The Calculator as a Cognitive Tool: Upper-Primary Pupils Tackling a Realistic Number Problem

  • Kenneth Ruthven
  • Di Chaplin


This paper examines the idea that the arithmetic calculator can act as a cognitive tool, supporting the amplification or reorganisation of systems of thought. It analyses how a structured sample of pupils in the last year of English primary education, with differing degrees of experience of a ’calculator-aware‘ number curriculum, tackled a realistic number problem, focusing on their use of calculator, written and mental modes of computation.

Examples were found in which use of the calculator helped pupils to work with unusual problem representations, and to adopt solution strategies in which they focused on planning and monitoring computations executed by the machine.

For most pupils, however, other issues were more salient. First, there was an important dissonance between pupils‘ conception of division and the calculator‘s operationalisation of it, although some cases showed how further experiment or computation with the machine could help to make appropriate connections. Second, while the calculator made it possible to redistribute computation from human to machine, important limitations arose from the transience of the calculator‘s record of operations and results.

The observations suggest the importance of developing pupils‘ skill in making effective use of the calculator beyond single, simple computations; and the need to help pupils apprehend the relationship between mathematical concepts and their operationalisation in the machine.

calculation calculator cognitive tool educational research mathematics numeracy primary education problem solving 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Department for Education: 1995, Mathematics in the National Curriculum. London: HMSO.Google Scholar
  2. Dörfler, W.: 1993, Computer use and views of the mind. In C. Keitel and K. Ruthven (Eds.), Learning from Computers: Mathematics Education and Technology(pp. 159–186). Berlin: Springer-Verlag.Google Scholar
  3. Fielker, D.: 1987, A calculator, a tape recorder, and thou, Educational Studies in Mathematics 18: 417–437.Google Scholar
  4. Foxman, D., Ruddock, G., McCallum, I. and Schagen, I.: 1991, APU Mathematics Monitoring (Phase 2). London: School Examinations and Assessment Council.Google Scholar
  5. Groves, S.: 1993, The effect of calculator use on third graders’ solutions of real world division and multiplication problems, Proceedings of PME 17, Tsukuba, 2: 9–16.Google Scholar
  6. Groves, S.: 1994, The effect of calculator use on third and fourth graders’ computation and choice of calculating device, Proceedings of PME 18, Lisbon, 3: 33–40.Google Scholar
  7. Moscovici, S.: 1981, On social representations. In J. P. Forgas (Ed.), Social Cognition: Perspectives on Everyday Understanding. London: Academic Press.Google Scholar
  8. Pea, R. D.: 1985, Beyond amplification: Using the computer to reorganise mental functioning, Educational Psychologist20(4): 167–182.CrossRefGoogle Scholar
  9. Ruthven, K.: 1998, The use of mental, written and calculator strategies of numerical computation by upper-primary pupils with a ‘calculator-aware’ number curriculum, British Educational Research Journal 24(I).Google Scholar
  10. Ruthven, K., Rousham, L. and Chaplin, D.: 1997, The long-term influence of a ‘calculator-aware’ number curriculum on pupils’ mathematical attainments and attitudes in the primary phase, Research Papers in Education 12 (3): 249–282.Google Scholar
  11. School Curriculum and Assessment Authority: 1995, Mathematics KS2 Test B. London: SCAA.Google Scholar
  12. Shuard, H., Walsh, A., Goodwin, J., Worcester, V.: 1991, Calculators, Children and Mathematics. London: Simon and Schuster.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Kenneth Ruthven
    • 1
  • Di Chaplin
    • 1
  1. 1.University of Cambridge School of EducationCambridgeUK

Personalised recommendations