The enigma of number: Why children find the meanings of even small number words hard to learn and how we can help them do better

PLoS ONE

Volumn 6, Issue 7, 2011, Pages

  Ramscar, Michael ^a   Dye, Melody ^a   Popick, Hanna Muenke ^a   O'Donnell McCarthy, Fiona ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHILD; COMPETENCE; COMPREHENSION; CONTROLLED STUDY; DISCRIMINATION LEARNING; FEMALE; HUMAN; HUMAN EXPERIMENT; INFORMATION PROCESSING; LEARNING ENVIRONMENT; LINGUISTICS; MALE; MATHEMATICAL COMPUTING; PREDICTION; PRESCHOOL CHILD; SIMULATION; TASK PERFORMANCE; TRAINING; COMPUTER SIMULATION; LEARNING; MATHEMATICAL PHENOMENA;

CHILD; CHILD, PRESCHOOL; COMPREHENSION; COMPUTER SIMULATION; FEMALE; HUMANS; LEARNING; LINGUISTICS; MALE; MATHEMATICAL CONCEPTS;

EID: 79960798412     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0022501     Document Type: Article

References (66)

1. Wynn K, (1992) Children's acquisition of the number words and the counting system. Cognitive Psychology 24: 220-251.
2. Wynn K, (1990) Children's understanding of counting. Cognition 36: 155-193.
3. Xu F, Spelke ES, (2000) Large number discrimination in 6-month-old infants. Cognition 74: B1-B11.
4. Xu F, (2003) Numerosity discrimination in infants: Evidence for two systems of representations. Cognition 89: B15-B25.
5. Xu F, Spelke ES, Goddard S, (2005) Number sense in human infants. Developmental Science 8: 88-101.
6. Lipton JS, Spelke ES, (2004) Discrimination of large and small numerosities by human infants. Infancy 5: 271-290.
7. Wynn K, (1998) Psychological foundations of number: Numerical competence in human infants. Trends in Cognitive Science 2: 296-303.
8. Feigenson L, Dehaene S, Spelke ES, (2004) Core systems of number. Trends in Cognitive Science 8: 307-314.
9. Van de Walle GA, Carey S, Prevor M, (2000) Bases for Object Individuation in Infancy: Evidence from Manual Search. Journal of Cognitive Development 1: 249-280.
10. Mix KS, Huttenlocher J, Levin SC, (2002) Multiple Cues for Quantification in Infancy: Is Number One of Them? Psychological Bulletin 128: 278-294.
11. Bloom P, Wynn K, (1997) Linguistic cues in the acquisition of number words. Journal of Child Language 24: 511-533.
12. Fuson KC, (1988) Children's counting and concepts of number New York Springer-Verlag.
13. Brannon EM, Van de Walle GA, (2001) The development of ordinal numerical competence in young children. Cognitive Psychology 43: 53-81.
14. Gelman R, Gallistel CR, (2004) Language and the origin of numerical concepts. Science 306: 441-443.
15. Jevons WS, (1871) The power of numerical discrimination. Nature 3: 363-372.
16. Kaufman EL, Lord MW, Reese TW, Volkmann J, (1949) The discrimination of visual number. American Journal of Psychology 62: 498-525.
17. Vetter P, Butterworth B, Bahrami B, (2008) Modulating Attentional Load Affects Numerosity Estimation: Evidence against a Pre-Attentive Subitizing Mechanism. PLoS ONE 3: e3269 doi:10.1371/journal.pone.0003269.
18. Huang Y, Spelke ES, Snedecker J, (2010) When is 'four' far more than 'three'? Children's generalization of newly-acquired number words. Psychological Science 21: 600-606.
19. Rescorla RA, (1988) Pavlovian conditioning: It's not what you think it is. American Psychologist 43: 151-160.
20. Schultz W, (2006) Behavioral theories and the neurophysiology of reward. Annual Review of Psychology 57: 87-115.
21. Ramscar M, Yarlett D, Dye M, Denny K, Thorpe K, (2010) The Effects of Feature-Label-Order and their implications for symbolic learning. Cognitive Science 34: 909-957.
