627
Views
10
CrossRef citations to date
0
Altmetric
Articles

Primitive Concepts of Number and the Developing Human Brain

&

References

  • Agrillo, C., & Beran, M. J. (2013). Number without language: Comparative psychology and the evolution of numerical cognition. Frontiers in Psychology, 4, 295. doi:10.3389/fpsyg.2013.00295
  • Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278–291. doi:10.1038/nrn2334
  • 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, 1820–1828. doi:10.1162/jocn.2006.18.11.1820
  • Ansari, D., Dhital, B., & Siong, S. C. (2006). Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes. Brain Research, 1067, 181–188. doi:10.1016/j.brainres.2005.10.083
  • Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. NeuroReport, 16, 1769–1773. doi:10.1097/01.wnr.0000183905.23396.f1
  • Barnard, A. M., Hughes, K. D., Gerhardt, R. R., DiVincenti, L., Bovee, J. M., & Cantlon, J. F. (2013). Inherently analog quantity representations in olive baboons (Papio anubis). Frontiers in Psychology, 4, 253. doi:10.3389/fpsyg.2013.00253
  • Barth, H., Kanwisher, N., & Spelke, E. (2003). The construction of large number representations in adults. Cognition, 86, 201–221. doi:10.1016/S0010-0277(02)00178-6
  • Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102, 14116–14121. doi:10.1073/pnas.0505512102
  • Beran, M. J., Decker, S., Schwartz, A., & Schultz, N. (2011). Monkeys (Macaca mulatta and Cebus apella) and human adults and children (Homo sapiens) compare subsets of moving stimuli based on numerosity. Frontiers in Psychology, 2, 61. doi:10.3389/fpsyg.2011.00061
  • Berteletti, I., Man, G., & Booth, J. R. (2014). How number line estimation skills relate to neural activations in single digit subtraction problems. NeuroImage, 107C, 198–206.
  • Biro, D., & Matsuzawa, T. (1999). Numerical ordering in a chimpanzee (Pan troglodytes): Planning, executing, and monitoring. Journal of Comparative Psychology, 113, 178–185. doi:10.1037/0735-7036.113.2.178
  • Biro, D., & Matsuzawa, T. (2008). Chimpanzee numerical competence: Cardinal and ordinal skills. In Primate Origins of Human Cognition and Behavior (pp. 199–225). Tokyo, Japan: Springer.
  • Bookheimer, S. (2002). Functional MRI of language: New approaches to understanding the cortical organization of semantic processing. In Tetsuro Matsuzawa (Ed.), Annual Review of Neuroscience, 25, 151–188. doi:10.1146/annurev.neuro.25.112701.142946
  • Boysen, S. T., & Hallberg, K. I. (2000). Primate numerical competence: Contributions toward understanding nonhuman cognition. Cognitive Science, 24, 423–443. doi:10.1207/s15516709cog2403_4
  • Brannon, E. M. (2006). The representation of numerical magnitude. Current Opinion in Neurobiology, 16, 222–229. doi:10.1016/j.conb.2006.03.002
  • Brannon, E. M., & van de Walle, G. A. (2001). The development of ordinal numerical competence in young children. Cognitive Psychology, 43, 53–81. doi:10.1006/cogp.2001.0756
  • Bugden, S., Price, G. R., McLean, D. A., & Ansari, D. (2012). The role of the left intraparietal sulcus in the relationship between symbolic number processing and children’s arithmetic competence. Developmental Cognitive Neuroscience, 2, 448–457. doi:10.1016/j.dcn.2012.04.001
  • Bulthé, J., de Smedt, B., & Op de Beeck, H. P. (2014). Format-dependent representations of symbolic and non-symbolic numbers in the human cortex as revealed by multi-voxel pattern analyses. NeuroImage, 87, 311–322. doi:10.1016/j.neuroimage.2013.10.049
  • Cantlon, J., Fink, R., Safford, K., & Brannon, E. M. (2007). Heterogeneity impairs numerical matching but not numerical ordering in preschool children. Developmental Science, 10, 431–440. doi:10.1111/desc.2007.10.issue-4
  • Cantlon, J. F. (2012). Math, monkeys, and the developing brain. Proceedings of the National Academy of Sciences, 109, 10725–10732. doi:10.1073/pnas.1201893109
  • Cantlon, J. F., & Brannon, E. M. (2006). Shared system for ordering small and large numbers in monkeys and humans. Psychological Science, 17, 401–406. doi:10.1111/j.1467-9280.2006.01719.x
  • 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. doi:10.1371/journal.pbio.0040125
