Open questions and a proposal: A critical review of the evidence on infant numerical abilities

Cognition

Volumn 128, Issue 3, 2013, Pages 331-352

  Cantrell, Lisa ^a   Smith, Linda B ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Infant; Number; Quantity discrimination

Indexed keywords

ARTICLE; AUDITORY DISCRIMINATION; COGNITION; CONCEPTUAL FRAMEWORK; HUMAN; KNOWLEDGE; PRIORITY JOURNAL; VISUAL DISCRIMINATION; VISUAL MEMORY; WORKING MEMORY;

INFANT; NUMBER; QUANTITY DISCRIMINATION;

CHILD DEVELOPMENT; COGNITION; DISCRIMINATION LEARNING; HUMANS; INFANT; MATHEMATICS;

EID: 84878932833     PISSN: 00100277     EISSN: 18737838     Source Type: Journal    
DOI: 10.1016/j.cognition.2013.04.008     Document Type: Article

References (124)

1. Allik J., Tuulmets T. Occupancy model of perceived numerosity. Perception & Psychophysics 1991, 49:303-314.
2. Antell S.E., Keating D.P. Perception of numerical invariance in neonates. Child Development 1983, 54(3):695-701.
3. Aslin R.N. What's in a look?. Developmental Science 2007, 10:48-53.
4. Attneave F. Dimensions of similarity. American Journal of Psychology 1950, 63:516-556.
5. Banks M.S., Ginsburg A.P. Early visual preferences: A review and a new theoretical treatment. Advances in child development and behavior 1985, 207-246. Academic Press, New York. H.W. Reese (Ed.).
6. Beals R., Krantz D.H., Tversky A. Foundations of multidimensional scaling. Psychological Review 1968, 75(2):127-142.
7. Bevan W., Turner E.D. Assimilation and contrast in the estimation of number. Journal of Experimental Psychology 1964, 67:458-462.
8. Bijeljacbabic R., Bertoncini J., Mehler J. How do 4-day-old infants categorize multisyllabic utterances. Developmental Psychology 1993, 29(4):711-721.
9. Brannon E.M. The development of ordinal numerical knowledge in infancy. Cognition 2002, 83(3):223-240.
10. Brannon E.M., Abbott S., Lutz D.J. Number bias for the discrimination of large visual sets in infancy. Cognition 2004, 93(2):B59-B68.
11. Brannon E.M., Lutz D., Cordes S. The development of area discrimination and its implications for number representation in infancy. Developmental Science 2006, 9(6):F59-F64.
12. Brannon E.M., Suanda S., Libertus K. Temporal discrimination increases in precision over development and parallels the development of numerosity discrimination. Developmental science 2007, 10(6):770-777.
13. Brannon E.M., Terrace H.S. Ordering of the numerosities 1 to 9 by monkeys. Science 1998, 282(5389):746-749.
14. Brez, C. C., & Colombo, J. (2011). Your eyes say "no", but your hear says "yes": Behavioral and psychophysiological indices in infant quantitative processing. Infancy?
15. Brez C.C., Cohen L., Colombo J. Infants' integration of featural and numerical information. Infant Behavior and Development 2012, 35:705-710.
16. Bronson G.W. Infant differences in rate of visual encoding. Child Development 1991, 62(1):44-54.
17. Burr D.C., Morrone M.C., Spinelli D. Evidence for edge and bar detectors in human vision. Vision Research 1989, 29:419-431.
18. Carey S. The origin of concepts 2009, Oxford University Press, New York.
19. Cheries E.W., Mitroff S.R., Wynn K., Scholl B.J. Cohesion as a constraint on object persistence in infancy. Developmental Science 2008, 11(3):427-432.
20. Clearfield M.W. Infants' enumeration of dynamic displays. Cognitive Development 2004, 2(3):309-324.
21. Clearfield M.W. A dynamic account of infant looking behavior in small and large number tasks. Focus on cognitive psychology research 2005, 59-86. Nova Science Publishers. M.A. Vanchevsky (Ed.).
22. Clearfield M.W., Mix K.S. Number versus contour length in infants' discrimination of small visual sets. Psychological Science 1999, 10(5):408-411.
