Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

  • Karina HamamoucheEmail author
  • Sara Cordes
Theoretical Review


Our ability to represent temporal, spatial, and numerical information is critical for understanding the world around us. Given the prominence of quantitative representations in the natural world, numerous cognitive, neurobiological, and developmental models have been proposed as a means of describing how we track quantity. One prominent theory posits that time, space, and number are represented by a common magnitude system, or a common neural locus (i.e., Bonn & Cantlon in Cognitive Neuropsychology, 29(1/2), 149–173, 2012; Cantlon, Platt, & Brannon in Trends in Cognitive Sciences, 13(2), 83–91, 2009; Meck & Church in Animal Behavior Processes, 9(3), 320, 1983; Walsh in Trends in Cognitive Sciences, 7(11), 483–488, 2003). Despite numerous similarities in representations of time, space, and number, an increasing body of literature reveals striking dissociations in how each quantity is processed, particularly later in development. These findings have led many researchers to consider the possibility that separate systems may be responsible for processing each quantity. This review will analyze evidence in favor of a common magnitude system, particularly in infancy, which will be tempered by counter evidence, the majority of which comes from experiments with children and adult participants. After reviewing the current data, we argue that although the common magnitude system may account for quantity representations in infancy, the data do not provide support for this system throughout the life span. We also identify future directions for the field and discuss the likelihood of the developmental divergence model of quantity representation, like that of Newcombe (Ecological Psychology, 2, 147–157, 2014), as a more plausible account of quantity development.


Nonsymbolic quantity processing Temporal precision Spatial processing Numerical acuity 



  1. Agrillo, C., Piffer, L., & Adriano, A. (2013). Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM. Behavioral and Brain Functions, 9(26), 1–14.Google Scholar
  2. Agrillo, C., Ranpura, A., & Butterworth, B. (2010). Time and numerosity estimations are independent: Behavioral evidence for two different systems using a conflict paradigm. Cognitive Neuroscience, 1(2), 96–101.PubMedCrossRefPubMedCentralGoogle Scholar
  3. Alexander, P. A., Willson, V. L., White, C. S., Fuqua, J. D., Clark, G. D., Wilson, A. F., & Kulikowich, J. M. (1989). Development of analogical reasoning in 4-and 5-year-old children. Cognitive Development, 4(1), 65–88.CrossRefGoogle Scholar
  4. Ansari, D., & Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience, 18(11), 1820–1828.PubMedCrossRefPubMedCentralGoogle Scholar
  5. Ansari, D., Lyons, I. M., van Eimeren, L., & Xu, F. (2006). Linking visual attention and number processing in the brain: The role of the temporo-parietal junction in small and large symbolic and nonsymbolic number comparison. Journal of Cognitive Neuroscience, 19, 1845–1853.CrossRefGoogle Scholar
  6. Ashkenazi, S. (2018). Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming. Cognition and Emotion, 32(8), 1700–1707.PubMedCrossRefPubMedCentralGoogle Scholar
  7. Aulet, L. S., & Lourenco, S. F. (2018). The developing mental number line: Does its directionality relate to 5-to 7-year-old children’s mathematical abilities?. Frontiers in Psychology, 9, 1142. CrossRefPubMedPubMedCentralGoogle Scholar
  8. Baker, J. M., Rodzon, K. S., & Jordan, K. (2013). The impact of emotion on numerosity estimation. Frontiers in Psychology, 4.
  9. Bar-Haim, Y., Kerem, A., Lamy, D., & Zakay, D. (2010). When time slows down: The influence of threat on time perception in anxiety. Cognition and Emotion, 24(2), 255–263.CrossRefGoogle Scholar
  10. Barth, H. C. (2008). Judgments of discrete and continuous quantity: An illusory Stroop effect. Cognition, 109(2), 251–266.PubMedCrossRefPubMedCentralGoogle Scholar
  11. Basso, G., Nichelli, P., Frassinetti, F., & di Pellegrino, G. (1996). Time perception in a neglected space. Neuroreport, 7(13), 2111–2114.PubMedCrossRefPubMedCentralGoogle Scholar
  12. Baumann, O., Borra, R. J., Bower, J. M., Cullen, K. E., Habas, C., Ivry, R. B., . . . Paulin, M. G. (2015). Consensus paper: The role of the cerebellum in perceptual processes. The Cerebellum, 14(2), 197–220.Google Scholar
  13. Beatty, W. W., & Shavalia, D. A. (1980). Spatial memory in rats: Time course of working memory and effect of anesthetics. Behavioral and Neural Biology, 28(4), 454–462.PubMedCrossRefPubMedCentralGoogle Scholar
  14. Bjoertomt, O., Cowey, A., & Walsh, V. (2002). Spatial neglect in near and far space investigated by repetitive transcranial magnetic stimulation. Brain, 125(9), 2012–2022.PubMedCrossRefPubMedCentralGoogle Scholar
  15. Block, R. A., Hancock, P. A., & Zakay, D. (2010). How cognitive load affects duration judgments: A meta-analytic review. Acta Psychologica, 134(3), 330–343.PubMedCrossRefPubMedCentralGoogle Scholar
  16. Bonato, M., Zorzi, M., & Umiltà, C. (2012). When time is space: Evidence for a mental time line. Neuroscience & Biobehavioral Reviews, 36(10), 2257–2273.CrossRefGoogle Scholar
  17. Bonn, C. D., & Cantlon, J. F. (2012). The origins and structure of quantitative concepts. Cognitive Neuropsychology, 29(1/2), 149–173.PubMedPubMedCentralCrossRefGoogle Scholar
  18. Bonn, C. D., & Cantlon, J. F. (2017). Spontaneous, modality-general abstraction of a ratio scale. Cognition, 169, 36–45.PubMedPubMedCentralCrossRefGoogle Scholar
  19. Bonny, J. W., & Lourenco, S. F. (2013). The approximate number system and its relation to early math achievement: Evidence from the preschool years. Journal of Experimental Child Psychology, 114(3), 375–388.PubMedCrossRefPubMedCentralGoogle Scholar
  20. Bonny, J. W., & Lourenco, S. F. (2015). Individual differences in children’s approximations of area correlate with competence in basic geometry. Learning and Individual Differences, 44, 16–24.CrossRefGoogle Scholar
  21. Borghesani, V., de Hevia, M. D., Viarouge, A., Chagas, P. P., Eger, E., & Piazza, M. (2018). Processing number and length in the parietal cortex: Sharing resources, not a common code. Cortex. Advance online publication.