  • Cantlon, J. F., & Li, R. (2013). Neural activity during natural viewing of Sesame Street statistically predicts test scores in early childhood. Plos Biology, 11, e1001462. doi:10.1371/journal.pbio.1001462
  • 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, 2217–2229. doi:10.1162/jocn.2008.21159
  • Cantlon, J. F., Piantadosi, S. T., Ferrigno, S., Hughes, K. D., & Barnard, A. M. (2015). The origins of counting algorithms. Psychological Science, 26, 853–865. doi:10.1177/0956797615572907
  • Cantrell, L., Boyer, T. W., Cordes, S., & Smith, L. B. (2015). Signal clarity: An account of the variability in infant quantity discrimination tasks. Developmental Science, 18, 877–893. doi:10.1111/desc.2015.18.issue-6
  • Cantrell, L., & Smith, L. B. (2013). Open questions and a proposal: A critical review of the evidence on infant numerical abilities. Cognition, 128, 331–352. doi:10.1016/j.cognition.2013.04.008
  • Carey, S. (2004). Bootstrapping & the origin of concepts. Daedalus, 133, 59–68. doi:10.1162/001152604772746701
  • Carey, S. (2009). The Origin of Concepts. New York, NY: Oxford University Press. Cambridge, UK: Cambridge University Press.
  • Carey, S., & Spelke, E. (1994). Domain-specific knowledge and conceptual change. In Lawrence A. Hirschfeld and Susan A. Gelman (Eds.), Mapping the Mind: Domain Specificity in Cognition and Culture (pp. 169–200). Cambridge, UK: Cambridge University Press.
  • Church, R. M., & Meck, W. H. (1984). The numerical attribute of stimuli. In H. L. Roitblat, T. G. Bever, & H. S. Terrace (Eds.), Animal Cognition (pp. 445–464). Hillsdale, NJ: Erlbaum.
  • Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A., & Goebel, R. (2007). Notation-dependent and -independent representations of numbers in the parietal lobes. Neuron, 53, 307–314. doi:10.1016/j.neuron.2006.12.025
  • Cordes, S., & Brannon, E. M. (2008). Quantitative competencies in infancy. Developmental Science, 11, 803–808. doi:10.1111/j.1467-7687.2008.00770.x
  • Cordes, S., Gelman, R., Gallistel, C. R., & Whalen, J. (2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin & Review, 8, 698–707. doi:10.3758/BF03196206
  • de Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2, 48–55. doi:10.1016/j.tine.2013.06.001
  • Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56, 384–398. doi:10.1016/j.neuron.2007.10.004
  • Dehaene, S., Molko, N., Cohen, L., & Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14, 218–224. doi:10.1016/j.conb.2004.03.008
  • Diamond, A. (1990). Developmental time course in human infants and infant monkeys, and the neural bases of, inhibitory control in reaching. Annals of the New York Academy of Sciences, 608, 637–676. doi:10.1111/nyas.1990.608.issue-1
  • Diamond, A. (1991). Neuropsychological insights into the meaning of object concept development. In The Epigenesis of Mind: Essays on Biology and Cognition, (pp. 67–100). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Diester, I., & Nieder, A. (2007). Semantic associations between signs and numerical categories in the prefrontal cortex. Plos Biology, 5, e294. doi:10.1371/journal.pbio.0050294
  • Ditz, H. M., & Nieder, A. (2015). Neurons selective to the number of visual items in the corvid songbird endbrain. Proceedings of the National Academy of Sciences, 112, 7827–7832. doi:10.1073/pnas.1504245112
  • Eger, E., Sterzer, P., Russ, M. O., Giraud, A.-L., & Kleinschmidt, A. (2003). A supramodal number representation in human intraparietal cortex. Neuron, 37, 719–726. doi:10.1016/S0896-6273(03)00036-9
  • Eickhoff, S. B., Bzdok, D., Laird, A. R., Kurth, F., & Fox, P. T. (2012). Activation likelihood estimation meta-analysis revisited. NeuroImage, 59, 2349–2361. doi:10.1016/j.neuroimage.2011.09.017
  • Eickhoff, S. B., Laird, A. R., Grefkes, C., Wang, L. E., Zilles, K., & Fox, P. T. (2009). Coordinate-based activation likelihood estimation meta-analysis of neuroimaging data: A random-effects approach based on empirical estimates of spatial uncertainty. Human Brain Mapping, 30, 2907–2926. doi:10.1002/hbm.v30:9
