Skip to main content
SpringerLink
Log in

Building a versatile understanding of algebraic variables with a graphic calculator

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

Abstract

Algebra has been recognised for some time as a difficult topic for many secondary school students. Discovering the best way(s) of introducing algebra into the students' experience and fostering understanding has stimulated much discussion and research. It is our belief that an understanding of the concept of variable is fundamental to further student progress in algebra. This paper describes a study using a module of work based on a graphic calculator which provided an environment where students could experience some aspects of variables and hence begin to build an understanding of them. The graphic calculator proved to be an instrument for achieving a significant improvement in student understanding, something which has often proved difficult previously.

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

  • Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K. and Vidakovic, D.: 1996, 'Understanding the limit concept: beginning with a coordinated process scheme', Journal of Mathematical Behavior 15, 167-192.

    Google Scholar 

  • Dubinsky, E. and Lewin, P.: 1986, 'Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness', Journal of Mathematical Behavior 5(1), 55-92.

    Google Scholar 

  • Dubinsky, E.: 1991, 'Reflective abstraction in advanced mathematical thinking', in D. Tall (ed.), Advanced Mathematical Thinking, Kluwer Academic Publishers, Dordrecht, pp. 95-123.

    Google Scholar 

  • Graham, A. and Galpin, B.: 1998, Calculator Maths, Corby, UK: A+B Books.

    Google Scholar 

  • Gray, E. and Tall, D.O.: 1991, 'Duality, ambiguity and flexibility in successful mathematical thinking', Proceedings of the 15th Conference of the International Group for the Psychology of Mathematics Education, Assisi 2, 72-79.

  • Gray, E. and Tall, D.O.: 1994, 'Duality, ambiguity and flexibility: A proceptual view of simple arithmetic', Journal for Research in Mathematics Education 26, 115-141.

    Google Scholar 

  • Hong, Y.Y. and Thomas, M.O.J.: 1998, 'Versatile understanding in integration', Proceedings of the International Congress of Mathematics Instruction-South East Asian Conference on Mathematics Education, Seoul, Korea, pp. 255-265

  • Kieran, C.: 1981, 'Pre-algebraic notions among 12 and 13 year olds', Proceedings of the Eighteenth International Conference of the International Group for the Psychology of Mathematics Education, Grenoble, pp. 158-164.

  • Kieran, C.: 1994, 'A functional approach to the introduction of algebra-some pros and cons', Proceedings of the Eighteenth International Conference of the International Group for the Psychology of Mathematics Education, Lisbon, Portugal, I, pp. 157-175.

    Google Scholar 

  • Kota, S. and Thomas, M.O.J.: 1998, 'Students' arithmetic preferences: effect on problem solving ability', Hiroshima Journal of Mathematics Education, Hiroshima, Japan: Hiroshima University, 6, 33-48.

    Google Scholar 

  • Küchemann, D.E.: 1981, 'Algebra', in K.M. Hart (ed.), Children's Understanding of Mathematics: 11-16, John Murray, pp. 102-119.

  • Leitzel, J.R.: 1989, 'Critical considerations for the future of algebra instruction or A reaction to: algebra: what should we teach and how should we teach it?', in S.Wagner and C. Kieran (eds.), Research Issues in the Learning and Teaching of Algebra, NCTM, Reston: Lawrence Erlbaum, pp. 25-32.

    Google Scholar 

  • Linchevski, L. and Herscovics, N.: 1996, 'Crossing the cognitive gap between arithmetic and algebra: operating on the unknown in the context of equations', Educational Studies in Mathematics 30, 39-65.

    Google Scholar 

  • MacGregor, M. and Stacey, K.: 1997, 'Students' understanding of algebraic notation', Educational Studies in Mathematics 33, 1-19.

    Google Scholar 

  • Penglase, M. and Arnold, S.: 1996, 'The graphics calculator in mathematics education: a critical review of recent research', Mathematics Education Research Journal 8(1), 58-90.

    Google Scholar 

  • Ruthven, K.: 1990, 'The Influence of graphic calculator use on translation from graphic to symbolic forms', Educational Studies in Mathematics 21, 431-450.

    Google Scholar 

  • Schoenfeld, A. and Arcavi, A.: 1988, 'On the meaning of variable', Mathematics Teacher 81(6), 420-427.

    Google Scholar 

  • Sfard, A. and Linchevski, L.: 1994, 'The gains and pitfalls of reification-the case of algebra'. Educational Studies in Mathematics 26, 191-228.

    Google Scholar 

  • Sfard, A.: 1991, 'On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin', Educational Studies in Mathematics 22(1), 1-36.

    Google Scholar 

  • Sfard, A.: 1994, 'Reification as the birth of metaphor', For The Learning of Mathematics 14(1), 44-54.

    Google Scholar 

  • Sfard, A.: 1995, 'The development of algebra: confronting historical and psychological perspectives', Journal of Mathematical Behavior 14, 15-39.

    Google Scholar 

  • Skemp, R.R.: 1971, The Psychology of Learning Mathematics, Penguin, Middlesex, UK.

    Google Scholar 

  • Skemp, R.R.: 1979c, Intelligence, Learning and Action: -A Foundation For Theory And Practice In Education, Wiley, Chichester, UK.

    Google Scholar 

  • Stacey, K. and MacGregor, M.: 1997, Learning to Use Algebra for Solving Problems: Research findings and their implications for Mathematics Education policy, Department of Science and Mathematics Education, The University of Melbourne.

  • Tall, D.O. and Thomas, M.O.J.: 1991, 'Encouraging versatile thinking in algebra using the computer', Educational Studies in Mathematics 22, 125-147.

    Google Scholar 

  • Tall, D.O. and Vinner, S.: 1981, 'Concept image and concept definition in mathematics, with special reference to limits and continuity', Educational Studies in Mathematics 12, 151-169.

    Google Scholar 

  • Thomas, M.O.J.: 1994, 'A process-oriented preference in the writing of algebraic equations', Proceedings of the 17th Mathematics Education Research Group of Australasia Conference, Lismore, Australia, pp. 599-606.

  • Thomas, M.O.J., Tyrrell, J. and Bullock, J.: 1996, 'Using computers in the mathematics classroom: the role of the teacher', Mathematics Education Research Journal April, 8(1), 38-57.

    Google Scholar 

  • Wagner, S., Rachlin, S.L. and Jensen, R.J.: 1984, Algebra Learning Project-Final Report, Department of Mathematics Education, University of Georgia.

Download references

Author information

Authors and Affiliations

  1. Centre for Mathematics Education, The Open University, Milton Keynes, United Kingdom

    Alan T. Graham

  2. Mathematics Education Unit, Department of Mathematics, The University of Auckland, Auckland, New Zealand

    Michael O.J. Thomas (Head)

Authors
  1. Alan T. Graham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael O.J. Thomas
    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

Graham, A.T., Thomas, M.O. Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics 41, 265–282 (2000). https://doi.org/10.1023/A:1004094013054

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004094013054

Search

Navigation