  22. Boroditsky, L. (2001). Does language shape thought?: Mandarin and English speakers’ conceptions of time. Cognitive Psychology, 43(1), 1–22.PubMedCrossRefPubMedCentralGoogle Scholar
  23. Boroditsky, L. (2008, January). Do English and Mandarin speakers think differently about time?. Proceedings of the Cognitive Science Society, 30(30).Google Scholar
  24. Boroditsky, L., Fuhrman, O., & McCormick, K. (2011). Do English and Mandarin speakers think about time differently?. Cognition, 118(1), 123–129.PubMedCrossRefPubMedCentralGoogle Scholar
  25. Boroditsky, L., & Gaby, A. (2010). Remembrances of times East: Absolute spatial representations of time in an Australian aboriginal community. Psychological Science, 21(11), 1635–1639.PubMedCrossRefPubMedCentralGoogle Scholar
  26. Bottini, R., & Casasanto, D. (2013). Space and time in the child’s mind: Metaphoric or ATOMic?. Frontiers in Psychology, 4, 803. CrossRefPubMedPubMedCentralGoogle Scholar
  27. Brannon, E., Lutz, D., & Cordes, S. (2006). The development of area discrimination and its implications for number representation in infancy. Developmental Science, 9(6), 59–64.CrossRefGoogle Scholar
  28. Brannon, E., Suanda, S., Libertus, K. (2007). Temporal discrimination increases in precision over development and parallels the development of numerosity discrimination. Developmental Science, 10(6), 770–777.PubMedPubMedCentralCrossRefGoogle Scholar
  29. Brown, S. W. (1997). Attentional resources in timing: Interference effects in concurrent temporal and nontemporal working memory tasks. Perception & Psychophysics, 59(7), 1118–1140.CrossRefGoogle Scholar
  30. Buhusi, C. V., & Meck, W. H. (2009). Relativity theory and time perception: Single or multiple clocks? PLoS ONE, 4(7), e6268.PubMedPubMedCentralCrossRefGoogle Scholar
  31. Bunge, S. A., Dudukovic, N. M., Thomason, M. E., Vaidya, C. J., & Gabrieli, J. D. (2002). Immature frontal lobe contributions to cognitive control in children: Evidence from fMRI. Neuron, 33(2), 301–311.PubMedPubMedCentralCrossRefGoogle Scholar
  32. Bunge, S. A., & Wright, S. B. (2007). Neurodevelopmental changes in working memory and cognitive control. Current Opinion in Neurobiology, 17(2), 243–250.PubMedCrossRefPubMedCentralGoogle Scholar
  33. Burr, D., & Ross, J. (2008). A visual sense of number. Current Biology, 18(6), 425–428.PubMedCrossRefPubMedCentralGoogle Scholar
  34. Cai, Z. G., & Connell, L. (2015). Space–time interdependence: Evidence against asymmetric mapping between time and space. Cognition, 136, 268–281.PubMedCrossRefPubMedCentralGoogle Scholar
  35. Cantlon, J. F., & Brannon, E. M. (2007). Basic math in monkeys and college students. PLoS Biology, 5(12), e328.PubMedPubMedCentralCrossRefGoogle Scholar
  36. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.PubMedPubMedCentralCrossRefGoogle Scholar
  37. Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13(2), 83–91.PubMedPubMedCentralCrossRefGoogle Scholar
  38. 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(6), 877–893.PubMedCrossRefPubMedCentralGoogle Scholar
  39. Cantrell, L., & Smith, L. B. (2013). Open questions and a proposal: A critical review of the evidence on infant numerical abilities. Cognition, 128(3), 331–352.PubMedPubMedCentralCrossRefGoogle Scholar
  40. Cappelletti, M., Barth, H., Fregni, F., Spelke, E. S., & Pascual-Leone, A. (2007). rTMS over the intraparietal sulcus disrupts numerosity processing. Experimental Brain Research, 179(4), 631.PubMedPubMedCentralCrossRefGoogle Scholar
  41. Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2007). The middle house or the middle floor: Bisecting horizontal and vertical mental number lines in neglect. Neuropsychologia, 45(13), 2989–3000.PubMedPubMedCentralCrossRefGoogle Scholar
  42. Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2009). Dissociations and interactions between time, numerosity and space processing. Neuropsychologia, 47(13), 2732–2748.PubMedPubMedCentralCrossRefGoogle Scholar
  43. Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2011). Numbers and time doubly dissociate. Neuropsychologia, 49(11), 3078–3092.PubMedCrossRefPubMedCentralGoogle Scholar
  44. Casasanto, D., & Boroditsky, L. (2008). Time in the mind: Using space to think about time. Cognition, 106(2), 579–593.PubMedCrossRefPubMedCentralGoogle Scholar
  45. Casasanto, D., Fotakopoulou, O., & Boroditsky, L. (2010). Space and time in the child’s mind: Evidence for a cross-dimensional asymmetry. Cognitive Science, 34(3), 387–405.PubMedCrossRefPubMedCentralGoogle Scholar
  46. Casini, L., & Ivry, R. B. (1999). Effects of divided attention on temporal processing in patients with lesions of the cerebellum or frontal lobe. Neuropsychology, 13(1), 10.PubMedCrossRefPubMedCentralGoogle Scholar
  47. 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 Sciences, 103(12), 4693–4698.CrossRefGoogle Scholar
  48. Chen, Z., Sanchez, R. P., & Campbell, T. (1997). From beyond to within their grasp: The rudiments of analogical problem solving in 10-and 13-month-olds. Developmental Psychology, 33(5), 790.PubMedCrossRefPubMedCentralGoogle Scholar
  49. Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. Zdm, 47(5), 759–770.CrossRefGoogle Scholar
  50. Clayton, S., Gilmore, C., & Inglis, M. (2015). Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement. Acta Psychologica, 161, 177–184.PubMedCrossRefPubMedCentralGoogle Scholar
  51. Conson, M., Cinque, F., Barbarulo, A. M., & Trojano, L. (2008). A common processing system for duration, order and spatial information: Evidence from a time estimation task. Experimental Brain Research, 187(2), 267–274.PubMedCrossRefPubMedCentralGoogle Scholar
  52. Conway, C. M., Bauernschmidt, A., Huang, S. S., & Pisoni, D. B. (2010). Implicit statistical learning in language processing: Word predictability is the key. Cognition, 114(3), 356–371.PubMedCrossRefPubMedCentralGoogle Scholar
  53. Cordes, S., & Brannon, E. M. (2008). The difficulties of representing continuous extent in infancy: Using number is just easier. Child Development, 79(2), 476–489.PubMedPubMedCentralCrossRefGoogle Scholar
  54. Coull, J. T., & Frith, C. D. (1998). Differential activation of right superior parietal cortex and intraparietal sulcus by spatial and nonspatial attention. NeuroImage, 8(2), 176–187.PubMedCrossRefPubMedCentralGoogle Scholar
  55. Coull, J. T., Vidal, F., Nazarian, B., & Macar, F. (2004). Functional anatomy of the attentional modulation of time estimation. Science, 303(5663), 1506–1508.PubMedCrossRefPubMedCentralGoogle Scholar
  56. Crisafi, M. A., & Brown, A. L. (1986). Analogical transfer in very young children: Combining two separately learned solutions to reach a goal. Child Development, 57(4), 953–968.PubMedCrossRefPubMedCentralGoogle Scholar
  57. Crollen, V., Grade, S., Pesenti, M., & Dormal, V. (2013). A common metric magnitude system for the perception and production of numerosity, length, and duration. Frontiers in Psychology, 4, 449.PubMedPubMedCentralCrossRefGoogle Scholar
  58. Danckert, J., Ferber, S., Pun, C., Broderick, C., Striemer, C., Rock, S., & Stewart, D. (2007). Neglected time: Impaired temporal perception of multisecond intervals in unilateral neglect. Journal of Cognitive Neuroscience, 19(10), 1706–1720.PubMedCrossRefPubMedCentralGoogle Scholar
  59. de Haan, M., Pascalis, O., & Johnson, M. H. (2002). Specialization of neural mechanisms underlying face recognition in human infants. Journal of Cognitive Neuroscience, 14(2), 199–209.PubMedCrossRefPubMedCentralGoogle Scholar
  60. de Hevia, M. D., Izard, V., Coubart, A., Spelke, E. S., & Streri, A. (2014). Representations of space, time, and number in neonates. Proceedings of the National Academy of Sciences, 201323628.