  • Emerson, R. W., & Cantlon, J. F. (2012). Early math achievement and functional connectivity in the fronto-parietal network. Developmental Cognitive Neuroscience, 2, S139–S151. doi:10.1016/j.dcn.2011.11.003
  • Emerson, R. W., & Cantlon, J. F. (2014). Continuity and change in children’s longitudinal neural responses to numbers. Developmental Science, 2, 314–326.
  • Evans, T. M., Kochalka, J., Ngoon, T. J., Wu, S. S., Qin, S., Battista, C., & Menon, V. (2015). Brain structural integrity and intrinsic functional connectivity forecast 6 year longitudinal growth in children’s numerical abilities. Journal of Neuroscience, 35, 11743–11750. doi:10.1523/JNEUROSCI.0216-15.2015
  • Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from infants’ manual search. Developmental Science, 6, 568–584. doi:10.1111/desc.2003.6.issue-5
  • Feigenson, L., & Carey, S. (2005). On the limits of infants’ quantification of small object arrays. Cognition, 97, 295–313. doi:10.1016/j.cognition.2004.09.010
  • Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants’ choice of more: Object files vs. analog magnitudes. Psychological Science, 13, 150–156. doi:10.1111/1467-9280.00427
  • Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. doi:10.1016/j.tics.2004.05.002
  • Ferrigno, S., Hughes, K. D., & Cantlon, J. F. (2015). Precocious quantitative cognition in monkeys. Psychonomic Bulletin & Review, 23, 141–147. doi:10.3758/s13423-015-0893-5
  • Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74. doi:10.1016/0010-0277(92)90050-R
  • Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59–65. doi:10.1016/S1364-6613(99)01424-2
  • Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43, 981–986. doi:10.3758/s13428-011-0097-5
  • Gelman, R. (1990). First principles organize attention to and learning about relevant data: Number and the animate-inanimate distinction as examples. Cognitive Science, 14, 79–106. doi:10.1207/s15516709cog1401_5
  • Gelman, R. (1993). A rational-constructivist account of early learning about numbers and objects. Learning and Motivation, 30, 61–96.
  • Gelman, R., & Gallistel, C. R. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.
  • Gentner, D. (2010). Bootstrapping the mind: Analogical processes and symbol systems. Cognitive Science, 34, 752–775. doi:10.1111/cogs.2010.34.issue-5
  • Gomez, J. (2005). Species comparative studies and cognitive development. Trends in Cognitive Sciences, 9, 118–125. doi:10.1016/j.tics.2005.01.004
  • Gould, S. J., & Vrba, E. S. (1982). Exaptation - A missing term in the science of form. Paleobiology, 8, 4–15. doi:10.1017/S0094837300004310
  • Gunderson, E. A., Spaepen, E., & Levine, S. C. (2015). Approximate number word knowledge before the cardinal principle. Journal of Experimental Child Psychology, 130, 35–55. doi:10.1016/j.jecp.2014.09.008
  • Güntürkün, O. (2005). The avian “prefrontal cortex” and cognition. Current Opinion in Neurobiology, 15, 686–693. doi:10.1016/j.conb.2005.10.003
  • Haist, F., Wazny, J. H., Toomarian, E., & Adamo, M. (2015). Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement. Human Brain Mapping, 36, 804–826. doi:10.1002/hbm.v36.2
  • Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465. doi:10.1037/a0012682
  • Hanus, D., & Call, J. (2007). Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus): The effect of presenting whole sets vs. item-by-item. Journal of Comparative Psychology, 121, 241–249. doi:10.1037/0735-7036.121.3.241
  • Hinde, R. A., & Spencer-Booth, Y. (1967). The behaviour of socially living rhesus monkeys in their first two and a half years. Animal Behaviour, 15, 169–196. doi:10.1016/S0003-3472(67)80029-0
  • Holloway, I. D., & Ansari, D. (2010). Developmental specialization in the right intraparietal sulcus for the abstract representation of numerical magnitude. Journal of Cognitive Neuroscience, 22, 2627–2637. doi:10.1162/jocn.2009.21399
  • Houdé, 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, 876–885. doi:10.1111/desc.2010.13.issue-6
  • Huntley-Fenner, G. (2001). Why count stuff ? Young preschoolers do not use number for measurement in continuous dimensions. Developmental Review, 4, 456–462.
