The development of ordinal numerical knowledge in infancy

A critical question in cognitive science concerns how numerical knowledge develops. One essential component of an adult concept of number is ordinality: the greater than and less than relationships between numbers. Here it is shown in two experiments that 11-month-old infants successfully discriminated, whereas 9-month-old infants failed to discriminate, sequences of numerosities that descended in numerical value from sequences that increased in numerical value. These results suggest that by 11 months of age infants possess the ability to appreciate the greater than and less than relations between numerical values but that this ability develops between 9 and 11 months of age. In an additional experiment 9-month-old infants succeeded at discriminating the ordinal direction of sequences that varied in the size of a single square rather than in number, suggesting that a capacity for non-numerical ordinal judgments may develop before a capacity for ordinal numerical judgments. These data raise many questions about how infants represent number and what happens between 9 and 11 months to support ordinal numerical judgments.

[1]  H S Terrace,et al.  Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). , 2000, Journal of experimental psychology. Animal behavior processes.

[2]  Karen Wynn,et al.  Addition and subtraction by human infants , 1992, Nature.

[3]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[4]  P. Starkey,et al.  Perception of numbers by human infants. , 1980, Science.

[5]  R. Gelman,et al.  Draft of Chapter that will appear in In E. Dupoux (Ed.).(2001). Essay in Honor of Jacques Mehler. Cambridge, MA: MIT Press. Counting in Animals and Humans , 2001 .

[6]  H S Terrace,et al.  Ordering of the numerosities 1 to 9 by monkeys. , 1998, Science.

[7]  E. Cannon,et al.  Preschoolers' Magnitude Comparisons are Mediated by a Preverbal Analog Mechanism , 2000, Psychological science.

[8]  C. Gallistel,et al.  Non-verbal numerical cognition: from reals to integers , 2000, Trends in Cognitive Sciences.

[9]  Elizabeth M. Brannon,et al.  The Development of Ordinal Numerical Competence in Young Children , 2001, Cognitive Psychology.

[10]  Kelly S. Mix,et al.  Number Versus Contour Length in Infants' Discrimination of Small Visual Sets , 1999 .

[11]  Stanislas Dehaene,et al.  Numerical Transformations in Five-month-old Human Infants. , 1997 .

[12]  J. Piaget.  The Child's Conception of Number , 1953 .

[13]  Susan J. Hespos,et al.  Do infants understand simple arithmetic? A replication of Wynn (1992) ☆ , 1995 .

[14]  Catherine Sophian,et al.  Infants' understanding of numerical transformations , 1986 .

[15]  Philip Kitcher,et al.  The nature of mathematical knowledge , 1985 .

[16]  P. Huttenlocher.  Morphometric study of human cerebral cortex development , 1990, Neuropsychologia.

[17]  A. Yonas,et al.  Four-month-old infants' sensitivity to binocular and kinetic information for three-dimensional-object shape. , 1987, Child development.

[18]  Susan Carey,et al.  What representations might underlie infant numerical knowledge , 1999 .

[19]  J. Piaget,et al.  The Child's Conception of Number , 1953 .

[20]  S. Dehaene,et al.  Abstract representations of numbers in the animal and human brain , 1998, Trends in Neurosciences.

[21]  Emmanuel Dupoux.  Language, Brain, and Cognitive Development , 2001 .

[22]  Rochel Gelman,et al.  Numerical Reasoning in Young Children: The Ordering Principle. , 1977 .

[23]  Elizabeth M. Brannon,et al.  The evolution and ontogeny of ordinal numerical ability , 2002 .

[24]  Ad W. Smitsman,et al.  Visual perception of numerosity in infancy. , 1990 .

[25]  C. Gallistel,et al.  Nonverbal Counting in Humans: The Psychophysics of Number Representation , 1999 .

[26]  E. Spelke,et al.  Numerical abstraction by human infants , 1990, Cognition.

[27]  T. Simon,et al.  Reconceptualizing the Origins of Number Knowledge: A "Non-Numerical" Account , 1997 .

[28]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[29]  S. Wilcox,et al.  Discrimination of number by infants , 1984 .

[30]  Stanislas Dehaene,et al.  Development of Elementary Numerical Abilities: A Neuronal Model , 1993, Journal of Cognitive Neuroscience.

[31]  M. Strauss,et al.  Infant perception of numerosity. , 1981, Child development.

[32]  Karen Wynn,et al.  Origins of Numerical Knowledge. , 1995 .

[33]  L. Weiskrantz,et al.  Thought Without Language , 1988 .

[34]  Patricia Howlin,et al.  Origins of cognitive skills , 1986 .

[35]  Jacques Mehler,et al.  How do 4-day-old infants categorize multisyllabic utterances? , 1993 .

[36]  S E Antell,et al.  Perception of numerical invariance in neonates. , 1983, Child development.

[37]  E. Spelke,et al.  Large number discrimination in 6-month-old infants , 2000, Cognition.

[38]  Karen Wynn,et al.  Psychological foundations of number: numerical competence in human infants , 1998, Trends in Cognitive Sciences.

[39]  M. Posner,et al.  Brain mechanisms of quantity are similar in 5-year-old children and adults. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[40]  E. Spelke,et al.  Infants' Discrimination of Number vs. Continuous Extent , 2002, Cognitive Psychology.