22. Kamin LJ, (1969) Predictability, surprise, attention, and conditioning. In: Campbell B, Church R, editors. Punishment and aversive behaviour New York Appleton-Century-Crofts pp. 279-296.
23. Rescorla RA, Wagner AR, (1972) A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In: Black AH, Prokasy WF, editors. Classical conditioning II: Current research and theory New York Appleton-Century-Crofts pp. 64-99.
24. Niv Y, Schoenbaum G, (2008) Dialogues on prediction errors. Trends in Cognitive Science 12: 265-272.
25. Montague PR, Dayan P, Sejnowski TJ, (1996) A Framework for Mesencephalic Dopamine Systems based on Predictive Hebbian Learning. Journal of Neuroscience 16: 1936-1947.
26. Schultz W, (1998) Predictive reward signal of dopamine neurons. Journal of Neurophysiology 80: 1-27.
27. Waelti P, Dickinson A, Schultz W, (2001) Dopamine responses comply with basic assumptions of formal learning theory. Nature 412: 43-48.
28. Schultz W, Dickinson A, (2000) Neural coding of prediction errors. Annual Review of Neuroscience 23: 473-500.
29. Schultz W, Dayan P, Montague RR, (1997) A neural substrate of prediction and reward. Science 275: 1593-1599.
30. Niv Y, (2009) Reinforcement learning in the brain. Journal of Mathematical Psychology 53: 139-154.
31. Wittgenstein L, (1953) Philosophical investigations Oxford Blackwell.
32. Rosenblatt F, (1959) Two theorems of statistical separability in the Perceptron. In: Blake V, Uttley AM, editors. Mechanisation of thought processes: Proceedings of a symposium held at the National Physical Laboratory London Her Majesty's Stationery Office pp. 419-456.
33. Gallistel CR, (2003) Conditioning from an information processing perspective. Behavioural Processes 61: 1234.
34. Darwin C, (1877) Biographische Skizze eines kleinen Kindes. Kosmos 1: 367-376.
35. Rice N, (1980) Cognition to language Baltimore University Park Press.
36. Landau B, Gleitman LR, (1985) Language and experience: Evidence from the blind child Cambridge Harvard University Press.
37. Roberson D, Davidoff J, Davies IRL, Shapiro LR, (2004) The development of color categories in two languages: A longitudinal study. Journal of Experimental Psychology: General 133: 554-571.
38. Ramscar M, Dye M, Yarlett D, (2009) No representation without taxation: The costs and benefits of learning to conceptualize the environment. Proceedings of the 31st Annual Conference of the Cognitive Science Society, Amsterdam, The Netherlands.
39. Elman JL, (1990) Finding structure in time. Cognitive Science 14: 179-211.
40. Ramscar M, Dye M, Gustafson J, Klein J, (2009) Two routes to cognitive flexibility: Learning and response conflict resolution in the Dimensional Change Card Sort Task. Proceedings of the 31st Annual Conference of the Cognitive Science Society, Amsterdam, The Netherlands.
41. Tanenhaus MK, Spivey-Knowlton MJ, Eberhard KM, Sedivy JC, (1995) Integration of visual and linguistic information in spoken language comprehension. Science 268: 1632-1634.
42. Kamide Y, Altmann GTM, Haywood SL, (2003) The time-course of prediction in incremental sentence processing: Evidence from anticipatory eye-movements. Journal of Memory and Language 49: 133-156.
43. Dahan D, Tanenhaus MK, (2005) Looking at the rope when looking for the snake: Conceptually mediated eye movements during spoken-word recognition. Psychonomic Bulletin and Review 12: 453-459.
44. Fernald A, Perfors A, Marchman VA, (2006) Picking up speed in understanding: Speech processing efficiency and vocabulary growth across the second year. Developmental Psychology 42: 98-116.
45. Clark EV, (2009) First Language Acquisition Cambridge, UK Cambridge University Press.
