| [1] | 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
|
| [2] | Gilmore CK, McCarthy SE, Spelke ES (2010) Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition 115: 394–406. doi: 10.1016/j.cognition.2010.02.002
|
| [3] | Brannon EM (2002) The development of ordinal numerical knowledge in infancy. Cognition 83: 223–240. doi: 10.1016/s0010-0277(02)00005-7
|
| [4] | Gallistel CR, Gelman R (2005) Mathematical cognition. In: Holyoak K, Morrison R, editors. The Cambridge handbook of thinking and reasoning. Cambridge, UK: Cambridge University Press. pp. 559–588.
|
| [5] | Izard Vr, Sann C, Spelke ES, Streri A (2009) Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences 106: 10382–10385. doi: 10.1073/pnas.0812142106
|
| [6] | Xu F, Spelke ES (2000) Large number discrimination in 6-month-old infants. Cognition 74: B1–B11. doi: 10.1016/s0010-0277(99)00066-9
|
| [7] | Lipton JS, Spelke ES (2003) Origins of number sense: large-number discrimination in human infants. Psychol Sci 14: 396–401. doi: 10.1111/1467-9280.01453
|
| [8] | 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. Dev Psychol 44: 1457–1465. doi: 10.1037/a0012682
|
| [9] | Pica P, Lemer C, Izard V, Dehaene S (2004) Exact and approximate arithmetic in an Amazonian indigene group. Science 306: 499–503. doi: 10.1126/science.1102085
|
| [10] | Gelman R, Gallistel CR (1978) The child's understanding of number. Cambridge, MA: Harvard University Press.
|
| [11] | Sekuler R, Mierkiewicz D (1977) Children's judgments of numerical inequality. Child Dev 48: 630–633. doi: 10.1111/j.1467-8624.1977.tb01208.x
|
| [12] | Temple E, Posner MI (1998) Brain mechanisms of quantity are similar in 5-year-olds and adults. Proc Natl Acad Sci U S A 95: 7836–7841. doi: 10.1073/pnas.95.13.7836
|
| [13] | Moyer RS, Landauer TK (1967) The time required for judgements of numerical inequality. Nature 215: 1519–1520. doi: 10.1038/2151519a0
|
| [14] | Holloway ID, Ansari D (2009) Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children's mathematics achievement. J Exp Child Psychol 103: 17–29. doi: 10.1016/j.jecp.2008.04.001
|
| [15] | Dehaene S (1997) The number sense: how the mind creates mathematics. New York: Oxford Univ. Press. 64–90 p.
|
| [16] | Wynn K (1992) Addition and subtraction by human infants. Nature 358: 749–750. doi: 10.1038/358749a0
|
| [17] | Carey S (2004) Bootstrapping and the origins of concepts. Daedalus 133: 59–68. doi: 10.1162/001152604772746701
|
| [18] | 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
|
| [19] | Brannon EM, Van de Walle GA (2001) The development of ordinal numerical competence in young children. Cogn Psychol 43: 53–81. doi: 10.1006/cogp.2001.0756
|
| [20] | Rousselle L, Palmers E, No？l M-P (2004) Magnitude comparison in preschoolers: what counts? Influence of perceptual variables. J Exp Child Psychol 87: 57–84. doi: 10.1016/j.jecp.2003.10.005
|
| [21] | Wagner JB, Johnson SC (2011) An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition 119: 10–22. doi: 10.1016/j.cognition.2010.11.014
|
| [22] | Slaughter V, Kamppi D, Paynter J (2006) Toddler subtraction with large sets: further evidence for an analog-magnitude representation of number. Developmental Science 9: 33–39. doi: 10.1111/j.1467-7687.2005.00460.x
|
| [23] | Huntley-Fenner G, Cannon E (2000) Preschoolers' magnitude comparisons are mediated by a preverbal analog mechanism. Psychol Sci 11: 147–152. doi: 10.1111/1467-9280.00230
|
| [24] | Halberda J, Mazzocco MMM, Feigenson L (2008) Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455: 665–668. doi: 10.1038/nature07246
|
| [25] | Libertus ME, Feigenson L, Halberda J (2011) Preschool acuity of the approximate number system correlates with school math ability. Psychon Bull Rev 14: 1292–1300. doi: 10.1111/j.1467-7687.2011.01080.x
|
| [26] | Inglis M, Attridge N, Batchelor S, Gilmore C (2011) Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychon Bull Rev 18..