  • Huntley-Fenner, G., & Cannon, E. (2000). Preschoolers’ Magnitude Comparisons are Mediated by a Preverbal Analog Mechanism. Psychological Science, 11, 147–152. doi:10.1111/1467-9280.00230
  • 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, 647–652. doi:10.1016/j.neuroimage.2010.06.030
  • Hyde, D. C., & Spelke, E. S. (2011). Neural signatures of number processing in human infants: Evidence for two core systems underlying numerical cognition. Developmental Science, 14, 360–371. doi:10.1111/desc.2011.14.issue-2
  • Izard, V., Dehaene-Lambertz, G., & Dehaene, S. (2008). Distinct cerebral pathways for object identity and number in human infants. Plos Biology, 6, e11. doi:10.1371/journal.pbio.0060011
  • Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America, 106, 10382–10385. doi:10.1073/pnas.0812142106
  • Izard, V., Streri, A., & Spelke, E. S. (2014). Toward exact number: Young children use one-to-one correspondence to measure set identity but not numerical equality. Cognitive Psychology, 72, 27–53. doi:10.1016/j.cogpsych.2014.01.004
  • Jordan, K. E., & Brannon, E. M. (2006). The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences of the United States of America, 103, 3486–3489. doi:10.1073/pnas.0508107103
  • Jordan, K. E., MacLean, E. L., & Brannon, E. M. (2008). Monkeys match and tally quantities across senses. Cognition, 108, 617–625. doi:10.1016/j.cognition.2008.05.006
  • Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L. B. … Ischebeck, A. (2006). Neural correlates of the number–size interference task in children. NeuroReport, 17, 587–591. doi:10.1097/00001756-200604240-00007
  • Kaufmann, L., Vogel, S. E., Wood, G., Kremser, C., Schocke, M., Zimmerhackl, L.-B., & Koten, J. W. (2008). A developmental fMRI study of nonsymbolic numerical and spatial processing. Cortex, 44, 376–385. doi:10.1016/j.cortex.2007.08.003
  • Kobayashi, T., Hiraki, K., & Hasegawa, T. (2005). Auditory-visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science, 8, 409–419. doi:10.1111/desc.2005.8.issue-5
  • Kovas, Y., Giampietro, V., Viding, E., Ng, V., Brammer, M., Barker, G. J. … Plomin, R. (2009). Brain correlates of non-symbolic numerosity estimation in low and high mathematical ability children. Plos One, 4, e4587. doi:10.1371/journal.pone.0004587
  • Krick, C. M., Neuhaus, A., Klewin, C., Wörner, T., Kreis, S., & Reith, W. (2015). fMRI and DTI in delayed development of number processing. Der Radiologe, 55, 788–794. doi:10.1007/s00117-015-2854-4
  • Krinzinger, H., Koten, J. W., Horoufchin, H., Kohn, N., Arndt, D., Sahr, K., … Willmes, K. (2011). The role of finger representations and saccades for number processing: An FMRI study in children. Frontiers in Psychology, 2, 373. doi:10.3389/fpsyg.2011.00373
  • Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395–438. doi:10.1016/j.cognition.2006.10.005
  • Lee, M. D., & Sarnecka, B. W. (2011). Number-knower levels in young children: Insights from Bayesian modeling. Cognition, 120, 391–402. doi:10.1016/j.cognition.2010.10.003