  61. de Hevia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21(5), 653–660.PubMedPubMedCentralCrossRefGoogle Scholar
  62. de Hevia, M. D., & Spelke, E. S. (2013). Not all continuous dimensions map equally: Number-brightness mapping in human infants. PLoS ONE, 8(11), e81241.PubMedPubMedCentralCrossRefGoogle Scholar
  63. de Hevia, M. D., Vanderslice, M., & Spelke, E. S. (2012). Cross-dimensional mapping of number, length and brightness by preschool children. PLoS ONE, 7(4), e35530.PubMedPubMedCentralCrossRefGoogle Scholar
  64. de Hevia, M. D., Veggiotti, L., Streri, A., & Bonn, C. D. (2017). At birth, humans associate “few” with left and “many” with right. Current Biology, 27(24), 3879-3884.PubMedCrossRefPubMedCentralGoogle Scholar
  65. De Visscher, A., Noël, M. P., Pesenti, M., & Dormal, V. (2017). Developmental dyscalculia in adults: beyond numerical magnitude impairment. Journal of Learning Disabilities.
  66. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.Google Scholar
  67. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.CrossRefGoogle Scholar
  68. Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355–361.PubMedCrossRefPubMedCentralGoogle Scholar
  69. 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), 1217–1220.PubMedPubMedCentralCrossRefGoogle Scholar
  70. DeWind, N. K., & Brannon, E. M. (2012). Malleability of the approximate number system: Effects of feedback and training. Frontiers in Human Neuroscience, 6.Google Scholar
  71. DeWind, N. K., & Brannon, E. M. (2016). Significant inter-test reliability across approximate number system assessments. Frontiers in Psychology, 7, 310.PubMedPubMedCentralCrossRefGoogle Scholar
  72. Diamond, A., & Doar, B. (1989). The performance of human infants on a measure of frontal cortex function, the delayed response task. Developmental Psychobiology: The Journal of the International Society for Developmental Psychobiology, 22(3), 271–294.CrossRefGoogle Scholar
  73. Diamond, A., Towle, C., & Boyer, K. (1994). Young children’s performance on a task sensitive to the memory functions of the medial temporal lobe in adults: The delayed nonmatching-to-sample task reveals problems that are due to non-memory-related task demands. Behavioral Neuroscience, 108(4), 659.PubMedCrossRefPubMedCentralGoogle Scholar
  74. Doi, H., & Shinohara, K. (2009). The perceived duration of emotional face is influenced by the gaze direction. Neuroscience Letters, 457(2), 97–100.PubMedCrossRefPubMedCentralGoogle Scholar
  75. Doi, H., & Shinohara, K. (2016). Emotional faces influence numerosity estimation without awareness. Cognitive Processing, 17(4), 389–397.PubMedCrossRefPubMedCentralGoogle Scholar
  76. Dormal, V., Andres, M., & Pesenti, M. (2008). Dissociation of numerosity and duration processing in the left intraparietal sulcus: a transcranial magnetic stimulation study. Cortex, 44(4), 462–469.PubMedCrossRefPubMedCentralGoogle Scholar
  77. Dormal, V., Andres, M., & Pesenti, M. (2012). Contribution of the right intraparietal sulcus to numerosity and length processing: An fMRI-guided TMS study. Cortex, 48(5), 623–629.PubMedCrossRefPubMedCentralGoogle Scholar
  78. Dormal, V., Dormal, G., Joassin, F., & Pesenti, M. (2012). A common right fronto-parietal network for numerosity and duration processing: An fMRI study. Human Brain Mapping, 33(6), 1490–1501.PubMedCrossRefPubMedCentralGoogle Scholar
  79. Dormal, V., Grade, S., Mormont, E., & Pesenti, M. (2012). Dissociation between numerosity and duration processing in aging and early Parkinson’s disease. Neuropsychologia, 50(9), 2365–2370.PubMedCrossRefPubMedCentralGoogle Scholar
  80. Dormal, V., & Pesenti, M. (2009). Common and specific contributions of the intraparietal sulci to numerosity and length processing. Human Brain Mapping, 30(8), 2466–2476.PubMedCrossRefPubMedCentralGoogle Scholar
  81. Dormal, V., & Pesenti, M. (2012). Processing magnitudes within the parietal cortex. Horizons in Neuroscience Research, 8, 107–140.Google Scholar
  82. Dormal, V. & Pesenti, M. (2013). Processing numerosity, length and duration in a three-dimensional Stroop-like task: Towards a gradient of processing automaticity? Psychological Research, 77(2), 116–127.CrossRefGoogle Scholar
  83. Dormal, V., Seron, X., & Pesenti, M. (2006). Numerosity-duration interference: A Stroop experiment. Acta Psychologica, 121(2), 109–124.PubMedCrossRefPubMedCentralGoogle Scholar
  84. Droit-Volet, S., Brunot, S., & Niedenthal, P. (2004). Perception of the duration of emotional events. Cognition and Emotion, 18(6), 849-858.CrossRefGoogle Scholar
  85. Droit-Volet, S., Clément, A., & Fayol, M. (2003). Time and number discrimination in a bisection task with a sequence of stimuli: A developmental approach. Journal of Experimental Child Psychology, 84(1), 63-76.PubMedCrossRefPubMedCentralGoogle Scholar
  86. Droit-Volet, S., Clément, A., Fayol, M. (2008). Time, number and length: Similarities and differences in discrimination in adults and children. The Quarterly Journal of Experimental Psychology, 61(12), 1827-1846.PubMedCrossRefPubMedCentralGoogle Scholar
  87. Droit-Volet, S., Fayolle, S., Lamotte, M., & Gil, S. (2013). Time, emotion and the embodiment of timing. Timing & Time Perception, 1(1), 99–126.CrossRefGoogle Scholar
  88. Droit-Volet, S., & Meck, W. H. (2007). How emotions colour our time perception. Trends in Cognitive Sciences, 1(12), 504-513.CrossRefGoogle Scholar
