Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-2qt69 Total loading time: 0.935 Render date: 2022-08-18T18:34:41.359Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

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

Published online by Cambridge University Press:  27 August 2009

Roi Cohen Kadosh
Affiliation:
Institute of Cognitive Neuroscience and Department of Psychology, University College London, London WC1N 3AR, United Kingdomroi.cohenkadosh@psy.ox.ac.ukhttp://www.ucl.ac.uk/neuroscience/Page.php?ID=12&ResearcherID=238
Vincent Walsh
Affiliation:
Institute of Cognitive Neuroscience and Department of Psychology, University College London, London WC1N 3AR, United Kingdomv.walsh@ucl.ac.ukhttp://www.icn.ucl.ac.uk/Research-Groups/Visual-Cognition-Group/index.php

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.

Type
Main Articles
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ansari, D. (2007) Does the parietal cortex distinguish between “10,” “Ten,” and ten dots? Neuron 53:165–67.CrossRefGoogle Scholar
Ansari, D. (2008) Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 9(4):278–91.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Ansari, D. & Karmiloff-Smith, A. (2002) Atypical trajectories of number development: A neuroconstructivist perspective. Trends in Cognitive Sciences 6:511–16.CrossRefGoogle Scholar
Ashkenazi, S., Henik, A., Ifergane, G. & Shelef, I. (2008) Basic numerical processing in left intraparietal sulcus (IPS) acalculia. Cortex 44:439–48.CrossRefGoogle ScholarPubMed
Bächtold, D., Baumuller, M. & Brugger, P. (1998) Stimulus-response compatibility in representational space. Neuropsychologia 36:731–35.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle Scholar
Barsalou, L. W. (1999) Perceptual symbol systems. Behavioral and Brain Sciences 22:577660.Google ScholarPubMed
Barsalou, L. W. (2003) Abstraction in perceptual symbol systems. Philosophical Transactions of the Royal Society B: Biological Sciences 358:1177–87.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Barth, H., Kanwisher, N. & Spelke, E. (2003) The construction of large number representations in adults. Cognition 86:201–21.CrossRefGoogle ScholarPubMed
Brannon, E. M. (2006) The representation of numerical magnitude. Current Opinion in Neurobiology 16:222–29.CrossRefGoogle ScholarPubMed
Butterworth, B. (1999) The mathematical brain. Macmillan.Google ScholarPubMed
Butterworth, B. (2004) Developmental dyscalculia. In: Handbook of mathematical cognition, ed. Campbell, J. I. D.. Psychology Press.Google Scholar
Butterworth, B. (2005) The development of arithmetical abilities. Journal of Child Psychology and Psychiatry 46:318.CrossRefGoogle ScholarPubMed
Calabrese, R. L. (2007) Motor networks: Shifting coalitions. Current Biology 17:R139R141.CrossRefGoogle ScholarPubMed
Campbell, J. I. D. (1994) Architectures for numerical cognition. Cognition 53(1):144.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Cantlon, J. F., Platt, M. L. & Brannon, E. M. (2009) Beyond the number domain. Trends in Cognitive Sciences 13:8391.CrossRefGoogle ScholarPubMed
Carr, T. H. (1992) Automaticity and cognitive anatomy: Is word recognition “automatic”? American Journal of Psychology 105:201–37.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
Cohen Kadosh, K. & Johnson, M. H. (2007) Developing a cortex specialized for face perception. Trends in Cognitive Sciences 11:367–69.CrossRefGoogle ScholarPubMed
Cohen Kadosh, R., (2008a) Numerical representation: Abstract or non-abstract? Quarterly Journal of Experimental Psychology 61(8):1160–68.CrossRefGoogle ScholarPubMed
Cohen Kadosh, R., (2008b) The laterality effect: Myth or truth? Consciousness and Cognition 17:350–54.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Cohen Kadosh, R., Cohen Kadosh, K. & Henik, A. (2008c) When brightness counts: The neuronal correlate of numerical-luminance interference. Cerebral Cortex 18:337–43.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Cohen Kadosh, R. & Henik, A. (2006) A common representation for semantic and physical properties: A cognitive-anatomical approach. Experimental Psychology 53:8794.CrossRefGoogle ScholarPubMed
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.Google ScholarPubMed
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.Google ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Cohen Kadosh, R., Muggleton, N., Slivanto, J. & Walsh, V. (submitted b) Modulating number-specific neurons in the human parietal cortex.Google Scholar
Cohen Kadosh, R., Tzelgov, J. & Henik, A. (2008g) A synesthetic walk on the mental number line: The size effect. Cognition 106:548–57.CrossRefGoogle Scholar
Cohen Kadosh, R. & Walsh, V. (2007) Dyscalculia. Current Biology 17:R946R947.CrossRefGoogle ScholarPubMed
