Advertisement

Educational Studies in Mathematics

, Volume 33, Issue 1, pp 1–19 | Cite as

STUDENTS' UNDERSTANDING OF ALGEBRAIC NOTATION: 11–15

  • Mollie MacGregor
  • Kaye Stacey
Article

Abstract

Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns. Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names. The principal explanation given in the literature has been a general link to levels of cognitive development. In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level. These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials. Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra.

Keywords

Research Study General Link Generalise Number Cognitive Development Teaching Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Assessment of Performance Unit [APU]: 1985, A Review of Monitoring in Mathematics 1978 to 1982, HMSO, London.Google Scholar
  2. Booth, L.: 1984, Algebra: Children's Strategies and Errors. A Report of the Strategies and Errors in Secondary Mathematics Project, NFER-Nelson, Windsor.Google Scholar
  3. Cambridge Institute of Education: 1985, New Perspectives on the Mathematics Curriculum. An Independent Appraisal of the Outcomes of the APU Mathematics Testing 1978–82, HMSO, London.Google Scholar
  4. Clement, J.: 1982, ‘Algebra word problem solutions: thought processes underlying a common misconception’, Journal for Research in Mathematics Education 13(1), 16–30.Google Scholar
  5. Cohors-Fresenborg, E.: 1993, ‘Integrating algorithmic and axiomatic ways of thinking in mathematics lessons in secondary schools’, in Proceedings of South East Asia Conference on Mathematics Education (SEACME-6) and the Seventh National Conference on Mathematics, Kampus Sukolilo, Surabaya, pp. 74–81.Google Scholar
  6. Hart, K.: 1981, Children's Understanding of Mathematics: 11–16, Murray, London.Google Scholar
  7. Herscovics, N.: 1989, ‘Cognitive obstacles encountered in the learning of algebra’, in S. Wagner and C. Kieran (eds.), Research Issues in the Learning and Teaching of Algebra, NCTM, Reston, pp. 60–86.Google Scholar
  8. Kaput, J.: 1987, ‘Towards a theory of symbol use in mathematics’, in C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics, Erlbaum, Hillsdale, pp. 159–195.Google Scholar
  9. Küchemann, D.: 1981, ‘Algebra’, in K. Hart (ed.), Children's Understanding of Mathematics: 11–16, Murray, London, pp. 102–119.Google Scholar
  10. Lakoff, G. and Johnson, M.: 1980, Metaphors We Live By, University of Chicago Press, Chicago.Google Scholar
  11. Lopez-Real, F.: 1995, ‘How important is the reversal error in algebra?, in B. Atweh and S. Flavel (eds.), Proceedings of the 18th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 390–396.Google Scholar
  12. MacGregor, M. and Stacey, K.: 1993, ‘Cognitive models underlying students' formulation of simple linear equations’, Journal for Research in Mathematics Education 24(3), 217–232.Google Scholar
  13. Paige, J.M. and Simon, H.A.: 1966, ‘Cognitive processes in solving algebra word problems’, in B. Kleinmuntz (ed.), Problem Solving: Research, Method, and Theory, Wiley, New York, pp. 51–148.Google Scholar
  14. Robitaille, D. and Garden, R.: 1989, The IEA Study of Mathematics II: Contexts and Outcomes of School Mathematics, Pergamon Press, Oxford.Google Scholar
  15. Stacey, K. and MacGregor, M.: 1994, ‘Algebraic sums and products: Students' concepts and symbolism’, in J.P. da Ponte and J.F. Matos (eds.), Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education (Vol.IV), University of Lisbon, Portugal: PME, pp. 289–296.Google Scholar
  16. Stacey, K. and MacGregor, M.: (in press), ‘Curriculum reform and approaches to algebra’, in R. Sutherland (ed.), Algebraic Processes and Structure.Google Scholar
  17. Sutherland, R.: 1991, ‘Some unanswered research questions on the teaching and learning of algebra’, For the Learning of Mathematics 11, 40–46.Google Scholar
  18. Tall, D. and Thomas, M.: 1991, ‘Encouraging versatile thinking in algebra using the computer’, Educational Studies in Mathematics 22, 1–36.Google Scholar
  19. Thomas, M.: 1994, ‘A process-oriented preference in the writing of algebraic equations’, in G. Bell, B. Wright, N. Leeson and J. Geake (eds.), Proceedings of the 17th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 599–606.Google Scholar
  20. Ursini, S.: 1990, ‘Generalization processes in elementary algebra: Interpretation and symbolization’, in G. Booker, P Cobb and T. Mendicati (eds.), Proceedings of the Fourteenth Conference, International Group for the Psychology of Mathematics Education Mexico: PME, pp. 149–156.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Mollie MacGregor
  • Kaye Stacey

There are no affiliations available

Personalised recommendations