  89. Feigenson, L. (2007). The equality of quantity. Trends in Cognitive Sciences, 11(5), 185-187.PubMedCrossRefPubMedCentralGoogle Scholar
  90. Feigenson, L., Libertus, M., Halberda, J. (2013). Links between the intuitive sense of number and formal mathematics ability. Child Development Perspectives, 7(2), 74–79.PubMedPubMedCentralCrossRefGoogle Scholar
  91. Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience, 15(1), 47–56.PubMedCrossRefPubMedCentralGoogle Scholar
  92. Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6(6), 555.PubMedCrossRefPubMedCentralGoogle Scholar
  93. Fuhrman, O., & Boroditsky, L. (2007, January). Mental time-lines follow writing direction: Comparing English and Hebrew speakers. Proceedings of the Cognitive Science Society, 29(29).Google Scholar
  94. Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16(1), 136–148.PubMedCrossRefPubMedCentralGoogle Scholar
  95. Gallistel, C. R. (1990). The organization of learning. Cambridge, MA: MIT Press.Google Scholar
  96. Geary, D. C., & Vanmarle, K. (2016). Young children’s core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement. Developmental Psychology, 52(12), 2130–2144.PubMedCrossRefPubMedCentralGoogle Scholar
  97. Gevers, W., Reynvoet, B., & Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition, 87(3), B87–B95.PubMedCrossRefPubMedCentralGoogle Scholar
  98. Gevers, W., Reynvoet, B., & Fias, W. (2004). The mental representation of ordinal sequences is spatially organized: Evidence from days of the week. Cortex: A Journal Devoted to the Study of the Nervous System and Behavior, 40, 171–172.CrossRefGoogle Scholar
  99. Gibson, J. J., & Gibson, E. J. (1955). Perceptual learning: Differentiation or enrichment?. Psychological Review, 62(1), 32.PubMedCrossRefPubMedCentralGoogle Scholar
  100. Giedd, J. N., Snell, J. W., Lange, N., Rajapakse, J. C., Casey, B. J., Kozuch, P. L., ... Rapoport, J. L. (1996). Quantitative magnetic resonance imaging of human brain development: Ages 4–18. Cerebral Cortex, 6(4), 551–559.Google Scholar
  101. Gil, S., & Droit-Volet, S. (2012). Emotional time distortions: the fundamental role of arousal. Cognition & Emotion, 26(5), 847–862.CrossRefGoogle Scholar
  102. Gil, S., Niedenthal, P. M., & Droit-Volet, S. (2007). Anger and time perception in children. Emotion, 7(1), 219–225.PubMedCrossRefPubMedCentralGoogle Scholar
  103. Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., . . . Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLOS ONE, 8(6), e67374.Google Scholar
  104. Göbel, S. M., Calabria, M., Farne, A., & Rossetti, Y. (2006). Parietal rTMS distorts the mental number line: Simulating ‘spatial’ neglect in healthy subjects. Neuropsychologia, 44(6), 860–868.PubMedCrossRefPubMedCentralGoogle Scholar
  105. Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798.PubMedCrossRefPubMedCentralGoogle Scholar
  106. Goldfield, B. A., & Reznick, J. S. (1990). Early lexical acquisition: Rate, content, and the vocabulary spurt. Journal of Child Language, 17(1), 171–183.PubMedCrossRefPubMedCentralGoogle Scholar
  107. Gooch, C. M., Wiener, M., Hamilton, C. A., & Coslett, B. H. (2011). Temporal discrimination of sub-and suprasecond time intervals: A voxel-based lesion mapping analysis. Frontiers in Integrative Neuroscience, 5, 1–10.CrossRefGoogle Scholar
  108. Goswami, U., & Brown, A. L. (1990). Melting chocolate and melting snowmen: Analogical reasoning and causal relations. Cognition, 35(1), 69–95.PubMedCrossRefPubMedCentralGoogle Scholar
  109. 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(5), 1457.PubMedCrossRefPubMedCentralGoogle Scholar
  110. Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665.PubMedCrossRefPubMedCentralGoogle Scholar
  111. Halit, H., De Haan, M., & Johnson, M. H. (2003). Cortical specialisation for face processing: Face-sensitive event-related potential components in 3-and 12-month-old infants. NeuroImage, 19(3), 1180–1193.PubMedCrossRefPubMedCentralGoogle Scholar
  112. Hamamouche, K., Hurst, M., & Cordes, S. (2016, August). The effect of emotion and induced arousal on numerical processing. Proceedings of the 38th Annual Meeting of the Cognitive Science Society. Philadelphia, PA: Cognitive Science Society.Google Scholar
  113. Hamamouche, K., Keefe, M., Jordan, K., & Cordes, S. (2018). Cognitive load affects temporal and numerical judgments in distinct ways. Manuscript submitted for publication.Google Scholar
  114. Hamamouche, K. A., Niemi, L., & Cordes, S. (2017). Quantifying a threat: Evidence of a numeric processing bias. Acta Psychologica, 177, 1–9.PubMedCrossRefPubMedCentralGoogle Scholar
  115. Harrington, D. L., Haaland, K. Y., & Knight, R. T. (1998). Cortical networks underlying mechanisms of time perception. Journal of Neuroscience, 18(3), 1085–1095.PubMedCrossRefPubMedCentralGoogle Scholar
  116. Hart, S. J., Davenport, M. L., Hooper, S. R., & Belger, A. (2006). Visuospatial executive function in Turner syndrome: functional MRI and neurocognitive findings. Brain, 129(5), 1125–1136.PubMedPubMedCentralCrossRefGoogle Scholar
  117. Harter, M. R., & Suitt, C. D. (1970). Visually-evoked cortical responses and pattern vision in the infant: A longitudinal study. Psychonomic Science, 18(4), 235–237.CrossRefGoogle Scholar