23. Clearfield M.W., Mix K.S. Amount versus number: Infants' use of area and contour length to discriminate small sets. Journal of Cognition and Development 2001, 2(3):243-260.
24. Cohen L.B., Marks K.S. How infants process addition and subtraction events. Developmental Science 2002, 5(2):186-201.
25. Colombo J., Mitchel D.W. Infant visual habituation. Neurobiology of Learning Memory 2009, 92(2):225-234.
26. Cooper R.G. Early number development: Discovering number space with addition and subtraction. Origins of cognitive skills 1984, 157-192. Erlbaum, Hillsdale, NJ. C. Sophian (Ed.).
27. Cordes S., Brannon E.M. The difficulties of representing continuous extent in infancy: Using number is just easier. Child Development 2008, 79(2):476-489.
28. Cordes S., Brannon E.M. Crossing the divide: Infants discriminate small from large numerosities. Developmental Psychology 2009, 45(6):1583-1594.
29. Cordes S., Brannon E.M. The relative salience of discrete and continuous quantity in young infants. Developmental Science 2009, 12(3):453-463.
30. Cordes S., Brannon E.M. Attending to one of many: When infants are surprisingly poor at discriminating an item's size. Frontiers in Psychology 2011, 2:65.
31. Cordes S., Gelman R., Gallistel C.R., Whalen J. Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin & Review 2001, 8(4):698-707.
32. Dehaene S. The number sense: How the mind creates mathematics 1997, Oxford University Press, USA.
33. Fantz R.L., Fagan J.F., Miranda S.B. Early visual selectivity. Infant Perception: From Sensation to Cognition 1975, 1:249-346.
34. Feigenson L. A double-dissociation in infants' representations of object arrays. Cognition 2005, 95(3):B37-B48.
35. Feigenson L., Carey S. Tracking individuals via object-files: Evidence from infants' manual search. Developmental Science 2003, 6(5):568-584.
36. Feigenson L., Carey S. On the limits of infants' quantification of small object arrays. Cognition 2005, 97(3):295-313.
37. Feigenson L., Carey S., Hauser M. The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological Science 2002, 13(2):150-156.
38. Feigenson L., Carey S., Spelke E. Infants' discrimination of number vs. continuous extent. Cognitive Psychology 2002, 44(1):33-66.
39. Feigenson L., Dehaene S., Spelke E. Core systems of number. Trends in Cognitive Sciences 2004, 8(7):307-314.
40. Feigenson L., Halberda J. Infants chunk object arrays into sets of individuals. Cognition 2004, 91(2):173-190.
41. Feron J., Gentaz E., Streri A. Evidence of amodal representation of small numbers across visuo-tactile modalities in 5-month-old infants. Cognitive Development 2006, 21(2):81-92.
42. Foard C.F., Kemler D.G. Holistic and analytic modes of processing: The multiple determinants of perceptual analysis. Journal of Experimental Psychology: General 1984, 113(1):94.
43. Garner W.R. The processing of information and structure 1974, Halsted Press, New York.
44. Garner W.R., Felfoldy G.L. Integrality of stimulus dimensions in various types of information processing. Cognitive Psychology 1970, 1(3):225-241.
45. Gebuis T., Reynvoet B. The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology 2011.
46. Gilmore R.O., Thomas H. Examining individual differences in infants' habituation patterns using objective quantitative techniques. Infant Behavior and Development 2002, 25(4):399-412.
47. Gao F., Levine S.C., Huttenlocher J. What do infants know about continuous quantity?. Journal of Experimental Child Psychology 2000, 77(1):20-29.
48. Goldstone R.L. Perceptual learning. Annual Review of Psychology 1998, 49:585-612.
49. Goldstone R.L., Steyvers M. The sensitization and differentiation of dimensions during category learning. Journal of Experimental Psychology: General 2001, 130:116-139.