  • Libertus, M. E., Brannon, E. M., & Woldorff, M. G. (2011). Parallels in stimulus-driven oscillatory brain responses to numerosity changes in adults and seven-month-old infants. Developmental Neuropsychology, 36, 651–667. doi:10.1080/87565641.2010.549883
  • Libertus, M. E., Pruitt, L. B., Woldorff, M. G., & Brannon, E. M. (2009). Induced alpha-band oscillations reflect ratio-dependent number discrimination in the infant brain. Journal of Cognitive Neuroscience, 21, 2398–2406. doi:10.1162/jocn.2008.21162
  • Lipton, J. S., & Spelke, E. S. (2003). Origins of the number sense: Large-number discrimination in human infants. Psychological Science, 14, 396–401. doi:10.1111/1467-9280.01453
  • Lipton, J. S., & Spelke, E. S. (2005). Preschool children’s mapping of number words to nonsymbolic numerosities. Child Development, 76, 978–988. doi:10.1111/cdev.2005.76.issue-5
  • Lipton, J. S., & Spelke, E. S. (2006). Preschool children master the logic of number word meanings. Cognition, 98, B57–B66. doi:10.1016/j.cognition.2004.09.013
  • Lourenco, S. F., & Longo, M. R. (2011). Origins and Development of Generalized Magnitude Representation. In Stanislas Dehaene and Elizabeth Brannon (Eds.), Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought (pp. 225–244). Burlington, MA: Academic Press.
  • Lussier, C. A., & Cantlon, J. F. (2016). Developmental bias for number words in the intraparietal sulcus. Developmental Science. doi:10.1111/desc.12385
  • Lyons, I. M., & Ansari, D. (2009). The cerebral basis of mapping nonsymbolic numerical quantities onto abstract symbols: An fMRI training study. Journal of Cognitive Neuroscience, 21, 1720–1735. doi:10.1162/jocn.2009.21124
  • McCrink, K., & Wynn, K. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15, 776–781. doi:10.1111/j.0956-7976.2004.00755.x
  • Meck, W. H., & Church, R. M. (1984). Simultaneous temporal processing. Journal of Experimental Psychology: Animal Behavior Processes, 10, 1–29.
  • Meintjes, E. M., Jacobson, S. W., Molteno, C. D., Gatenby, J. C., Warton, C., Cannistraci, C. J., … Jacobson, J. L. (2010). An fMRI study of magnitude comparison and exact addition in children. Magnetic Resonance Imaging, 28, 351–362. doi:10.1016/j.mri.2009.11.010
  • Menon, V., Rivera, S. M., White, C. D., Glover, G. H., & Reiss, A. L. (2000). Dissociating prefrontal and parietal cortex activation during arithmetic processing. NeuroImage, 12, 357–365. doi:10.1006/nimg.2000.0613
  • Michie, S. (1985). Development of absolute and relative concepts of number in preschool children. Developmental Psychology, 21, 247–252. doi:10.1037/0012-1649.21.2.247
  • Mix, K. S. (1999). Similarity and numerical equivalence. Cognitive Development, 14, 269–297. doi:10.1016/S0885-2014(99)00005-2
  • Mix, K. S. (2002). The construction of number concepts. Cognitive Development, 17, 1345–1363. doi:10.1016/S0885-2014(02)00123-5
  • Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002a). Multiple cues for quantification in infancy: Is number one of them? Psychological Bulletin, 128, 278–294. doi:10.1037/0033-2909.128.2.278
  • Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002b). Quantitative development in infancy and early childhood. Oxford, UK: Oxford University Press.