  118. Harvey, B. M., & Dumoulin, S. O. (2017). Can responses to basic non-numerical visual features explain neural numerosity responses?. NeuroImage, 149, 200–209.PubMedCrossRefPubMedCentralGoogle Scholar
  119. Harvey, B. M., Fracasso, A., Petridou, N., & Dumoulin, S. O. (2015). Topographic representations of object size and relationships with numerosity reveal generalized quantity processing in human parietal cortex. Proceedings of the National Academy of Sciences, 112(44), 13525–13530.CrossRefGoogle Scholar
  120. Harvey, B. M., Klein, B. P., Petridou, N., & Dumoulin, S. O. (2013). Topographic representation of numerosity in the human parietal cortex. Science, 341(6150), 1123-1126.PubMedCrossRefPubMedCentralGoogle Scholar
  121. Hayashi, M. J., Kanai, R., Tanabe, H. C., Yoshida, Y., Carlson, S., Walsh, V., & Sadato, N. (2013). Interaction of numerosity and time in prefrontal and parietal cortex. Journal of Neuroscience, 33(3), 883–893.PubMedCrossRefPubMedCentralGoogle Scholar
  122. Hinton, S. C., & Meck, W. H. (2004). Frontal–striatal circuitry activated by human peak-interval timing in the supra-seconds range. Cognitive Brain Research, 21(2), 171–182.PubMedCrossRefPubMedCentralGoogle Scholar
  123. 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), 17–29.PubMedCrossRefPubMedCentralGoogle Scholar
  124. Honig, W. K. (2018). Studies of working memory in the pigeon. In Cognitive processes in animal behavior (pp. 211–248). New York, NY: Routledge.CrossRefGoogle Scholar
  125. Hurewitz, F., Gelman, R., & Schnitzer, B. (2006). Sometimes area counts more than number. Proceedings of the National Academy of Sciences of the United States of America, 103(51), 19599–19604.PubMedPubMedCentralCrossRefGoogle Scholar
  126. Hurst, M., Leigh Monahan, K., Heller, E., & Cordes, S. (2014). 123s and ABC s: developmental shifts in logarithmicto-linear responding reflect fluency with sequence values. Developmental Science, 17(6), 892–904.PubMedCrossRefPubMedCentralGoogle Scholar
  127. Hyde, D. C., Khanum, S., & Spelke, E. S. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92–107.PubMedPubMedCentralCrossRefGoogle Scholar
  128. Hyde, D. C., Porter, C. L., Flom, R., & Stone, S. A. (2013). Relational congruence facilitates neural mapping of spatial and temporal magnitudes in preverbal infants. Developmental Cognitive Neuroscience, 6, 102–112.PubMedCrossRefPubMedCentralGoogle Scholar
  129. Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychonomic Bulletin & Review, 18(6), 1222–1229.CrossRefGoogle Scholar
  130. Irving-Bell, L., Small, M., & Cowey, A. (1999). A distortion of perceived space in patients with right-hemisphere lesions and visual hemineglect. Neuropsychologia, 37(8), 919–925.PubMedCrossRefPubMedCentralGoogle Scholar
  131. Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. PNAS, 106(25), 10382–10385.PubMedCrossRefPubMedCentralGoogle Scholar
  132. Jang, S., & Cho, S. (2016). The acuity for numerosity (but not continuous magnitude) discrimination correlates with quantitative problem solving but not routinized arithmetic. Current Psychology, 35(1), 44–56.CrossRefGoogle Scholar
  133. Jordan, K., & Brannon, E. (2006). The multisensory representation of number in infancy. PNAS, 103(9), 3486–3489.PubMedCrossRefPubMedCentralGoogle Scholar
  134. Kadosh, R. C., Kadosh, K. C., Linden, D. E., Gevers, W., Berger, A., & Henik, A. (2007). 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(6), 957–970.CrossRefGoogle Scholar
  135. Kaufmann, L., & Nuerk, H. C. (2008). Basic number processing deficits in ADHD: A broad examination of elementary and complex number processing skills in 9-to 12-year-old children with ADHD-C. Developmental Science, 11(5), 692–699.PubMedCrossRefPubMedCentralGoogle Scholar
  136. 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(4), 376–385.PubMedCrossRefPubMedCentralGoogle Scholar
  137. Khanum, S., Hanif, R., Spelke, E. S., Berteletti, I., & Hyde, D. C. (2016). Effects of non-symbolic approximate number practice on symbolic numerical abilities in Pakistani children. PLoS ONE, 11(10), e0164436.PubMedPubMedCentralCrossRefGoogle Scholar
  138. Kramer, P., Bressan, P., & Grassi, M. (2011). Time estimation predicts mathematical intelligence. PLoS ONE, 6(12), e28621.PubMedPubMedCentralCrossRefGoogle Scholar
  139. Kuntsi, J., Oosterlaan, J., & Stevenson, J. (2001). Psychological mechanisms in hyperactivity: I response inhibition deficit, working memory impairment, delay aversion, or something else? The Journal of Child Psychology and Psychiatry and Allied Disciplines, 42(2), 199–210.CrossRefGoogle Scholar
  140. Lakoff, G., & Johnson, M. (1980). Conceptual metaphor in everyday language. The Journal of Philosophy, 77(8), 53–486.CrossRefGoogle Scholar
  141. Lambrechts, A., Walsh, V., & van Wassenhove, V. (2013). Evidence accumulation in the magnitude system. PLoS ONE, 8(12), e82122.PubMedPubMedCentralCrossRefGoogle Scholar
  142. Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40.Google Scholar
  143. Levey, D. J. (1988). Spatial and temporal variation in Costa Rican fruit and fruit-eating bird abundance. Ecological Monographs, 58(4), 251–269.CrossRefGoogle Scholar
  144. Lewis, E. A., Zax, A., & Cordes, S. (2017). The impact of emotion on numerical estimation: A developmental perspective. The Quarterly Journal of Experimental Psychology, 1–36. Advance online publication.