Cohen Kadosh, R. & Walsh, V. (2008) From magnitude to natural numbers: A developmental neurocognitive perspective. Behavioral and Brain Sciences 31:647–48.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Dehaene, S. (1992) Varieties of numerical abilities. Cognition 44:142.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.Google ScholarPubMed
Dehaene, S., Bossini, S. & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 122:371–96.CrossRefGoogle Scholar
Dehaene, S. & Cohen, L. (1997) Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33:219–50.CrossRefGoogle ScholarPubMed
Dehaene, S., Dehaene-Lambertz, G. & Cohen, L. (1998a) Abstract representations of numbers in the animal and human brain. Trends in Neurosciences 21:355–61.CrossRefGoogle ScholarPubMed
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.Google ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2003) Three parietal circuits for number processing. Cognitive Neuropsychology 20(3–6):487506.CrossRefGoogle ScholarPubMed
Delazer, M. & Benke, T. (1997) Arithmetic facts without meaning. Cortex 33:697710.CrossRefGoogle ScholarPubMed
Delazer, M., Karner, E., Zamarian, L., Donnemiller, E. & Benke, T. (2006) Number processing in posterior cortical atrophy – a neuropsycholgical case study. Neuropsychologia 44:3651.CrossRefGoogle ScholarPubMed
Diester, I. & Nieder, A. (2007) Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biology 5 (11):e294; 2684–95.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Dormal, V., Seron, X. & Pesenti, M. (2006) Numerosity-duration interference: A Stroop experiment. Acta Psychologica 121:109124.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Duncan, J. (2001) An adaptive coding model of neural function in prefrontal cortex. Nature Reviews Neuroscience 2:820–29.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Fias, W. (2001) Two routes for the processing of verbal numbers: Evidence from the SNARC effect. Psychological Research – Psychologische Forschung 65(4):242–49.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Fias, W. & Fischer, M. H. (2004) Spatial representation of numbers. In: Handbook of mathematical cognition, ed. Campbell, J. I. D.. Psychology Press.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Fias, W., Reynvoet, B. & Brysbaert, M. (2001b) Are arabic numerals processed as pictures in a Stroop inteference task? Psychological Research 65:242–49.CrossRefGoogle Scholar
Fischer, M. H. & Rottmann, J. (2005) Do negative numbers have a place on the mental number line? Psychology Science 47(1):2232.Google Scholar
Gallistel, C. R. & Gelman, R. (1992) Preverbal and verbal counting and computation. Cognition 44:4374.CrossRefGoogle ScholarPubMed
Ganor-Stern, D. & Tzelgov, J. (2008) Across-notation automatic numerical processing. Journal of Experimental Psychology: Learning, Memory and Cognition 34(2):430–37.Google ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Gevers, W. & Lammertyn, J. (2005) The hunt for SNARC. Psychology Science 47:1021.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Gilbert, S. J. & Burgess, P. W. (2008) Executive function. Current Biology 19:R110R114.CrossRefGoogle Scholar
Girelli, L., Lucangeli, D. & Butterworth, B. (2000) The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology 76(2): 104–22.CrossRefGoogle ScholarPubMed
Glaser, W. R. (1992) Picture naming. Cognition 42:61105.CrossRefGoogle ScholarPubMed
Glickstein, M. (2007) What does the cerebellum really do? Current Biology 17:R824–27.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Grill-Spector, K., Henson, R. & Martin, A. (2006a) Repetition and the brain: Neural models of stimulus-specific effects. Trends in Cognitive Sciences 10:1423.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Hasher, L. & Zacks, R. T. (1979) Automatic and effortful processes in memory. Journal of Experimental Psychology: General 108:356–88.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Holloway, I. D. & Ansari, D. (2008) Domain-specific and domain-general changes in children's development of number comparison. Developmental Science 11:644–49.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Ischebeck, A. (2003) Differences between digit naming and number word reading in a flanker task. Memory and Cognition 31:529–37.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Ito, Y. & Hatta, T. (2004) Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect. Memory and Cognition 32(4):662–73.CrossRefGoogle ScholarPubMed
Izard, V. & Dehaene, S. (2008) Calibrating the mental number line. Cognition 106:1221–47.CrossRefGoogle Scholar
Izard, V., Dehaene-Lambertz, G. & Dehaene, S. (2008) Distinct cerebral pathways for object identity and number in human infants. PLoS Biology 6:e11.CrossRefGoogle Scholar
Johnson, M. H. (2001) Functional brain development in humans. Nature Reviews Neuroscience 2(7):475–83.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Johnson, M. H. & Munakata, Y. (2005) Processes of change in brain and cognitive development. Trends in Cognitive Sciences 9:152–58.CrossRefGoogle ScholarPubMed