46. Gentner D, Boroditsky L, (2001) Individuation, relativity and early word learning. In: Bowerman M, Levinson S, editors. Language acquisition and conceptual development Cambridge, UK Cambridge University Press pp. 215-256.
47. Fernald A, Thorpe K, Marchman VA, (2010) Blue car, red car: Developing efficiency in online interpretation of adjective-noun phrases. Cognitive Psychology 60: 190-217.
48. Thorpe K, Fernald A, (2006) Knowing what a novel word is not: Two-year-olds "listen through" ambiguous adjectives in fluent speech. Cognition 100: 389-433.
49. Baldwin DA, (1995) Understanding the link between joint attention and language. In: Moore C, Dunham PJ, editors. Joint attention: Its origins and role in development Hillsdale, NJ Lawrence Erlbaum pp. 131-158.
50. Carpenter M, Nagell K, Tomasello M, (1998) Social Cognition, Joint Attention, and Communicative Competence from 9 to 15 Months of Age. Monographs of the Society for Research in Child Development 63: 1-166.
51. Triesch J, Teuscher C, Deák GO, Carlson E, (2006) Gaze following: why (not) learn it? Developmental Science 9: 125-147.
52. Rowe ML, (2008) Child-directed speech: relation to socioeconomic status, knowledge of child development and child vocabulary skill. Journal of Child Language 35: 185-205.
53. Davies M, (2009) The 385+ Million Word Corpus of Contemporary American English (1990-present). International Journal of Corpus Linguistics 14: 159-90.
54. Davies M, (2010) Creating Useful Historical Corpora: A Comparison of CORDE, the Corpus del Español, and the Corpus do Português. In: Enrique-Arias A, editors. Diacronía de las lenguas iberorromances: nuevas perspectivas desde la lingüística de corpus Frankfurt, Germany/Madrid, Spain Vervuert/Iberoamericana pp. 137-166.
55. Benford F, (1938) The law of anomalous numbers. Proceedings of the American Philosophical Society 78: 551-572.
56. Revkin SK, Piazza M, Izard V, Cohen L, Dehaene S, (2008) Does subitizing reflect numerical estimation? Psychological Science 19: 607-614.
57. Cordes S, Gelman R, Gallistel CR, (2001) Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin and Review 8: 698-707.
58. Sonnenschein S, Whitehurst GJ, (1982) The effects of redundant communications on the behavior of listeners: Does a picture need a thousand words? Journal of Psycholinguistic Research 11: 115-125.
59. Spivey MJ, Tyler MJ, Eberhard KM, Tanenhaus MK, (2001) Linguistically Mediated Visual Search. Psychological Science 12: 282-286.
60. Booth JL, Sigler RS, (2008) Numerical Magnitude Representations Influence Arithmetic Learning. Child Development 79: 1016-1031.
61. Jordan NC, Glutting J, Ramineni C, (2010) The importance of number sense to mathematics achievement in first through third grades. Learning and Individual Differences 20: 82-88.
62. Jordan NC, Kaplan D, Ramineni C, Locuniak MN, (2009) Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology 45: 850-867.
63. Clements DH, Sarama J, (2007) Effects of a Preschool Math Curriculum: Summative Research on Building Blocks Project. Journal for Research in Mathematics Education 38: 136-163.
64. Ramscar M, Suh E, Dye M, (2011) How pitch category learning comes at a cost to absolute frequency representations. Proceedings of the 33rd Meeting of the Cognitive Science Society, Boston, MA.
65. Rescorla RA, (1968) Probability of Shock in the Presence and Absence of CS in Fear Conditioning. Journal of Comparative and Physiological Psychology 66: 1-5.
66. Roberts S, Pashler H, (2000) How persuasive is a good fit? A comment on theory testing. Psychological Review 107: 358-367.