  145. Libertus, M. E., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica, 141(3), 373-379.PubMedPubMedCentralCrossRefGoogle Scholar
  146. Lindskog, M., Winman, A., & Poom, L. (2016). Arithmetic training does not improve approximate number system acuity. Frontiers in Psychology, 7, 1634. PubMedPubMedCentralCrossRefGoogle Scholar
  147. Loiselle, B. A., & Blake, J. G. (1991). Temporal variation in birds and fruits along an elevational gradient in Costa Rica. Ecology, 72(1), 180–193.CrossRefGoogle Scholar
  148. Lourenco, S., & Longo, M. (2010). General magnitude representation in human infants. Psychological Science, 21(6), 873–881. CrossRefPubMedPubMedCentralGoogle Scholar
  149. Lourenco, S. F., Ayzenberg, V., & Lyu, J. (2016). A general magnitude system in human adults: Evidence from a subliminal priming paradigm. Cortex, 81, 93–103.PubMedCrossRefPubMedCentralGoogle Scholar
  150. Lourenco, S. F., & Bonny, J. W. (2017). Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children. Developmental Science, 20(4), e12418.CrossRefGoogle Scholar
  151. Lourenco, S. F., Bonny, J. W., Fernandez, E. P., & Rao, S. (2012). Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences, 109(46), 18737–18742.CrossRefGoogle Scholar
  152. Lusardi, A. (2012). Numeracy, financial literacy, and financial decision-making (NBER Working Paper No. 17821). Retrieved from
  153. Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261.PubMedCrossRefPubMedCentralGoogle Scholar
  154. Mariani, M. A., & Barkley, R. A. (1997). Neuropsychological and academic functioning in preschool boys with attention deficit hyperactivity disorder. Developmental Neuropsychology, 13(1), 111–129.CrossRefGoogle Scholar
  155. Mattell, M., & Meck, W. (2004). Cortico-striatal circuits and interval timing: Coincidence detection of oscillatory processes. Cognitive Brain Research, 21, 139–170.CrossRefGoogle Scholar
  156. Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS ONE
  157. Meck, W. H., & Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9(3), 320.PubMedPubMedCentralGoogle Scholar
  158. Meck, W. H., Church, R. M., Wenk, G. L., & Olton, D. S. (1987). Nucleus basalis magnocellularis and medial septal area lesions differentially impair temporal memory. Journal of Neuroscience, 7(11), 3505–3511.PubMedCrossRefPubMedCentralGoogle Scholar
  159. Meck, W. H., Penney, T. B., & Pouthas, V. (2008). Cortico-striatal representation of time in animals and humans. Current Opinion in Neurobiology, 18(2), 145–152.PubMedCrossRefPubMedCentralGoogle Scholar
  160. Merritt, D., Casasanto, D., & Brannon, E. (2010). Do monkeys think in metaphors? Representations of space and time in monkeys and humans. Cognition, 117(2), 191–202.PubMedPubMedCentralCrossRefGoogle Scholar
  161. Mills, D. L., Coffey-Corina, S., & Neville, H. J. (1997). Language comprehension and cerebral specialization from 13 to 20 months. Developmental Neuropsychology, 13(3), 397–445.CrossRefGoogle Scholar
  162. Minagawa-Kawai, Y., Mori, K., Naoi, N., & Kojima, S. (2007). Neural attunement processes in infants during the acquisition of a language-specific phonemic contrast. Journal of Neuroscience, 27(2), 315–321.PubMedCrossRefPubMedCentralGoogle Scholar
  163. Mix, K. S. , & Cheng, Y.-L. (2012). Space and math: The developmental and educational implications. In J. Benson (Ed.), Advances in child development and behavior (pp. 179 – 243). New York, NY : Elsevier.Google Scholar
  164. Möhring, W., Frick, A., & Newcombe, N. S. (2018). Spatial scaling, proportional thinking, and numerical understanding in 5-to 7-year-old children. Cognitive Development, 45, 57–67.CrossRefGoogle Scholar
  165. Möhring, W., Libertus, M. E., & Bertin, E. (2012). Speed discrimination in 6-and 10-month-old infants follows Weber’s law. Journal of Experimental Child Psychology, 111(3), 405–418.PubMedCrossRefPubMedCentralGoogle Scholar
  166. Mussolin, C., De Volder, A., Grandin, C., Schlögel, X., Nassogne, M. C., & Noël, M. P. (2010). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22(5), 860–874.PubMedCrossRefPubMedCentralGoogle Scholar
  167. Newcombe, N. (2014). The origins and development of magnitude estimation. Ecological Psychology, 2, 147–157.CrossRefGoogle Scholar
  168. Newcombe, N. S., Levine, S. C., & Mix, K. S. (2015). Thinking about quantity: the intertwined development of spatial and numerical cognition. Wiley Interdisciplinary Reviews: Cognitive Science, 6(6), 491–505.PubMedPubMedCentralGoogle Scholar
  169. Norris, J. E., & Castronovo, J. (2016). Dot display affects approximate number system acuity and relationships with mathematical achievement and inhibitory control. PloS one, 11(5), e0155543.PubMedPubMedCentralCrossRefGoogle Scholar
  170. Nys, J., & Content, A. (2012). Judgments of discrete and continuous quantity in adults: Number counts!. The Quarterly Journal of Experimental Psychology, 65(4), 675–690.PubMedCrossRefPubMedCentralGoogle Scholar
  171. Odic, D. (2018). Children’s intuitive sense of number develops independently of their perception of area, density, length, and time. Developmental Science. Advance online publication.
  172. Odic, D., Libertus, M., Feigenson, L., & Halberda, J. (2013). Developmental change in the acuity of approximate number and area representations. Developmental Psychology, 49(6), 1103–1112.PubMedCrossRefPubMedCentralGoogle Scholar
  173. Odic, D., Lisboa, J. V., Eisinger, R., Olivera, M. G., Maiche, A., & Halberda, J. (2016). Approximate number and approximate time discrimination each correlate with school math abilities in young children. Acta Psychologica, 163, 17–26.PubMedCrossRefPubMedCentralGoogle Scholar
  174. Odic, D., & Starr, A. (2018). An introduction to the approximate number system. Child Development Perspectives
  175. Osborne, J. L., Clark, S. J., Morris, R. J., Williams, I. H., Riley, J. R., Smith, A. D., ... Edwards, A. S. (1999). A landscape-scale study of bumble bee foraging range and constancy, using harmonic radar. Journal of Applied Ecology, 36(4), 519–533.Google Scholar
  176. Ouellet, M., Santiago, J., Israeli, Z., & Gabay, S. (2010). Is the future the right time?. Experimental Psychology, 57(4), 308–314. CrossRefPubMedPubMedCentralGoogle Scholar
  177. Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M. (2016). Non-symbolic approximate arithmetic training improves math performance in preschoolers. Journal of Experimental Child Psychology, 152, 278–293.PubMedPubMedCentralCrossRefGoogle Scholar
  178. Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019.PubMedPubMedCentralCrossRefGoogle Scholar
  179. Park, J., & Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133(1), 188–200.PubMedPubMedCentralCrossRefGoogle Scholar
  180. Patro, K., & Haman, M. (2012). The spatial–numerical congruity effect in preschoolers. Journal of Experimental Child Psychology, 111(3), 534–542.PubMedCrossRefPubMedCentralGoogle Scholar
  181. Perani, D., Saccuman, M. C., Scifo, P., Anwander, A., Spada, D., Baldoli, C., ... Friederici, A. D. (2011). Neural language networks at birth. Proceedings of the National Academy of Sciences, 108(38), 16056–16061.Google Scholar
  182. 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(3), 461–479.PubMedCrossRefPubMedCentralGoogle Scholar
  183. Peters, E., Västfjäll, D., Slovic, P., Mertz, C. K., Mazzocco, K., & Dickert, S. (2006). Numeracy and decision making. Psychological Science, 17(5), 407–413.PubMedCrossRefPubMedCentralGoogle Scholar
  184. Piazza, M., Mechelli, A., Butterworth, B., & Price, C. J. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes?. NeuroImage, 15(2), 435–446.PubMedCrossRefPubMedCentralGoogle Scholar
