognition 80:223–37.
Neely, J. H. (1977) Semantic priming and retrieval from lexical memory: Roles of inhibitionless spreading activation and limited-capacity attention. Journal of Experimental Psychology: General 106:226–54.
Nieder, A. (2004) The number domain – can we count on parietal cortex? Neuron 44:407–09.
Nieder, A. (2005) Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience 6:177–90.
Nieder, A., Diester, I. & Tudusciuc, O. (2006) Temporal and spatial enumeration processes in the primate parietal cortex. Science 313(5792):1431–35.
Nieder, A., Freedman, D. J. & Miller, E. K. (2002) Representation of the quantity of visual items in the primate prefrontal cortex. Science 297:1708–11.
Nieder, A. & Miller, E. K. (2003) Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37:149–57.
Nieder, A. & Miller, E. K. (2004) A parieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Science, USA 101:7457–62.
Noël, M.-P. & Seron, X. (1993) Arabic number reading deficit: A single case study. Cognitive Neuropsychology 10:317–39.
Noël, M.-P. & Seron, X. (1997) On the existence of intermediate representations in numerical processing. Journal of Experimental Psychology: Learning, Memory, and Cognition 23:697720.
Nuerk, H.-C., Kaufmann, L., Zoppoth, S. & Willmes, K. (2004a) On the development of the mental number line: More, less, or never holistic with increasing age? Developmental Psychology 40:11991211.
Nuerk, H.-C., Weger, U. & Willmes, K. (2001) Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition 82:B25B33.
Nuerk, H.-C., Weger, U. & Willmes, K. (2002) A unit-decade compatibility effect in German number words. Current Psychology Letters: Behaviour, Brain, and Cognition 2:1938.
Nuerk, H.-C., Weger, U. & Willmes, K. (2004b) On the perceptual generality of the unit-decade compatibility effect. Experimental Psychology 51:7279.
Nuerk, H. C., Wood, G. & Willmes, K. (2005) The universal SNARC effect: The association between number magnitude and space is amodal. Experimental Psychology 52:187–94.
Orban, G. A., Dupont, P., Vogels, R., De Bruyn, B., Bormans, G. & Mortelmans, L. (1996) Task dependency of visual processing in the human visual system. Behavioural Brain Research 76:215–23.
Otten, L. J. & Rugg, M. D. (2001) Electrophysiological correlates of memory encoding are task-dependent. Cognitive Brain Research 12:1118.
Paivio, A. (1971) Imagery and mental processes. Holt, Rinehart, & Winston.
Pakkenberg, B. & Gundersen, H. J. G. (1997) Neocortical neuron number in humans: Effect of sex and age. The Journal of Comparative Neurology 384:312–20.
Parsons, S. & Bynner, J. (2005). Does numeracy matter more? NRDC (National Research and Development Centre for adult literacy and numeracy).
Passarotti, A. M., Paul, B. M., Bussiere, J. R., Buxton, R. B., Wong, E. C. & Stiles, J. (2003) The development of face and location processing: An fMRI study. Developmental Science 6:100–17.
Pavese, A. & Umiltà, C. (1998) Symbolic distance between numerosity and identity modulates Stroop interference. Journal of Experimental Psychology: Human Perception and Performance 24:1535–45.
Perlman, A. & Tzelgov, J. (2006) Interactions between encoding and retrieval in the domain of sequence-learning. Journal of Experimental Psychology: Learning, Memory and Cognition 32:118–30.
Pesenti, M., Thioux, M., Seron, X. & De Volder, A., (2000) Neuroanatomical substrates of Arabic number processing, numerical comparison, and simple addition: A PET study. Journal of Cognitive Neuroscience 12:461–79.
Piazza, M., Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. (2004) Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44(3):547–55.
Piazza, M., Mechelli, A., Price, C. J. & Butterworth, B. (2006) Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research 1106:177–88.
Piazza, M., Pinel, P., Le Bihan, D. & Dehaene, S. (2007) A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53(2):293305.
Pillon, A. & Pesenti, M. (2001) Calculating without reading? Comments on Cohen and Dehaene (2000). Cognitive Neuropsychology 18:275–84.
Pinel, P., Dehaene, S., Rivière, D. & Le Bihan, D. (2001) Modulation of parietal activation by semantic distance in a number comparison task. NeuroImage 14:1013–26.
Pinel, P., Piazza, M., Le Bihan, D. & Dehaene, S. (2004) Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 41(6):983–93.
Pitcher, D., Walsh, V., Yovel, G. & Duchaine, B. (2007) TMS evidence for the involvement of the right occipital face area in early face processing. Current Biology 17:1568–73.
Posner, M. I. (1978) Chronometric explorations of mind. Erlbaum.
Posner, M. I. (2003) Imaging a science of mind. Trends in Cognitive Sciences 7:450–53.
Price, C. J. & Devlin, J. T. (2003) The myth of the visual word form area. NeuroImage 19:473–81.
