The Development of Quantity Concepts: Perceptual and Linguistic Factors

  • Linda S. Siegel
Part of the Springer Series in Cognitive Development book series (SSCOG)


In this chapter I shall be concerned with the development of various quantity concepts and some of the factors which influence their development. Two aspects of early quantity concepts will be examined: (a) linguistic factors and (b) perceptual factors. The relationship between children’s linguistic skills and their quantitative concepts will be considered in an attempt to separate cognitive processes from linguistic abilities. I shall also examine the perceptual and nonquantitative factors that influence the development of these concepts in order to understand the growth of number as a conceptual dimension.


Cardinal Number Language Task Language Training Equivalence Task Correct Alternative 
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Reference Notes

  1. 1.
    Greenberg, N. A. Young children’s perceptual judgments of nonredundant cardinal number equivalence. Unpublished doctoral dissertation. University of Western Ontario, London, Ontario, 1981.Google Scholar
  2. 2.
    Koff, E., & Luria, Z. Concept and language: The comparative relation. Paper presented at the SRCD meeting, Philadelphia, 1973.Google Scholar
  3. 3.
    Weil, J. The relationship between time conceptualizations and time language in young children. Unpublished doctoral dissertation, The Graduate Center, City University of New York, 1970.Google Scholar


  1. Baron, J., Lawson, G., & Siegel, L. S. Effects of training and set size on children’s judgments of number and length. Developmental Psychology, 1975, 11, 583–588.CrossRefGoogle Scholar
  2. Beilin, H., & Kagan, J. Pluralization rules and the conceptualization of number. Developmental Psychology, 1969, 7, 692–706.Google Scholar
  3. Bever, T. G. The cognitive basis for linguistic structures. In J. R. Hayes (Ed.), Cognition and the development of language. New York: Wiley, 1970.Google Scholar
  4. Blank, M. Cognitive functions of language in the preschool years. Development Psychology, 1974, 10, 229–245.CrossRefGoogle Scholar
  5. Blank, M., & Bridger, W. H. Cross-modal transfer in nursery school children. Journal of Comparative and Physiological Psychology, 1964, 58, 277–282.PubMedCrossRefGoogle Scholar
  6. Brainerd, C. J. Mathematical and behavioral foundations of number. Journal of General Psychology Monograph, 1913, 88, 221–281.CrossRefGoogle Scholar
  7. Brainerd, C. J. The effects of spatial cues on children’s cardinal number judgments. Developmental Psychology, 1977, 13, 425–430.CrossRefGoogle Scholar
  8. Brainerd, C. J., & Howe, M. L. An attentional analyses of small cardinal number concepts in five year olds. Canadian Journal of Behavioural Science, 1979, 11, 112–123.CrossRefGoogle Scholar
  9. Brainerd, C. J., & Howe, M. L. Developmental invariance in a mathematical model of associative learning. Child Development, 1980, 51, 349–363.CrossRefGoogle Scholar
  10. Bruner, J. S. The course of cognitive growth. American Psychologist, 1964, 19, 1–15.CrossRefGoogle Scholar
  11. Clark, E. V. Some aspects of the conceptual basis for first language acquisition. In R. L. Schiefelbusch & L. L. Lloyd (Eds.), Language perspective-Acquisition, retardation and intervention. Baltimore, Maryland: University Park Press, 1974.Google Scholar
  12. Clark, H. H. The primitive nature of children’s relational concepts. In J. R. Hayes (Ed.), Cognition and the development of language. New York: Wiley, 1970.Google Scholar
  13. Conrad, R. The chronology of the development of covert speech in children. Developmental Psychology, 1971, 5, 298–405.CrossRefGoogle Scholar
  14. Donaldson, M., & Balfour, G. Less is more: A study of language comprehension in children. British Journal of Psychology, 1968, 59, 461–471.CrossRefGoogle Scholar
  15. Donaldson, M., & Wales, R. J. On the acquisition of some relational terms. In J. R. Hayes (Ed.), Cognition and the development of language. New York: Wiley, 1970.Google Scholar
  16. Flavell, J. H. Developmental studies of mediated memory. Advances in Child Development and Behavior, 1970, 5, 181–211.PubMedCrossRefGoogle Scholar
  17. Furth, H. G. Thinking without language. New York: Free Press, 1966.Google Scholar
  18. Furth, H. G. Linguistic deficiency and thinking: Research with deaf subjects, 1964-1969. Psychological Bulletin, 1971, 76, 58–72.PubMedCrossRefGoogle Scholar
  19. Gelman, R. The nature and developments of early number concepts. In H. W. Reese (Ed.), Advances in child development and behavior (Vol. 7 ). New York: Academic Press, 1972, pp. 115–167.Google Scholar
  20. Gelman, R., & Tucker, M. F. Further investigations of the young child’s con-ception of number. Child Development, 1915, 46, 167–175.CrossRefGoogle Scholar
  21. Griffiths, J. A., Shantz, C. U., & Sigel, I. E. A methodological problem in conser-vation studies: The use of relational terms. Child Development, 1967, 38, 841–848.Google Scholar
  22. Inhelder, B., & Piaget, J. The early growth of logic in the child. New York: Harper & Row, 1964.Google Scholar
  23. Jones, P. A. Formal operational reasoning and the use of tentative statements. Cognitive Psychology, 1972, 3, 467–471.CrossRefGoogle Scholar