50. Grau J.W., Nelson D.K. The distinction between integral and separable dimensions: Evidence for the integrality of pitch and loudness. Journal of Experimental Psychology: General 1988, 117(4):347.
51. Haith M.M. Eye contact and face scanning in early infancy. Science 1977, 198(4319):853-855.
52. Hespos S.J., Dora B., Rips L.J., Christie S. Infants make quantity discriminations for substances. Child Development 2012, 83(2):554-567.
53. Hyde D.C., Spelke E.S. Neural signatures of number processing in human infants: evidence for two core systems underlying numerical cognition. Developmental science 2011, 14(2):360-371.
54. Izard V., Sann C., Spelke E.S., Streri A. Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America 2009, 106(25):10382-10385.
55. Jones M., Goldstone R.L. The structure of integral dimensions: Contrasting topological and Cartesian representations. Journal of Experimental Psychology: Human Perception and Performance 2012.
56. Jordan K.E., Brannon E.M. The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences of the United States of America 2006, 103(9):3486-3489.
57. Jordan K.E., Suanda S.H., Brannon E.M. Intersensory redundancy accelerates preverbal numerical competence. Cognition 2008, 108:210-221.
58. Kafman E., Lord M., Reese T., Volkmann J. The discrimination of visual number. American Journal of Psychology 1949, 62:498-525.
59. Karmel B.Z. The effect of age, complexity, and amount of contour on pattern preferences in human infants. Journal of Experimental Child Psychology 1969, 7(2):339-354.
60. Kobayashi T., Hiraki K., Hasegawa T. Auditory-visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science 2005, 8(5):409-419.
61. Krueger L.E. Perceived numerosity. Attention, Perception, & Psychophysics 1972, 11(1):5-9.
62. Libertus M.E., Pruitt L.B., Woldorff M.G., Brannon E.M. Induced alpha-band oscillations reflect ratio-dependent number discrimination in the infant brain. Journal of Cognitive Neuroscience 2009, 21(12):2398-2406.
63. Libertus M.E., Brannon E.M. Stable individual differences in number discrimination in infancy. Developmental Science 2010, 13(6):900-906.
64. Lipton J.S., Spelke E.S. Origins of number sense: Large-number discrimination in human infants. Psychological Science 2003, 14(5):396-401.
65. Lipton J.S., Spelke E.S. Discrimination of large and small numerosities by human infants. Infancy 2004, 5(3):271-290.
66. Lockhead G.R. Processing dimensional stimuli: A note. Psychological Review 1972, 79(5):410.
67. Lourenco S.F., Longo M.R. Origins and development of generalized magnitude representation. Space, time, and number in the brain: Searching for the foundations of mathematical thought 2011, Elsevier. S. Dehaene, E. Brannon (Eds.).
68. Macchi Cassia V., Picozzi M., Girelli, de Hevia M.D. Increasing magnitude counts more: Asymmetrical processing of ordinality in 4-month-old infants. Cognition 2012, 124:183-193.
69. Mandler G., Shebo B. Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General 1982, 111:1-22.
70. Mansfield R.J. Neural basis of orientation perception in primate vision. Science 1974, 186:1133-1135.
71. McCrink K., Wynn K. Large-number addition and subtraction by 9-month-old infants. Psychological Science 2004, 15(11):776-781.
72. Meck W.H., Church R.M. A mode control model of counting and timing processes. Journal of Experimental Psychology - Animal Behavior Processes 1983, 9(3):320-334.
73. Melara R.D., Marks L.E., Potts B.C. Primacy of dimensions in color perception. Journal of Experimental Psychology: Human perception and performance 1993, 19(5):1082.
74. Mix K.S., Huttenlocher J., Levine S.C. Do preschool children recognize auditory-visual numerical correspondences?. Child Development 1996, 67(4):1592-1608.