Revkin, S. K., Piazza, M., Izard, V., Zamarian, L., Karner, E. & Delazer, M. (2008) Verbal numerosity estimation deficit in the context of spared semantic representation of numbers: A neuropsychological study of a patient. Neuropsychologia 46:2463–75.
Reynvoet, B. & Ratinckx, E. (2004) Hemispheric differences between left and right number representations: Effects of conscious and unconscious priming. Neuropsychologia 42:713–26.
Roitman, J. D., Brannon, E. M. & Platt, M. L. (2007) Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biology 5(8):e208.
Rosenbaum, D. A., Carlson, R. A. & Gilmore, R. O. (2001) Acquisition of intellectual and perceptual-motor skills. Annual Review of Psychology 52:453–70.
Rubinsten, O. & Henik, A. (2005) Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology 19:641–48.
Rubinsten, O. & Henik, A. (2006) Double dissociation of functions in developmental dyslexia and dyscalculia. Journal of Educational Psychology 98:854–67.
Rubinsten, O. & Henik, A. (2009) Developmental dyscalculia: Heterogeneity may not mean different mechanisms. Trends in Cognitive Sciences 13:9299.
Rubinsten, O., Henik, A., Berger, A. & Shahar-Shalev, S. (2002) The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology 81:7492.
Rumelhart, D. E. & McClelland, J. L. (1986) Parallel distributed processing: Explorations in the microstructure of cognition. MIT Press/Bradford Books.
Sato, T. R. & Schall, J. D. (2003) Effects of stimulus-response compatibility on neural selection in frontal eye field. Neuron 38:637–48.
Sawamura, H., Orban, G. A. & Vogels, R. (2006) Selectivity of neuronal adaptation does not match response selectivity: A single-cell study of the fMRI adaptation paradigm. Neuron 49(2):307–18.
Schafer, R. J. & Moore, T. (2007) Attention governs action in the primate frontal eye field. Neuron 56:541–51.
Schwarz, W. & Heinze, H. J. (1998) On the interaction of numerical and size information in digit comparison: A behavioral and event-related potential study. Neuropsychologia 36:1167–79.
Schwarz, W. & Ischebeck, A. (2000) Sequential effects in number comparison. Journal of Experimental Psychology: Human Perception and Performance 26:1606–21.
Schwarz, W. & Ischebeck, A. (2003) On the relative speed account of the number-size interference in comparative judgment of numerals. Journal of Experimental Psychology: Human Perception and Performance 29:507–22.
Schwarz, W. & Keus, I. M. (2004) Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses. Perception and Psychophysics 66:651–64.
Shaki, S. & Fischer, M. H. (2008) Reading space into numbers – a cross-linguistic comparison of the SNARC effect. Cognition 108:590–99.
Shaki, S. & Petrusic, W. M. (2005) On the mental representation of negative numbers: Context-dependent SNARC effects with comparative judgments. Psychonomic Bulletin and Review 12:931–37.
Shuman, M. & Kanwisher, N. (2004) Numerical magnitude in the human parietal lobe: Tests of representational generality and domain specificity. Neuron 44(3):557–69.
Siegler, R. S. & Booth, J. L. (2004) Development of numerical estimation in young children. Child Development 75:428–44.
Silvanto, J. & Muggleton, N. G. (2008a) New light through old windows: Moving beyond the “virtual lesion” approach to transcranial magnetic stimulation. NeuroImage 39:549–52.
Silvanto, J. & Muggleton, N. G. (2008b) Testing the validity of the TMS state-dependency approach: Targeting functionally distinct motion-selective neural populations in visual areas V1/V2 and V5/MT+. NeuroImage 40:1841–48.
Silvanto, J., Muggleton, N. G., Cowey, A. & Walsh, V. (2007) Neural adaptation reveals state-dependent effects of transcranial magnetic stimulation. European Journal of Neuroscience 25:1874–81.
Silvanto, J., Muggleton, N. & Walsh, V. (2008) State dependency in brain stimulation studies of perception and cognition. Trends in Cognitive Sciences 12:447–54.
Soetens, E. (1998) Localizing sequential effects in serial choice reaction time with the information reduction procedure. Journal of Experimental Psychology: Human Perception and Performance 24:547–68.
Sokol, S. M., McCloskey, M., Cohen, N. J. & Aliminosa, D. (1991) Cognitive representations and processes in arithmetic: Inferences from the performance of brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory and Cognition 17:355–76.
Solomon, K. O. & Barsalou, L. W. (2004) Perceptual simulation in property verification. Memory and Cognition 32: 244–59.
Szűcs, D. & Soltész, F. (2007) Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia 45:3190–202.
Szűcs, D., Soltész, F., Jármi, É. & Csépe, V. (2007) The speed of magnitude processing and executive functions in controlled and automatic number comparison in children: An electro-encephalography study. Behavioral and Brain Functions 3 (23). (Online journal).
