Children's understanding of number is similar to adults' and rats': numerical estimation by 5–7-year-olds

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the standard deviation of estimates to mean estimates decreased with age.

[1]  T. Indow,et al.  Scaling of dot numerosity , 1977 .

[2]  Emmanuel Dupoux,et al.  Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. , 1990 .

[3]  K. Fuson.  Children's Counting and Concepts of Number , 1987 .

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

[5]  C. Gallistel.  The organization of learning , 1990 .

[6]  John Gibbon,et al.  Ubiquity of scalar timing with Poisson clock , 1992 .

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

[8]  Peter Bryant,et al.  Children Doing Mathematics , 1996 .

[9]  S. Carey,et al.  Knowledge of Number: Its Evolution and Ontogeny , 1998, Science.

[10]  V. Gathercole.  More and more and more about more. , 1985, Journal of experimental child psychology.

[11]  S. Dehaene,et al.  The Number Sense: How the Mind Creates Mathematics. , 1998 .

[12]  Z. Pylyshyn,et al.  Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. , 1994, Psychological review.

[13]  R. Case,et al.  Operational efficiency and the growth of short-term memory span , 1982 .

[14]  C. Gallistel.  Can a decay process explain the timing of conditioned responses? , 1999, Journal of the experimental analysis of behavior.

[15]  T. Tuulmets,et al.  Occupancy model of perceived numerosity , 1991, Perception & psychophysics.

[16]  Stanislas Dehaene,et al.  Two mental calculation systems: A case study of severe acalculia with preserved approximation , 1991, Neuropsychologia.

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

[18]  G. Mandler,et al.  Subitizing: an analysis of its component processes. , 1982, Journal of experimental psychology. General.

[19]  K. Miller,et al.  Preschool Origins of Cross-National Differences in Mathematical Competence: The Role of Number-Naming Systems , 1995 .

[20]  Rochel Gelman,et al.  The Child's Representation of Number: A Multidimensional Scaling Analysis. , 1983 .

[21]  R. Church,et al.  A mode control model of counting and timing processes. , 1983, Journal of experimental psychology. Animal behavior processes.

[22]  Frank H. Durgin,et al.  Texture density adaptation and the perceived numerosity and distribution of texture. , 1995 .

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

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

[25]  P. Starkey,et al.  The development of subitizing in young children , 1995 .

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

[27]  Eli Maor,et al.  The universal history of numbers : from prehistory to the invention of the computer , 2001 .

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

[29]  E. Spelke,et al.  Sources of mathematical thinking: behavioral and brain-imaging evidence. , 1999, Science.

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

[31]  S. Dehaene,et al.  Attention, automaticity, and levels of representation in number processing , 1995 .

[32]  William A. Roberts,et al.  Can a pigeon simultaneously process temporal and numerical information , 1994 .

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

[34]  S. Dehaene.  Varieties of numerical abilities , 1992, Cognition.

[35]  James R. Hurford,et al.  Language and Number: The Emergence of a Cognitive System , 1987 .

[36]  Stanislas Dehaene,et al.  The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method , 1996, Journal of Cognitive Neuroscience.

[37]  D. Klahr,et al.  Span and rate of apprehension in children and adults. , 1975, Journal of experimental child psychology.

[38]  Robert Sekuler,et al.  Children's Judgments of Numerical Inequality. , 1977 .

[39]  J. Allik,et al.  Size invariance in visual number discrimination , 1991, Psychological research.

[40]  E. L. Kaufman,et al.  The discrimination of visual number. , 1949, The American journal of psychology.