75. Mix K.S., Huttenlocher J., Levine S.C. Multiple cues for quantification in infancy: Is number one of them?. Psychological Bulletin 2002, 128(2):278-294.
76. Mix K.S., Levine S.C., Huttenlocher J. Numerical abstraction in infants: Another look. Developmental Psychology 1997, 33(3):423-428.
77. Moore D., Benenson J., Reznick J.S., Peterson M., Kagan J. Effect of auditory numerical information on infants' looking behavior: Contradictory evidence. Developmental Psychology 1987, 23(5):665-670.
78. Nelson D.G. Processing integral dimensions: The whole view. Journal of Experimental Psychology: Human Perception and Performance 1993, 19.
79. Norcia A.M., Pei F., Bonneh Y., Hou C., Sampath V., Pettet M.W. Development of sensitivity to texture and contour information in the human infant. Journal of Cognitive Neuroscience 2005, 17(4):569-579.
80. Norcia A.M., Tyler C.W., Hamer R.D. Development of contrast sensitivity in the human infant. Vision research 1990, 30(10):1475-1486.
81. Oakes L.M. Using habituation of looking time to assess mental processes in infancy. Journal of Cognition and Development 2010, 11(3):255-268.
82. Pettigrew J.D., Nikara T., Bishop P.O. Responses to moving slits by single units in cat striate cortex. Experimental Brain Research 1968, 6(4):373-390.
83. Piaget, J. (1952). The child's concept of number (C. Gattegno, & F. M. Hodgson). London: Routledge.
84. Picozzi M., Dolores de Hevia M., Girelli L., Cassia V.M. Seven-month-olds detect ordinal numerical relationships within temporal sequences. Journal of Experimental Child Psychology 2010, 107:359-367.
85. Rackin C.H., Abrams T., Barry R.J., Bhatnagar S., Clayto D.F., Colombo J., et al. Habituation revisited: An updated and revised description of the behavioral characteristics of habituation. Neurobiology of Learning and Memory 2009, 92(2):135-138.
86. Reith C., Sireteanu R. Texture segmentation and visual search based on orientation contrast: An infant study with the familiarization-novelty preference method. Infant Behavior and Development 1994, 17(4):359-369.
87. Roberts W.A., Mitchell S. Can a pigeon simultaneously process temporal and numerical information?. Journal of Experimental Psychology - Animal Behavior Processes 1994, 20(1):66-78.
88. Salapatek P. Pattern perception in early infancy. Infant perception: From sensation to cognition 1975, Academic Press, New York. L.B. Cohen, Salapatek (Eds.).
89. Shepard R.N. Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology 1964, 1:54-87.
90. Shepp B.E., Barrett S.E. The development of perceived structure and attention: Evidence from divided and selective attention tasks. Journal of Experimental Child Psychology 1991, 51(3):434-458.
91. Schiller P.H., Finlay B.L., Volman S.F. Quantitative studies of single-cell properties in monkey striate cortex. II. Orientation specificity and ocular dominance. Journal of Neurophysiology 1976, 39(6):1320-1333.
92. Simon T.J., Hespos S.J., Rochat P. Do infants understand simple arithmetic: A replication of Wynn (1992). Cognitive Development 1995, 10(2):253-269.
93. Smith L.B., Kemler D.G. Levels of experienced dimensionality in children and adults. Cognitive Psychology 1978, 10(4):502-532.
94. Sophian C., Chu Y. How do people apprehend large numerosities?. Cognition 2008, 107(2):460-478.
95. Spelke E.S., Kinzer K.D. Core knowledge. Developmental Science 2007, 10(1):89-96.
96. Starkey P., Cooper R.G. Perception of numbers by human infants. Science 1980, 210(4473):1033-1035.
97. Starkey P., Spelke E.S., Gelman R. Detection of intermodal numerical correspondences by human infants. Science 1983, 222(4620):179-181.