Takayama, Y., Sugishita, M., Akiguchi, I. & Kimura, J. (1994) Isolated acalculia due to left parietal lesion. Archives of Neurology 51:286–91.
Tang, J., Critchley, H. D., Glaser, D., Dolan, R. J. & Butterworth, B. (2006a) Imaging informational conflict: A functional magnetic resonance imaging study of numerical Stroop. Journal of Cognitive Neuroscience 18:2049–62.
Tudusciuc, O. & Nieder, A. (2007) Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proceedings of the National Academy of Sciences USA 104(36):14513–18.
Turconi, E., Jemel, B., Rossion, B. & Seron, X. (2004) Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research 21:2238.
Tzelgov, J. & Ganor-Stern, D. (2005) Automaticity in processing ordinal information. In: Handbook of mathematical cognition, ed. Campbell, J. I. D., pp. 5566. Psychology Press.
Tzelgov, J., Henik, A., Sneg, R. & Baruch, O. (1996) Unintentional word reading via the phonological route: The Stroop effect in cross-script homophones. Journal of Experimental Psychology: Learning, Memory, and Cognition 22:336–49.
Tzelgov, J., Meyer, J. & Henik, A. (1992) Automatic and intentional processing of numerical information. Journal of Experimental Psychology: Learning, Memory and Cognition 18:166–79.
Van Harskamp, N. J. & Cipolotti, L. (2001) Selective impairment for addition, subtraction and multiplication. Implication for the organisation of arithmetical facts. Cortex 37:363–88.
Van Harskamp, N. J., Rudge, P. & Cipolotti, L. (2002) Are multiplication facts implemented by the left supramarginal and angular gyri? Neuropsychologia 40:1786–93.
Van Opstal, F., Gevers, W., De Moor, W. & Verguts, T. (2008a) Dissecting the symbolic distance effect: Comparison and priming effects in numerical and non-numerical orders. Psychonomic Bulletin and Review 15:419–25.
Venkatraman, V., Ansari, D. & Chee, M. W. L. (2005) Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia 43:744–53.
Verguts, T. & Fias, W. (2004) Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience 16(9):1493–504.
Verguts, T., Fias, W. & Stevens, M. (2005) A model of exact small-number representation. Psychonomic Bulletin and Review 12:6680.
Verguts, T. & Van Opstal, F., (2005) Dissociation of the distance effect and size effect in one-digit numbers. Psychonomic Bulletin and Review 12:925–30.
von Aster, M. G. & Shalev, R. S. (2007) Number development and developmental dyscalculia. Developmental Medicine and Child Neurology 49:868–73.
Vuilleumier, P., Ortigue, S. & Brugger, P. (2004) The number space and neglect. Cortex 40:399410.
Walsh, V. (2003) A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences 7(11):483–88.
Walsh, V. & Pascual-Leone, A. (2003) Transcranial magnetic stimulation: A neurochronometric of mind. MIT Press.
Washburn, D. A. (1994) Stroop-like effects for monkeys and humans: Processing speed or strength of association? Psychological Science 5:375–79.
Watanabe, T., Harner, A., Miyauchi, S., Sasaki, Y., Nielsen, M., Palomo, D. & Mukai, I. (1998) Task-dependent influences of attention on the activation of human primary visual cortex. Proceedings of the National Academy of Sciences USA 95:11489–92.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L. & Cohen, D. (2006a) Principles underlying the design of “The Number Race,” an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions 2:19.
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L. & Dehaene, S. (2006b) An open trial assessment of “The Number Race,” an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions 2:20.
Wood, G., Nuerk, H.-C. & Willmes, K. (2006a) Crossed hands and the SNARC effect: A failure to replicate Dehaene, Bossini and Giraux (1993). Cortex 42:1069–79.
Wood, G., Nuerk, H.-C. & Willmes, K. (2006b) Neural representations of two-digit numbers: A parametric fMRI study. NeuroImage 29:358–67.
Wood, G., Nuerk, H.-C., Willmes, K. & Fischer, M. H. (2008) On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly 50:489525.
Xue, G. & Poldrack, R. A. (2007) The neural substrates of visual perceptual learning of words: Implications for the visual word form area hypothesis. Journal of Cognitive Neuroscience 19:1643–55.
Zeki, S. (1974) Functional organization of a visual area in the posterior bank of the superior temporal sulcus of the rhesus monkey. Journal of Physiology 236:549–73.
Zeki, S. (1980) The representation of colours in the cerebral cortex. Nature 284:412–18.
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H. & Dong, Q. (2007) Chinese kindergartners' automatic processing of numerical magnitude in Stroop-like tasks. Memory and Cognition 35:464–70.
Zorzi, M., Priftis, K. & Umiltà, C. (2002) Neglect disrupts the number line. Nature 417:138–39.
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Behavioral and Brain Sciences
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  • EISSN: 1469-1825
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