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.Google ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
Lammertyn, J., Fias, W. & Lauwereyns, J. (2002) Semantic influences on feature-based attention due to overlap of neural circuits. Cortex 38:878–82.CrossRefGoogle Scholar
Lemer, C., Dehaene, S., Spelke, E. & Cohen, L. (2003) Approximate quantities and exact number words: Dissociable systems. Neuropsychologia 41:1942–58.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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).CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Link, S. (1990) Modeling imageless thought: The relative judgment theory of numerical comparisons. Journal of Mathematical Psychology 34:241.CrossRefGoogle Scholar
Logan, G. D. (1985) Skill and automaticity: Relations, implications, and future directions. Canadian Journal of Psychology 39:367–86.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Mapelli, D., Rusconi, E. & Umilta, C. (2003) The SNARC effect: An instance of the Simon effect? Cognition 88:B1B10.CrossRefGoogle ScholarPubMed
Markman, A. B. & Dietrich, E. (2000) Extending the classical view of representation. Trends in Cognitive Sciences 4:470–75.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
McCloskey, M. (1992) Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition 44:107–57.CrossRefGoogle ScholarPubMed
McCloskey, M., Caramazza, A. & Basili, A. (1985) Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. Brain and Cognition 4:171–96.CrossRefGoogle ScholarPubMed
Merigan, W. H. (1996) Basic visual capacities and shape discrimination after lesions of extrastriate area V4 in macaques. Visual Neuroscience 13:5160.CrossRefGoogle ScholarPubMed
Miller, E. K. & Cohen, J. D. (2001) An integrative theory of prefrontal cortex function. Annual Review of Neuroscience 24:167202.CrossRefGoogle ScholarPubMed
Moyer, R. S. & Landauer, T. K. (1967) Time required for judgment of numerical inequality. Nature 215:1519–20.CrossRefGoogle ScholarPubMed
Mussolin, C. & Noel, M.-P. (2007) The nonintentional processing of Arabic numbers in children. Journal of Clinical and Experimental Neuropsychology 29:225–34.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Naccache, L. & Dehaene, S. (2001b) Unconscious semantic priming extends to novel unseen stimuli. Cognition 80:223–37.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Nieder, A. (2004) The number domain – can we count on parietal cortex? Neuron 44:407–09.CrossRefGoogle ScholarPubMed
Nieder, A. (2005) Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience 6:177–90.CrossRefGoogle ScholarPubMed
Nieder, A., Diester, I. & Tudusciuc, O. (2006) Temporal and spatial enumeration processes in the primate parietal cortex. Science 313(5792):1431–35.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Nieder, A. & Miller, E. K. (2003) Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37:149–57.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Noël, M.-P. & Seron, X. (1993) Arabic number reading deficit: A single case study. Cognitive Neuropsychology 10:317–39.Google Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.Google Scholar
Nuerk, H.-C., Weger, U. & Willmes, K. (2004b) On the perceptual generality of the unit-decade compatibility effect. Experimental Psychology 51:7279.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Otten, L. J. & Rugg, M. D. (2001) Electrophysiological correlates of memory encoding are task-dependent. Cognitive Brain Research 12:1118.CrossRefGoogle ScholarPubMed
Paivio, A. (1971) Imagery and mental processes. Holt, Rinehart, & Winston.Google Scholar
Pakkenberg, B. & Gundersen, H. J. G. (1997) Neocortical neuron number in humans: Effect of sex and age. The Journal of Comparative Neurology 384:312–20.3.0.CO;2-K>CrossRefGoogle ScholarPubMed
Parsons, S. & Bynner, J. (2005). Does numeracy matter more? NRDC (National Research and Development Centre for adult literacy and numeracy).Google Scholar
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.CrossRefGoogle Scholar
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.Google ScholarPubMed
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.Google ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Pillon, A. & Pesenti, M. (2001) Calculating without reading? Comments on Cohen and Dehaene (2000). Cognitive Neuropsychology 18:275–84.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Posner, M. I. (1978) Chronometric explorations of mind. Erlbaum.Google Scholar
Posner, M. I. (2003) Imaging a science of mind. Trends in Cognitive Sciences 7:450–53.CrossRefGoogle ScholarPubMed
Price, C. J. & Devlin, J. T. (2003) The myth of the visual word form area. NeuroImage 19:473–81.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Reynvoet, B. & Ratinckx, E. (2004) Hemispheric differences between left and right number representations: Effects of conscious and unconscious priming. Neuropsychologia 42:713–26.CrossRefGoogle ScholarPubMed
