Skip to main content
SpringerLink
Log in

Child-methods in secondary mathematics

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

An earlier research project, the Concepts in Secondary Mathematics and Science (Mathematics) project, identified both a hierarchy of levels of understanding in different areas of secondary mathematics, and a number of particular errors which were made by significant proportions of the children tested. Preliminary consideration of these errors and the strategies which appear to have given rise to them suggests that the use of informal ‘naive’ methods which are limited in their applicability is widespread even at fourth-year level. The suggestion is made that there may be two ‘systems’ of mathematics coexisting in the secondary school classroom: the formal taught system, and a system of child-methods which are based upon a ‘counting’, ‘adding-on’ or ‘building-up’ approach, and by which children attempt to solve mathematical problems within a ‘human-sense’ framework. The difficulties which some children appear to experience in mathematics is suggested to be due in part to these children's non-initiation into the formal taught system. The implication of such a view for teaching and research are indicated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Brown, M.: 1976, ‘Investigating mathematics’, Times Educational Supplement, April 23.

  • Brown, M. and Küchemann, D. E.: 1976, ‘Is it an add, Miss?’ Parts I and II, Mathematics in School 5 (5,6).

  • Bruner J. S., Olver R. and Greenfield P. M.: 1966, Studies in Cognitive Growth, Wiley, New York.

    Google Scholar 

  • Case R.: 1975, ‘Gearing the demands of instruction to the developmental capacities of the learner’, Review of Educational Research 45, 59–87.

    Article  Google Scholar 

  • Case R.: 1978, ‘A developmentally based theory and technology of instruction’, Review of Educational Research 48, 439–463.

    Article  Google Scholar 

  • CSMS Mathematics Team: 1980 (in press), in K. Hart (ed.), Children's Understanding of Mathematics (11–16), Murray, London.

    Google Scholar 

  • Donaldson M.: 1978, Children's Minds, Croom Helm, London.

    Google Scholar 

  • Hart K.: 1978, ‘The understanding of ratio in the secondary school’, Mathematics in School 7, 4–6.

    Google Scholar 

  • Hart, K.: 1980a, in D. Johnson (ed.), Children's Understanding of Mathematics, Chelsea College Centre for Science Education Research Monographs, London.

  • Hart, K.: 1980b, ‘Secondary school children's understanding of ratio and proportion’, unpublished Ph.D. dissertation, University of London.

  • Küchemann D. E.: 1978, ‘Children's understanding of numerical variables’, Mathematics in School 7, 23–26.

    Google Scholar 

  • Plunkett S.: 1979, ‘Decomposition and all that rot’, Mathematics in School 8, 2–5.

    Google Scholar 

  • Rosenthal, D. A.: 1975, An investigation of some factors influencing development of formal operational thinking, unpublished Ph.D. dissertation, University of Melbourne.

Download references

Author information

Authors and Affiliations

  1. Chelsea College, University of London, UK

    Lesley R. Booth

Authors
  1. Lesley R. Booth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Booth, L.R. Child-methods in secondary mathematics. Educ Stud Math 12, 29–41 (1981). https://doi.org/10.1007/BF00386044

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00386044

Keywords

Search

Navigation