  • Mundy, E., & Gilmore, C. K. (2009). Children’s mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103, 490–502. doi:10.1016/j.jecp.2009.02.003
  • Murofushi, K. (1997). Numerical matching behavior by a chimpanzee (Pan troglodytes): Subitizing and analogue magnitude estimation. Japanese Psychological Research, 39, 140–153. doi:10.1111/jpr.1997.39.issue-3
  • Mussolin, C., Noël, M.-P., Pesenti, M., Grandin, C., & De Volder, A. G. (2013). Neural correlates of the numerical distance effect in children. Frontiers in Psychology, 4, 663. doi:10.3389/fpsyg.2013.00663
  • Nieder, A. (2009). Prefrontal cortex and the evolution of symbolic reference. Current Opinion in Neurobiology, 19, 99–108. doi:10.1016/j.conb.2009.04.008
  • Nieder, A. (2016). The neuronal code for number. Nature Reviews Neuroscience, 17, 366–382. doi:10.1038/nrn.2016.40
  • Nieder, A., & Merten, K. (2007). A labeled-line code for small and large numerosities in the monkey prefrontal cortex. The Journal of Neuroscience, 27, 5986–5993. doi:10.1523/JNEUROSCI.1056-07.2007
  • Nieder, A., & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37, 149–157. doi:10.1016/S0896-6273(02)01144-3
  • Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Sciences of the United States of America, 101, 7457–7462. doi:10.1073/pnas.0402239101
  • Northcutt, R. G., & Kaas, J. H. (1995). The emergence and evolution of mammalian neocortex. Trends in Neurosciences, 18, 373–379. doi:10.1016/0166-2236(95)93932-N
  • Odic, D., Le Corre, M., & Halberda, J. (2015). Children’s mappings between number words and the approximate number system. Cognition, 138, 102–121. doi:10.1016/j.cognition.2015.01.008
  • Opfer, J. E., Thompson, C. A., & Furlong, E. E. (2010). Early development of spatial-numeric associations: Evidence from spatial and quantitative performance of preschoolers. Developmental Science, 13, 761–771. doi:10.1111/desc.2010.13.issue-5
  • Orban, G. A., Claeys, K., Nelissen, K., Smans, R., Sunaert, S., Todd, J. T., … Vanduffel, W. (2006). Mapping the parietal cortex of human and non-human primates. Neuropsychologia, 44, 2647–2667. doi:10.1016/j.neuropsychologia.2005.11.001
  • Park, J., Li, R., & Brannon, E. M. (2014). Neural connectivity patterns underlying symbolic number processing indicate mathematical achievement in children. Developmental Science, 17, 187–202. doi:10.1111/desc.2014.17.issue-2
  • Pepperberg, I. M., & Carey, S. (2012). Grey parrot number acquisition: The inference of cardinal value from ordinal position on the numeral list. Cognition, 125, 219–232. doi:10.1016/j.cognition.2012.07.003
  • Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547–555. doi:10.1016/j.neuron.2004.10.014
  • 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, 293–305. doi:10.1016/j.neuron.2006.11.022
  • 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, 983–993. doi:10.1016/S0896-6273(04)00107-2
  • Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15, 1779–1790. doi:10.1093/cercor/bhi055
  • Rosenberg-Lee, M., Barth, M., & Menon, V. (2011). What difference does a year of schooling make? Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving. NeuroImage, 57, 796–808. doi:10.1016/j.neuroimage.2011.05.013
  • Rugani, R., Vallortigara, G., & Regolin, L. (2013). Numerical Abstraction in Young Domestic Chicks (Gallus gallus). Plos ONE, 8, e65262. doi:10.1371/journal.pone.0065262
  • Sella, F., Berteletti, I., Lucangeli, D., & Zorzi, M. (2016). Spontaneous non-verbal counting in toddlers. Developmental Science, 19, 329–337. doi:10.1111/desc.2016.19.issue-2
  • Sereno, M. I., & Tootell, R. B. H. (2005). From monkeys to humans: What do we now know about brain homologies? Current Opinion in Neurobiology, 15, 135–144. doi:10.1016/j.conb.2005.03.014