98. Starkey P., Spelke E.S., Gelman R. Numerical abstraction by human infants. Cognition 1990, 36(2):97-127.
99. Starr A.B., Libertus M.E., Brannon E.M. Infants show ratio-dependent number discrimination regardless of set size. Infancy 2013.
100. Stoianov, I., & Zorzi, M. (2012). Emergence of a 'visual number sense' in hierarchical generative models. Nature Neuroscience.
101. Strauss M.S., Curtis L.E. Infant perception of numerosity. Child Development 1981, 52(4):1146-1152.
102. Suanda S.H., Tompson W., Brannon E.M. Changes in the ability to detect ordinal numerical relationships between 9 and 11 months of age. Infancy 2008, 13(4):308-337.
103. Taves E. Two mechanisms for the perception of numerousness. Archives of Psychology 1941, 37:156-177.
104. Treiber F., Wilcox S. Discrimination of number by infants. Infant Behavior and Development 1984, 7(1):93-100.
105. Treiman R., Breaux A.B. Common phoneme and overall similarity relations among spoken syllables: Their use by children and adults. Journal of Psycholinguistic Research 1982, 11(6):569-598.
106. Trick L.M., Pylyshyn Z.W. Why are small and large numbers enumerated differently: A limited capacity preattentive stage in vision. Psychological Review 1994, 101(1):80-102.
107. Uller C., Carey S., Huntley-Fenner G., Klatt L. What representations might underlie infant numerical knowledge?. Cognitive Development 1999, 14(1):1-36.
108. Van de Walle G.A., Carey S., Prevor M. Bases for object individuation in infancy: Evidence from manual search. Journal of Cognition and Development 1997, 1(3):249-280.
109. van Loosbroek E., Smitsman A.W. Visual perception of numerosity in infancy. Developmental Psychology 1990, 26(6):916-922.
110. vanMarle K., Wynn K. Six-month-old infants use analog magnitudes to represent duration. Developmental Science 2006, 9(5):F41-F49.
111. vanMarle K., Wynn K. Infants' auditory enumeration: Evidence for analog magnitudes in the small number range. Cognition 2009, 111(3):302-316.
112. vanMarle K., Wynn K. Tracking and quantifying objects and noncohesive substances. Developmental Science 2011, 14(3):501-515.
113. Ward T.B. Separable and integral responding by children and adults to the dimensions of length and density. Child Development 1980, 676-684.
114. Ward T.B. Response tempo and separable-integral responding: Evidence for an integral-to-separable processing sequence in visual perception. Journal of Experimental Psychology: Human Perception and Performance 1983, 9(1):103-112.
115. Whalen J., Gallistel C.R., Gelman R. Nonverbal counting in humans: The psychophysics of number representation. Psychological Science 1999, 10(2):130-137.
116. Wood J.N., Spelke E.S. Chronometric studies of numerical cognition in five-month-old infants. Cognition 2005, 97(1):23-39.
117. Wood J.N., Spelke E.S. Infants' enumeration of actions: Numerical discrimination and its signature limits. Developmental Science 2005, 8(2):173-181.
118. Wynn K. Addition and subtraction by human infants. Nature 1992, 360(6406):768.
119. Wynn K. Infants' individuation and enumeration of actions. Psychological Science 1996, 4(6):164-169.
120. Wynn K., Bloom P., Chiang W.C. Enumeration of collective entities by 5-month-old infants. Cognition 2002, 83(3):B55-B62.
121. Xu F. Numerosity discrimination in infants: Evidence for two systems of representations. Cognition 2003, 89(1):B15-B25.
122. Xu F., Arriaga R.I. Number discrimination in 10-month-old infants. British Journal of Developmental Psychology 2007, 25:103-108.
123. Xu F., Spelke E.S. Large number discrimination in 6-month-old infants. Cognition 2000, 74(1):B1-B11.
124. Xu F., Spelke E.S., Goddard S. Number sense in human infants. Developmental Science 2005, 8(1):88-101.