Abstract
In this chapter we describe children’s acquisition and elaboration of the sequence of counting words from its beginnings around age two up to its general extension to the base ten system notions beyond one hundred (around age eight). This development occurs, in our view, in two distinct, though overlapping, phases: an initial acquisition phase of learning the conventional sequence of number words and an elaboration phase, during which this sequence is decomposed into separate words and relations upon these pieces and words are established. During acquisition, the sequence begins to be used for counting objects. Near the end of the elaborative phase, the words in the sequence themselves become items which are counted for arithmetic and relational purposes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
References Notes
Bell, M., & Burns, J. Personal communication, May, 1981.
Bell, M., & Burns, J. Counting, numeration, and arithmetic capabilities of primary school children. Proposal submitted to National Science Foundation, April, 1981.
Fuson, K. C., & Mierkiewicz, D. A detailed analysis of the act of counting. Paper presented at the Annual Meeting of the American Educational Research Association, Boston, April, 1980.
Fuson, K. C., & Richards, J. Children’s construction of the counting numbers: From a spew to a bidirectional chain. Unpublished manuscript, Northwestern University, 1979, and paper presented at the Annual Meeting of the American Educational Research Association, Boston, April, 1980.
Greeno, J. G., Riley, M. S., & Gelman, R. Young children’s counting and understanding of principles. Unpublished manuscript.
Gelman, R. Personal communication, March, 1979.
Steffe, L. P., Richards, J., & von Glasersfeld, E. Children’s counting types. Unpublished manuscript, University of Georgia, 1980.
Nesher, P. Personal communication, February, 1980, April, 1981.
Klahr, D., & Chase, W. G. Developmental changes in latency patterns for access to the alphabet. Paper presented at the Annual Meeting of the Psychonomic Society. San Antonio, November, 1978.
Brainerd, C. J. Working-memory analyses of children’s mental arithmetic. Paper presented at the Biennial Meeting of the Society for Research in Child Development, Boston, April, 1981.
Case, R., Kurland, M., & Daneman, M. Operational efficiency and the growth of M-space. Paper presented at the Biennial Meeting of the Society for Research in Child Development, San Francisco, March, 1979.
Moser, J. A longitudinal study of the effect of number size and presence of manipulative materials on children’s processes in solving addition and subtraction verbal problems. Paper presented at the Annual Meeting of the American Educational Research Association, Boston, April, 1980.
Secada, W., Fuson, K. C., & Hall, J. W. The development of counting on from counting-all in cardinal addition. In progress.
Secada, W. Personal communication, January, 1981.
Mierkiewicz (Briars), D. J., personal communication, July, 1978.
Steffe, L. P., Spikes, W. C., & Hirstein, J. J. Summary of quantitive comparisons and class inclusion as readiness variables for learning first grade arithmetical content. Working Paper 1, University of Georgia, Center for Research in the Learning and Teaching of Mathematics, 1976.
Steffe, L., Richards, J., & von Glasersfeld, E. Children’s counting types: Philosophy, theory, & case studies. Monograph presented at the Interdisciplinary Conference on Counting Types. Athens, Georgia, April, 1981.
Secada, W. Counting solution procedures spontaneously employed on an addition task. Unpublished manuscript, Northwestern University, 1980.
Briars, D., & Larkin, J. An integrated model of skill in solving elementary word problems. Paper presented at the Biennial Meeting of the Society for Research in Child Development, Boston, April, 1981.
Davydov, V. V., & Andronov, V. P. Psychological conditions of the origination of ideal actions (English translation). Madison, WI: (Project Paper 81-2 ) Madison, Wisconsin: Wisconsin Research and Development Center for Individualized Schooling, The University of Wisconsin, 1981.
Blevins, B., Mace, P. G., Cooper, R. G., & Leitner, E, What do children know about addition and subtraction? Paper presented at the Biennial Meeting of the Society for Research in Child Development, Boston, April, 1981.
Nesher, P. An analysis and review of addition and subtraction verbal problems. Paper given at the Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, St. Louis, April, 1981.