  185. Pouthas, V., George, N., Poline, J. B., Pfeuty, M., VandeMoorteele, P. F., Hugueville, L., ... Renault, B. (2005). Neural network involved in time perception: An fMRI study comparing long and short interval estimation. Human Brain Mapping, 25(4), 433–441.Google Scholar
  186. Previtali, P., de Hevia, M. D., & Girelli, L. (2010). Placing order in space: The SNARC effect in serial learning. Experimental Brain Research, 201(3), 599–605.PubMedCrossRefPubMedCentralGoogle Scholar
  187. Price, G. R., & Fuchs, L. S. (2016). The mediating relation between symbolic and nonsymbolic foundations of math competence. PLoS ONE, 11(2), e0148981.PubMedPubMedCentralCrossRefGoogle Scholar
  188. Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), R1042–R1043.PubMedCrossRefPubMedCentralGoogle Scholar
  189. Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140(1), 50–57.PubMedCrossRefPubMedCentralGoogle Scholar
  190. Provasi, J., Rattat, A. C., & Droit-Volet, S. (2011). Temporal bisection in 4-month-old infants. Journal of Experimental Psychology: Animal Behavior Processes, 37(1), 108.PubMedPubMedCentralGoogle Scholar
  191. Rammsayer, T., & Classen, W. (1997). Impaired temporal discrimination in Parkinson’s disease: Temporal processing of brief durations as an indicator of degeneration of dopaminergic neurons in the basal ganglia. International Journal of Neuroscience, 91(1/2), 45–55.PubMedCrossRefPubMedCentralGoogle Scholar
  192. Reyna, V. F., Nelson, W. L., Han, P. K., & Dieckmann, N. F. (2009). How numeracy influences risk comprehension and medical decision making. Psychological Bulletin, 135(6), 943.PubMedPubMedCentralCrossRefGoogle Scholar
  193. Reznick, J. S., Morrow, J. D., Goldman, B. D., & Snyder, J. (2004). The onset of working memory in infants. Infancy, 6(1), 145–154.CrossRefGoogle Scholar
  194. Roberts, W. A., Coughlin, R., & Roberts, S. (2000). Pigeons flexibly time or count on cue. Psychological Science, 11(3), 218–222.PubMedCrossRefPubMedCentralGoogle Scholar
  195. Romberg, A. R., & Saffran, J. R. (2010). Statistical learning and language acquisition. Wiley Interdisciplinary Reviews: Cognitive Science, 1(6), 906–914.PubMedPubMedCentralGoogle Scholar
  196. Rose, S. A., Feldman, J. F., & Jankowski, J. J. (2002). Processing speed in the 1st year of life: A longitudinal study of preterm and full-term infants. Developmental Psychology, 38(6), 895.PubMedCrossRefPubMedCentralGoogle Scholar
  197. Ross-Sheehy, S., Oakes, L. M., & Luck, S. J. (2003). The development of visual short-term memory capacity in infants. Child Development, 74(6), 1807–1822.PubMedCrossRefPubMedCentralGoogle Scholar
  198. Rugani, R., Lunghi, M., Di Giorgio, E., Regolin, L., Dalla Barba, B., Vallortigara, G., & Simion, F. (2017). A mental number line in human newborns. bioRxiv, 159335.Google Scholar
  199. Rugani, R., Vallortigara, G., Priftis, K., & Regolin, L. (2015). Number-space mapping in the newborn chick resembles humans’ mental number line. Science, 347(6221), 534–536.PubMedCrossRefPubMedCentralGoogle Scholar
  200. Saffran, J. R., Aslin, R. N., & Newport, E. L. (1996). Statistical learning by 8-month-old infants. Science, 274(5294), 1926–1928.PubMedCrossRefPubMedCentralGoogle Scholar
  201. Santiago, J., Lupáñez, J., Pérez, E., & Funes, M. J. (2007). Time (also) flies from left to right. Psychonomic Bulletin & Review, 14(3), 512–516.CrossRefGoogle Scholar
  202. Schafer, G., & Plunkett, K. (1998). Rapid word learning by fifteen-month-olds under tightly controlled conditions. Child Development, 69(2), 309–320.PubMedCrossRefPubMedCentralGoogle Scholar
  203. Schmitt, V., Kröger, I., Zinner, D., Call, J., & Fischer, J. (2013). Monkeys perform as well as apes and humans in a size discrimination task. Animal Cognition, 16(5), 829–838.PubMedPubMedCentralCrossRefGoogle Scholar
  204. Shettleworth, S. J., Krebs, J. R., Stephens, D. W., & Gibbon, J. (1988). Tracking a fluctuating environment: A study of sampling. Animal Behaviour, 36(1), 87–105.CrossRefGoogle Scholar
  205. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250.PubMedCrossRefPubMedCentralGoogle Scholar
  206. Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545.CrossRefGoogle Scholar
  207. Silbert, A., Wolff, P. H., & Lilienthal, J. (1977). Spatial and temporal processing in patients with Turner’s syndrome. Behavior Genetics, 7(1), 11–21.PubMedPubMedCentralGoogle Scholar
  208. Simon, T. J. (2008). A new account of the neurocognitive foundations of impairments in space, time, and number processing in children with chromosome 22q11.2 deletion syndrome. Developmental Disabilities Research Reviews, 14(1), 52–58.PubMedPubMedCentralCrossRefGoogle Scholar
  209. Simon, T. J., Bearden, C. E., Mc-Ginn, D. M., & Zackai, E. (2005). Visuospatial and numerical cognitive deficits in children with chromosome 22q11.2 deletion syndrome. Cortex, 41(2), 145–155.PubMedPubMedCentralCrossRefGoogle Scholar
  210. Simon, T. J., Takarae, Y., DeBoer, T., McDonald-McGinn, D. M., Zackai, E. H., & Ross, J. L. (2008). Overlapping numerical cognition impairments in children with chromosome 22q11.2 deletion or Turner syndromes. Neuropsychologia, 46(1), 82–94.PubMedCrossRefPubMedCentralGoogle Scholar
  211. Skagerlund, K., & Träff, U. (2014). Development of magnitude processing in children with developmental dyscalculia: Space, time, and number. Frontiers in Psychology, 5.Google Scholar
  212. Skagerlund, K., & Träff, U. (2016). Processing of space, time, and number contributes to mathematical abilities above and beyond domain-general cognitive abilities. Journal of Experimental Child Psychology, 143, 85–101.Google Scholar
  213. Smith, A., Taylor, E., Rogers, J. W., Newman, S., & Rubia, K. (2002). Evidence for a pure time perception deficit in children with ADHD. Journal of Child Psychology and Psychiatry, 43(4), 529–542.PubMedCrossRefPubMedCentralGoogle Scholar
  214. Sokolowski, H. M., Fias, W., Mousa, A., & Ansari, D. (2017). Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging meta-analysis. NeuroImage, 146, 376–394.PubMedCrossRefPubMedCentralGoogle Scholar
  215. Srinivasan, M., & Carey, S. (2010). The long and the short of it: On the nature and origin of functional overlap between representations of space and time. Cognition, 116(2), 217–241.PubMedPubMedCentralCrossRefGoogle Scholar
  216. Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences, 110(45), 18116–18120.CrossRefGoogle Scholar
  217. Starr, A., & Brannon, E. M. (2015). Developmental continuity in the link between sensitivity to numerosity and physical size. Journal of Numerical Cognition, 1(1), 7–20.Google Scholar
  218. Stevens, S. S. (1957). On the psychophysical law. Psychological Review, 64(3), 153.PubMedCrossRefPubMedCentralGoogle Scholar
  219. Thompson, P. M., Giedd, J. N., Woods, R. P., MacDonald, D., Evans, A., & Toga, A. (2000). Growth patterns in the developing brain detected by using continuum mechanical tensor maps. Nature, 404(6774), 190.PubMedCrossRefPubMedCentralGoogle Scholar
  220. Tipples, J. (2008). Negative emotionality influences the effects of emotion on time perception. Emotion, 8(1), 127.PubMedCrossRefPubMedCentralGoogle Scholar
  221. Tipples, J. (2011). When time stands still: Fear-specific modulation of temporal bias due to threat. Emotion, 11(1), 74–80.PubMedCrossRefPubMedCentralGoogle Scholar
  222. Tobia, V., Rinaldi, L., & Marzocchi, G. M. (2016). Time processing impairments in preschoolers at risk of developing difficulties in mathematics. Developmental Science.