  24. Kendler, H. H., & Kendler, T. S. Vertical and horizontal processes in problem solv-ing. Psychological Review, 1962, 69, 1–16.PubMedCrossRefGoogle Scholar
  25. Klatzky, R. L., Clark, E. V., & Macken, M. Asymmetries in the acquisition of polar adjectives: Linguistic or conceptual? Journal of Experimental Child Psychology, 1913, 16, 32–46.CrossRefGoogle Scholar
  26. Lawson, G., Baron, J., & Siegel, L. S. The role of number and length cues in children’s quantitative judgments. Child Development, 1974, 45, 731–736.PubMedCrossRefGoogle Scholar
  27. Lenneberg, E. H. Biological foundations of language. New York: Wiley, 1967.Google Scholar
  28. Macnamara, J. Cognitive basis of language learning in infants. Psychological Review, 1972, 79, 1–13.PubMedCrossRefGoogle Scholar
  29. Nelson, D. Concept, word, and sentence: Interrelations in acquisition and development. Psychological Review, 1974, 81, 267–285.CrossRefGoogle Scholar
  30. Olson, D. R. Language and thought: Aspects of a cognitive theory of semantics. Psychological Review, 1970, 77, 257–273.PubMedCrossRefGoogle Scholar
  31. Osler, S. F., & Madden, J. The verbal label: Mediator or classifier? Journal of Experimental Child Psychology, 1973, 16, 303–317.CrossRefGoogle Scholar
  32. Palermo, D. S. More about less: A study of language comprehension. Journal of Verbal Learning and Verbal Behavior, 1973, 72, 211–221.CrossRefGoogle Scholar
  33. Pascual-Leone, J., & Smith, J. The encoding and decoding of symbols by children: A new experimental paradigm and a neo-Piagetian model. Journal of Experimental Child Psychology, 1969, 8, 328–355.CrossRefGoogle Scholar
  34. Piaget, J. The child’s conception of number. New York: Norton, 1965.Google Scholar
  35. Piaget, J., & Inhelder, B. The early growth of logic in the child. New York: Harper & Row, 1956.Google Scholar
  36. Pufall, P. B., & Shaw, R. E. Precocious thoughts on number: The long and short of it. Developmental Psychology, 1972, 7, 62–69.CrossRefGoogle Scholar
  37. Reese, H. W. Verbal mediation as a function of age level. Psychological Bulletin, 1962, 59, 502–509.CrossRefGoogle Scholar
  38. Scholnick, E. K., & Adams, M. J. Relationships between language and cognitive skills: Passive-voice comprehension, backward repetition, and matrix permutation. Child Development, 1913, 44, 741–46.CrossRefGoogle Scholar
  39. Siegel, L. S. The sequence of development of certain number concepts in preschool children. Developmental Psychology, 1971, 5, 357–361. (a)Google Scholar
  40. Siegel, L. S. The development of certain number concepts. Developmental Psychology, 1971, 5, 362–363. (b)CrossRefGoogle Scholar
  41. Siegel, L. S. The development of the concept of seriation. Developmental Psychology, 1972,(5, 135–137. (a)Google Scholar
  42. Siegel, L. S. The development of concepts of numerical magnitude. Psychonomic Science, 1972, 28, 245–246. (b)Google Scholar
  43. Siegel, L. S. The role of spatial arrangements and heterogeneity in the development of concepts of numerical equivalence. Canadian Journal of Psychology, 1973, 27, 351–355.CrossRefGoogle Scholar
  44. Siegel, L. S. Heterogeneity and spatial factors as determinants of numeration ability. Child Development, 1974, 45, 532–534. (a)CrossRefGoogle Scholar
  45. Siegel, L. S. The development of number concepts: Ordering and correspondence operations and the role of length cues. Developmental Psychology, 1974, 10, 907–912. (b)CrossRefGoogle Scholar
  46. Siegel, L. S. The relationship of language and thought in the preoperational child: A reconsideration of nonverbal alternatives to Piagetian Tasks. In L. S. Siegel & C. J. Brainerd (Eds.), Alternatives to Piaget: Critical essays on the theory. New York: Academic Press, 1978.Google Scholar
  47. Siegel, L. S., & Goldstein, A. G. Conservation of number in young children: Recency versus relational response strategies. Developmental Psychology, 1969, 1, 128–130.Google Scholar
  48. Siegel, L. S., Lees, A., Allan, L., & Bolton, B. Nonverbal assessment of Piagetian concepts in preschool children with impaired language development. Educational Psychology, 1981, 1, 153–158.CrossRefGoogle Scholar
  49. Siegel, L. S., McCabe, A. E., Brand, J., & Matthews, J. Evidence for class inclusion in the preschool child: Linguistic factors and training effects. Child Development, 1978, 49, 688–693.CrossRefGoogle Scholar
  50. Sinclairde Zwart, H. Developmental psycholinguistics. In D. Elkind & J. H. Flavell (Eds.), Studies in cognitive development. New York: Oxford University Press, 1969.Google Scholar
  51. Slobin, D. I. Cognitive prerequisites for the development of grammar. In C. A. Ferguson & D. I. Slobin (Eds.), Studies of child language development. New York: Holt, Rinehart, & Winston, 1973, pp. 175–208.Google Scholar
  52. Vygotsky, L. S. Thought and language. Cambridge, Massachusetts: MIT Press, 1962.CrossRefGoogle Scholar
  53. White, S. H. Evidence for a hierarchical arrangement of learning processes. In Advances in child development and behavior (Vol. 2 ). New York: Academic Press, 1965.Google Scholar

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© Springer-Verlag New York, Inc. 1982

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  • Linda S. Siegel

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