References
Bewley, W. L. The functional stimulus in serial learning. In R. F. Thompson & J. F. Voss (Eds.), Topics in learningand performance. New York: Academic Press, 1972.
Brush, L. Preschool children’s knowledge of addition and subtraction. Journal for Research in Mathematics Education, 1978, 9 (1), 44–54.
Carpenter, T., Hiebert, J., & Moser, F. The effect of problem structure on first grader’s initial solution procedures for simple addition and subtraction problems. Journal for Research in Mathematics Education, 1981, 12, 27–39.
Carpenter, T., & Moser, J. The development of addition and subtraction problem solving skills. In T. Romberg, T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A developmental perspective. Hillsdale, New Jersey: Erlbaum Assoc., in press.
Fuson, K. C. An analysis of the counting-on solution procedure in addition. In T. Romberg, T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A develop-mental perspective. Hillsdale, New Jersey: Erlbaum Assoc., in press.
Fuson, K. C., & Hall, J. W. The acquisition of early number word meanings. In H. Ginsburg (Ed.), The development of children’s mathematical thinking. New York: Academic Press, in press.
Gelman, R., & Gallistel, C. R. The child’s understanding of number. Cambridge, Massachusetts: Harvard University Press, 1978.
Groen, G. J., & Resnick, L. B. Can preschool children invent addition algorithms? Journal of Educational Psychology, 1977, 69 (6), 645–652.
Hamilton, J. M. E., & Sanford, A. J. The symbolic distance effect for alphabetic order judgements: A subjective report and reaction time analysis. Quarterly Journal of Experimental Psychology, 1978, 30, 33–43.
Harcum, E. R. Serial learning and paralearning. New York: Wiley, 1975.
Hovancik, J. R. Reaction times for naming the first next and second next letters of the alphabet. American Journal of Psychology, 1975, 88 (4), 643–647.
Houlihan, D. M., & Ginsburg, H. P. The addition methods of first- and second-grade children. Journal for Research in Mathematics Education, 1981, 2, 95–106.
Lovelace, E. A., Powell, C. M., & Brooks, R. J. Alphabetic position effects in covert and overt alphabetic recitation times. Journal of Experimental Psychology, 1973, 99 (3), 405–408.
Lovelace, E. A., & Spence, W. A. Reaction times for naming successive letters of the alphabet. Journal of Experimental Psychology, 1972, 94, 231–233.
Parkman, J. M. Temporal aspects of digit and letter inequality judgments. Journal of Experimental Psychology, 1971, Pi, 191–205.
Riley, M., Greeno, J., & Heller, J. Development of children’s problem-solving ability in arithmetic. In H. Ginsburg (Ed.), The development of children’s mathematical thinking. New York: Academic Press, in press.
Schaeffer, B., Eggleston, V. H., & Scott, J. L. Number development in young chil-dren. Cognitive Psychology, 1974, 6, 357–379.
Sekuler, R., & Mierkiewicz, D. Children’s judgments of numerical inequality. Child Development, 1977, 48, 630–633.
Siegler, R. S., & Robinson, M. The development of numerical understandings. In H. W. Reese & L. P. Lipsitt (Eds.), Advances in child development and behavior (Vol. 16). New York: Academic Press, in press.
Slobin, D. I. Psycholinguistics. Glenview, Illinois: Scott, Foresman, 1976.
Starkey, P., & Gelman, R. Addition and subtraction algorithms in preschool children. In T. Romberg, T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A developmental perspective. Hillsdale, New Jersey: Erlbaum Assoc., in press.
Steffe, L., Thompson, P., & Richards, J. Children’s counting and arithmetical problem solving. In T. Romberg, T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A developmental perspective. Hillsdale, New Jersey: Erlbaum Assoc., in press.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Fuson, K.C., Richards, J., Briars, D.J. (1982). The Acquisition and Elaboration of the Number Word Sequence. In: Brainerd, C.J. (eds) Children’s Logical and Mathematical Cognition. Springer Series in Cognitive Development. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9466-2_2
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9466-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9468-6
Online ISBN: 978-1-4613-9466-2
eBook Packages: Springer Book Archive