|
| [27] | Mundy E, Gilmore CK (2009) Children's mapping between symbolic and nonsymbolic representations of number. J Exp Child Psychol 103: 490–502. doi: 10.1016/j.jecp.2009.02.003
|
| [28] | Lonnemann J, Linkersd？rfer J, Hasselhorn M, Lindberg S (2011) Symbolic and non-symbolic distance effects in children and their connection with arithmetic skills. Journal of Neurolinguistics 24: 583–591. doi: 10.1016/j.jneuroling.2011.02.004
|
| [29] | Price GR, 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 Psychol (Amst) 140: 50–57. doi: 10.1016/j.actpsy.2012.02.008
|
| [30] | Libertus M, Odic D, Halberda J (2012) Intuitive sense of number correlates with scores on college-entrance examination. Acta Psychol (Amst) 141: 373–379. doi: 10.1016/j.actpsy.2012.09.009
|
| [31] | DeWind NK, Brannon EM (2012) Malleability of the approximate number system: effects of feedback and training. Frontiers in Cognitive Neuroscience 6: 1–10. doi: 10.3389/fnhum.2012.00068
|
| [32] | Lyons IM, Beilock SL (2011) Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition 121: 256–261. doi: 10.1016/j.cognition.2011.07.009
|
| [33] | Mazzocco MMM, Feigenson L, Halberda J (2011) Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS ONE 6: e23749. doi: 10.1371/journal.pone.0023749
|
| [34] | Mussolin C, Nys J, Leybaert J, Content A (2012) Relationships between approximate number system acuity and early symbolic number abilities. Trends in Neuroscience and Education 1: 21–31. doi: 10.1016/j.tine.2012.09.003
|
| [35] | Libertus ME, Feigenson L, Halberda J (2013) Is approximate number precision a stable predictor of math ability? Learning and Individual Differences 25: 126–133. doi: 10.1016/j.lindif.2013.02.001
|
| [36] | Ellis N, Large B (1988) The early stages of reading: A longitudinal study. Applied Cognitive Psychology 2: 47–76. doi: 10.1002/acp.2350020106
|
| [37] | Crano WD, Mellon PM (1978) Causal influence of teachers' expectations on children's academic performance: A cross-lagged panel analysis. J Educ Psychol 70: 39–49. doi: 10.1037/0022-0663.70.1.39
|
| [38] | Gathercole SE, Willis C, Emslie H, Baddeley AD (1992) Phonological memory and vocabulary development during the early school years: A longitudinal study. Dev Psychol 28: 887–898. doi: 10.1037/0012-1649.28.5.887
|
| [39] | Trick L, Pylyshyn Z (1994) Why are small and large numbers enumerated differently? A limited capacity preattentive stage in vision. Psychol Rev 101: 80–102. doi: 10.1037/0033-295x.101.1.80
|
| [40] | Schneider W, Eschmann A, Zuccolotto A (2002) E-prime reference guide. Pittsburgh, USA: Psychology Software Tools Inc.
|
| [41] | Fuson KC (1988) Children's counting and concepts of number. New York, USA: Springer.
|
| [42] | Van Nieuwenhoven C, No？l M-P, Grégoire J (2001) TEst DIagnostique des compétences de base en MATHématiques TEDI-MATH In: ECPA, editor.
|
| [43] | von Aster MG, Dellatolas G (2006) ZAREKI-R: Batterie pour l'évaluation du traitement des nombres et du calcul chez l'enfant; Adaptation francaise. Paris: ECPA.
|
| [44] | Raven J (1977) Raven's Coloured Progressive Matrices. London: H. K. Lewis.
|
| [45] | Coquet F, Roustit J, Jeunier B (2007) La Batterie Evalo 2-6. évaluation du langage oral et des comportements non verbaux du jeune enfant. Rééducation Orthophonique 231: 203–226.
|
| [46] | Corsi PM (1972) Human memory and the medial temporal region of the brain [thesis]. Montreal: Canada.
|
| [47] | Chevrié-Muller C, Plaza M, editors (2001) Nouvelles Epreuves pour l'Examen du Langage (N-EEL). Paris: Les Editions du Centre de Psychologie Appliquée.
|
| [48] | Mandler G, Shebo BJ (1982) Subitizing: An analysis of its component processes. J Exp Psychol Gen 111: 1–22.
|
| [49] | Elzhov TV, Mullen KM, Spiess AN, Bolker B, Mullen MKM (2012) R interface to the Levenberg-Marquardt nonlinear least-squares algorithm found in MINPACK, plus support for bounds. Available: http://cran.r-project.org/web/packages/m？inpack.lm/index.html.
|
| [50] | Williams EJ (1959) The comparison of regression variables. Journal of the Royal Statistical Society (Series B) 21: 396–399.