  • Smith, L. B., & Thelen, E. (2003). Development as a dynamic system. Trends in Cognitive Sciences, 7, 343–348. doi:10.1016/S1364-6613(03)00156-6
  • Spelke, E. S. (2000). Core Knowledge of Objects. American Psychologist, 55, 1233–1243. doi:10.1037/0003-066X.55.11.1233
  • Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10, 89–96. doi:10.1111/desc.2007.10.issue-1
  • Starke, M., Kiechl-Kohlendorfer, U., Kucian, K., Pupp Peglow, U., Kremser, C., Schocke, M., & Kaufmann, L. (2013). Brain structure, number magnitude processing, and math proficiency in 6- to 7-year-old children born prematurely: A voxel-based morphometry study. NeuroReport, 24, 419–424. doi:10.1097/WNR.0b013e32836140ed
  • Thompson-Schill, S. L., D’Esposito, M., Aguirre, G. K., & Farah, M. J. (1997). Role of left inferior prefrontal cortex in retrieval of semantic knowledge: A reevaluation. Proceedings of the National Academy of Sciences of the United States of America, 94, 14792–14797. doi:10.1073/pnas.94.26.14792
  • Tomonaga, M. (2008). Relative numerosity discrimination by chimpanzees (Pan troglodytes): Evidence for approximate numerical representations. Animal Cognition, 11, 43–57. doi:10.1007/s10071-007-0089-0
  • Turkeltaub, P. E., Eickhoff, S. B., Laird, A. R., Fox, M., Wiener, M., & Fox, P. (2012). Minimizing within-experiment and within-group effects in Activation Likelihood Estimation meta-analyses. Human Brain Mapping, 33, 1–13. doi:10.1002/hbm.21186
  • van Marle, K., Chu, F. W., Li, Y., & Geary, D. C. (2014). Acuity of the approximate number system and preschoolers’ quantitative development. Developmental Science, 17, 492–505. doi:10.1111/desc.2014.17.issue-4
  • vanMarle, K., & Wynn, K. (2011). Tracking and quantifying objects and non-cohesive substances. Developmental Science, 14, 502–515. doi:10.1111/desc.2011.14.issue-3
  • Varga, M. E., Pavlova, O. G., & Nosova, C. V. (2008). Function of counting and its representation in the parietal cortex in humans and animals. Zhurnal Vysshei Nervnoi Deyatelnosti Imeni I P Pavlova, 58, 663–677.
  • Vigneau, M., Beaucousin, V., Hervé, P. Y., Duffau, H., Crivello, F., Houdé, O., … Tzourio-Mazoyer, N. (2006). Meta-analyzing left hemisphere language areas: Phonology, semantics, and sentence processing. NeuroImage, 30, 1414–1432. doi:10.1016/j.neuroimage.2005.11.002
  • Vogel, S. E., Goffin, C., & Ansari, D. (2015). Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: An fMR-adaptation study. Developmental Cognitive Neuroscience, 12, 61–73. doi:10.1016/j.dcn.2014.12.001
  • Wagner, A. D., Paré-Blagoev, E. J., Clark, J., & Poldrack, R. A. (2001). Recovering meaning: Left prefrontal cortex guides controlled semantic retrieval. Neuron, 31, 329–338. doi:10.1016/S0896-6273(01)00359-2
  • Wagner, J. B., & Johnson, S. C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition, 119, 10–22. doi:10.1016/j.cognition.2010.11.014
  • Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488. doi:10.1016/j.tics.2003.09.002
  • Wang, L., Uhrig, L., Jarraya, B., & Dehaene, S. (2015). Representation of numerical and sequential patterns in macaque and human brains. Current Biology, 25, 1966–1974. doi:10.1016/j.cub.2015.06.035
  • Wood, G., Ischebeck, A., Koppelstaetter, F., Gotwald, T., & Kaufmann, L. (2009). Developmental trajectories of magnitude processing and interference control: An fMRI study. Cerebral Cortex, 19, 2755–2765. doi:10.1093/cercor/bhp056
  • Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193. doi:10.1016/0010-0277(90)90003-3
  • Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251. doi:10.1016/0010-0285(92)90008-P
  • Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11. doi:10.1016/S0010-0277(99)00066-9

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.