  223. Tudusciuc, O., & Nieder, A. (2010). Comparison of length judgments and the Müller-Lyer illusion in monkeys and humans. Experimental Brain Research, 207(3/4), 221–231.PubMedCrossRefPubMedCentralGoogle Scholar
  224. Tversky, B., Kugelmass, S., & Winter, A. (1991). Cross-cultural and developmental trends in graphic productions. Cognitive Psychology, 23(4), 515–557.CrossRefGoogle Scholar
  225. Vallesi, A., Binns, M. A., & Shallice, T. (2008). An effect of spatial–temporal association of response codes: Understanding the cognitive representations of time. Cognition, 107(2), 501–527.PubMedCrossRefPubMedCentralGoogle Scholar
  226. van der Knaap, M. S., van der Grond, J., van Rijen, P. C., Faber, J. A., Valk, J., & Willemse, K. (1990). Age-dependent changes in localized proton and phosphorus MR spectroscopy of the brain. Radiology, 176(2), 509–515.PubMedCrossRefPubMedCentralGoogle Scholar
  227. Van Galen, M. S., & Reitsma, P. (2008). Developing access to number magnitude: A study of the SNARC effect in 7-to 9-year-olds. Journal of Experimental Child Psychology, 101(2), 99–113.PubMedCrossRefPubMedCentralGoogle Scholar
  228. VanMarle, K., & Wynn, K. (2006). Six-month-old infants use analog magnitudes to represent duration. Developmental Science, 9(5), F41–F49.PubMedCrossRefPubMedCentralGoogle Scholar
  229. Vasilyeva, M., & Lourenco, S. F. (2012). Development of spatial cognition. Wiley Interdisciplinary Reviews: Cognitive Science, 3(3), 349–362.PubMedPubMedCentralGoogle Scholar
  230. Venkatraman, V., Ansari, D., & Chee, M. W. (2005). Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia, 43(5), 744–753.PubMedCrossRefPubMedCentralGoogle Scholar
  231. Vicario, C. M., Rappo, G., Pepi, A., Pavan, A., & Martino, D. (2012). Temporal abnormalities in children with developmental dyscalculia. Developmental Neuropsychology, 37(7), 636–652.PubMedCrossRefPubMedCentralGoogle Scholar
  232. Vicario, C. M., Yates, M. J., & Nicholls, M. E. (2013). Shared deficits in space, time, and quantity processing in childhood genetic disorders. Frontiers in Psychology, 4.
  233. Vuokko, E., Niemivirta, M., & Helenius, P. (2013). Cortical activation patterns during subitizing and counting. Brain Research, 1497, 40–52.PubMedCrossRefPubMedCentralGoogle Scholar
  234. Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488.PubMedCrossRefPubMedCentralGoogle Scholar
  235. Walsh, V., & Pascual-Leone, A. (2003). Transcranial magnetic stimulation: A neurochronometrics of mind. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  236. Wang, J., Odic, D., Halberda, J., & Feigenson, L. (2016). Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance. Journal of Experimental Child Psychology, 147, 82–99.PubMedCrossRefPubMedCentralGoogle Scholar
  237. Wearden, J. H., Norton, R., Martin, S., & Montford-Bebb, O. (2007). Internal clock processes and the filled-duration illusion. Journal of Experimental Psychology: Human Perception and Performance, 33(3), 716.PubMedPubMedCentralGoogle Scholar
  238. Westerberg, H., Hirvikoski, T., Forssberg, H., & Klingberg, T. (2004). Visuo-spatial working memory span: a sensitive measure of cognitive deficits in children with ADHD. Child Neuropsychology, 10(3), 155–161.PubMedCrossRefPubMedCentralGoogle Scholar
  239. Woodward, A. L., Markman, E. M., & Fitzsimmons, C. M. (1994). Rapid word learning in 13-and 18-month-olds. Developmental Psychology, 30(4), 553.CrossRefGoogle Scholar
  240. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11.PubMedCrossRefPubMedCentralGoogle Scholar
  241. Xuan, B., Zhang, D., He, S., & Chen, X. (2007). Larger stimuli are judged to last longer. Journal of Vision, 7(10), 2–2.PubMedCrossRefPubMedCentralGoogle Scholar
  242. Yang, T., Chen, C., Zhou, X., Xu, J., Dong, Q., & Chen, C. (2014). Development of spatial representation of numbers: A study of the SNARC effect in Chinese children. Journal of Experimental Child Psychology, 117, 1–11.PubMedCrossRefPubMedCentralGoogle Scholar
  243. Yates, M. J., Loetscher, T., & Nicholls, M. E. (2012). A generalized magnitude system for space, time, and quantity? A cautionary note. Journal of Vision, 12(7), 9–9.PubMedCrossRefPubMedCentralGoogle Scholar
  244. Young, L., & Cordes, S. (2013). Fewer things, lasting longer the effect of emotion on quantity judgments. Psychological Science
  245. Zimmermann, E., & Fink, G. R. (2016). Numerosity perception after size adaptation. Scientific Reports, 6, 32810.PubMedPubMedCentralCrossRefGoogle Scholar
  246. Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417(6885), 138–139.PubMedCrossRefPubMedCentralGoogle Scholar

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© The Psychonomic Society, Inc. 2019

Authors and Affiliations

  1. 1.Boston CollegeChestnut HillUSA

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