|
| [51] | Steiger JH (1980) Tests for comparing elements of a correlation matrix. Psychol Bull 87: 245–251. doi: 10.1037/0033-2909.87.2.245
|
| [52] | Sikora P, Moore S, Greenberg E, Grunberg L (2008) Downsizing and alcohol use: A cross-lagged longitudinal examination of the spillover hypothesis. Work & Stress 22: 51–68. doi: 10.1080/02678370801999651
|
| [53] | Quartana PJ, Wickwire EM, Klick B, Grace E, Smith MT (2010) Naturalistic changes in insomnia symptoms and pain in temporomandibular joint disorder: A cross-lagged panel analysis. Pain 149: 325–331. doi: 10.1016/j.pain.2010.02.029
|
| [54] | Brunswick N, Neil Martin G, Rippon G (2012) Early cognitive profiles of emergent readers: A longitudinal study. J Exp Child Psychol 111: 268–285. doi: 10.1016/j.jecp.2011.08.001
|
| [55] | Luo YLL, Kovas Y, Haworth CMA, Plomin R (2011) The etiology of mathematical self-evaluation and mathematics achievement: Understanding the relationship using a cross-lagged twin study from ages 9 to 12. Learning and Individual Differences 21: 710–718. doi: 10.1016/j.lindif.2011.09.001
|
| [56] | Rogosa D (1980) A critique of cross-lagged correlation. Psychol Bull 88: 245–258. doi: 10.1037/0033-2909.88.2.245
|
| [57] | Piazza M, Facoetti A, Trussardi AN, Berteletti I, Conte S, et al. (2010) Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition 116: 33–41. doi: 10.1016/j.cognition.2010.03.012
|
| [58] | Lindskog M, Winman A, Juslin P, Poom L (2013) Measuring acuity of the Approximate Number System reliably and validly: The evaluation of an adaptive test procedure. Frontiers in Psychology 4..
|
| [59] | Inglis M, Gilmore C (2014) Indexing the approximate number system. Acta Psychol (Amst) 145: 147–155. doi: 10.1016/j.actpsy.2013.11.009
|
| [60] | Gilmore CK, McCarthy SE, Spelke ES (2007) Symbolic arithmetic knowledge without instruction. Nature 447: 589–591. doi: 10.1038/nature05850
|
| [61] | Carey S (2001) Cognitive foundations of arithmetic: Evolution and ontogenesis. Mind & Language and Speech 16: 37–55. doi: 10.1111/1468-0017.00155
|
| [62] | Carey S, editor (2009) The origin of concepts (Oxford series in cognitive development). New York: Oxford University Press.
|
| [63] | Verguts T, Fias W (2004) Representation of number in animals and humans: A neural model. J Cogn Neurosci 16: 1493–1504. doi: 10.1162/0898929042568497
|
| [64] | Nys J, Ventura P, Fernandes T, Querido L, Leybaert J, et al. (2013) Does math education modify the approximate number system? A comparison of literate, ex-illiterate and illiterate adults. Trends in Neuroscience and Education 2: 13–22. doi: 10.1016/j.tine.2013.01.001
|
| [65] | Landerl K, Bevan A, Butterworth B (2004) Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition 93: 99–125. doi: 10.1016/j.cognition.2003.11.004
|
| [66] | Geary DC (1993) Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychol Bull 114: 345–362. doi: 10.1037/0033-2909.114.2.345
|
| [67] | Ostad SA (1997) Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children. Br J Educ Psychol 67: 345–357. doi: 10.1111/j.2044-8279.1997.tb01249.x
|
| [68] | Shalev RS (2007) Prevalence of developmental dyscalculia. In: Berch DB, Mazzocco MMM, editors. Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities. Baltimore, MD: Paul H. Brookes Publishing Co. pp. 49–60.
|
| [69] | De Smedt B, Gilmore CK (2011) Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. J Exp Child Psychol 108: 278–292. doi: 10.1016/j.jecp.2010.09.003
|
| [70] | Rousselle L, No？l M-P (2007) Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition 102: 361–395. doi: 10.1016/j.cognition.2006.01.005
|
| [71] | Mussolin C, Mejias S, No？l M-P (2010) Symbolic and non-symbolic number comparison in children with and without dyscalculia. Cognition 115: 10–25. doi: 10.1016/j.cognition.2009.10.006
|
| [72] | Landerl K, Fussenegger B, Moll K, Willburger E (2009) Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. J Exp Child Psychol 103: 309–324. doi: 10.1016/j.jecp.2009.03.006
|
| [73] | No？l M-P, Rousselle L (2011) Developmental changes in the profiles of dyscalculia: an explanation based on a double exact-and-approximate number representation model. Frontiers in Human Neuroscience 5..
|
| [74] | Mussolin C (2009) When [5] looks like [6] - A deficit of the number magnitude representation in developmental dyscalculia: Behavioural and brain-imaging investigation. Louvain-la-Neuve: Université Catholique de Louvain, Belgium.
|