Roitman, J. D., Brannon, E. M. & Platt, M. L. (2007) Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biology 5(8):e208.CrossRefGoogle ScholarPubMed
Rosenbaum, D. A., Carlson, R. A. & Gilmore, R. O. (2001) Acquisition of intellectual and perceptual-motor skills. Annual Review of Psychology 52:453–70.CrossRefGoogle ScholarPubMed
Rubinsten, O. & Henik, A. (2005) Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology 19:641–48.CrossRefGoogle ScholarPubMed
Rubinsten, O. & Henik, A. (2006) Double dissociation of functions in developmental dyslexia and dyscalculia. Journal of Educational Psychology 98:854–67.CrossRefGoogle Scholar
Rubinsten, O. & Henik, A. (2009) Developmental dyscalculia: Heterogeneity may not mean different mechanisms. Trends in Cognitive Sciences 13:9299.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Rumelhart, D. E. & McClelland, J. L. (1986) Parallel distributed processing: Explorations in the microstructure of cognition. MIT Press/Bradford Books.Google Scholar
Sato, T. R. & Schall, J. D. (2003) Effects of stimulus-response compatibility on neural selection in frontal eye field. Neuron 38:637–48.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Schafer, R. J. & Moore, T. (2007) Attention governs action in the primate frontal eye field. Neuron 56:541–51.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Schwarz, W. & Ischebeck, A. (2000) Sequential effects in number comparison. Journal of Experimental Psychology: Human Perception and Performance 26:1606–21.Google ScholarPubMed
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.Google ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Shaki, S. & Fischer, M. H. (2008) Reading space into numbers – a cross-linguistic comparison of the SNARC effect. Cognition 108:590–99.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Shuman, M. & Kanwisher, N. (2004) Numerical magnitude in the human parietal lobe: Tests of representational generality and domain specificity. Neuron 44(3):557–69.CrossRefGoogle ScholarPubMed
Siegler, R. S. & Booth, J. L. (2004) Development of numerical estimation in young children. Child Development 75:428–44.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Silvanto, J., Muggleton, N. & Walsh, V. (2008) State dependency in brain stimulation studies of perception and cognition. Trends in Cognitive Sciences 12:447–54.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.Google ScholarPubMed
Solomon, K. O. & Barsalou, L. W. (2004) Perceptual simulation in property verification. Memory and Cognition 32: 244–59.CrossRefGoogle ScholarPubMed
Szűcs, D. & Soltész, F. (2007) Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia 45:3190–202.CrossRefGoogle ScholarPubMed
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).CrossRefGoogle ScholarPubMed
Takayama, Y., Sugishita, M., Akiguchi, I. & Kimura, J. (1994) Isolated acalculia due to left parietal lesion. Archives of Neurology 51:286–91.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Van Harskamp, N. J., Rudge, P. & Cipolotti, L. (2002) Are multiplication facts implemented by the left supramarginal and angular gyri? Neuropsychologia 40:1786–93.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Venkatraman, V., Ansari, D. & Chee, M. W. L. (2005) Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia 43:744–53.CrossRefGoogle ScholarPubMed
Verguts, T. & Fias, W. (2004) Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience 16(9):1493–504.CrossRefGoogle ScholarPubMed
Verguts, T., Fias, W. & Stevens, M. (2005) A model of exact small-number representation. Psychonomic Bulletin and Review 12:6680.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
von Aster, M. G. & Shalev, R. S. (2007) Number development and developmental dyscalculia. Developmental Medicine and Child Neurology 49:868–73.CrossRefGoogle ScholarPubMed
Vuilleumier, P., Ortigue, S. & Brugger, P. (2004) The number space and neglect. Cortex 40:399410.CrossRefGoogle ScholarPubMed
Walsh, V. (2003) A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences 7(11):483–88.CrossRefGoogle ScholarPubMed
Walsh, V. & Pascual-Leone, A. (2003) Transcranial magnetic stimulation: A neurochronometric of mind. MIT Press.Google Scholar
Washburn, D. A. (1994) Stroop-like effects for monkeys and humans: Processing speed or strength of association? Psychological Science 5:375–79.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Wood, G., Nuerk, H.-C. & Willmes, K. (2006b) Neural representations of two-digit numbers: A parametric fMRI study. NeuroImage 29:358–67.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Zeki, S. (1980) The representation of colours in the cerebral cortex. Nature 284:412–18.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Zorzi, M., Priftis, K. & Umiltà, C. (2002) Neglect disrupts the number line. Nature 417:138–39.CrossRefGoogle ScholarPubMed
191
Cited by