Abstract
Using a computer algebra system (CAS) in the classroom provides many opportunities for improving student learning. However, to take advantage of such a powerful instrument as CAS requires changes to many aspects of the classroom. The different ways in which three pioneering Australian teachers adapted their teaching to use CAS are described (see also Appendix 4-1, for a comparison with similar experiences in other countries). Two of the teachers taught an eight-week course in each of two consecutive years (the CAS-Calculus project) at secondary school level, using a symbolic calculator. They gave CAS different roles in the instruction and in defining their curriculum goals. One teacher used CAS in a restricted way with the primary goal of increasing understanding while the second teacher adopted CAS as another technique freely available for solving standard problems and emphasized efficient routines. Over several years (in a separate project, at university level, using the computer program DERIVE), the third teacher has evolved a method of teaching with CAS, moving from an early emphasis on teaching about CAS as a tool and using it for difficult problems to incorporating its use for primarily pedagogical aims. In reporting on these case studies we comment on different ways of organising the classroom; the variety in approaches to teaching the use of CAS; the increased range of methods for solving problems and for teaching; the contrast between using graphics and symbolic calculators; the place of paper-and-pencil skills; devoting time to mathematics or technology; and finally the curriculum and assessment changes required in schools.
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References
Berry J., Monaghan J., Kronfellner M. & Kutzler B. (Eds.), (1997) The state of computer algebra in mathematics education. Lund, Sweden: Chartwell-Bratt.
Bottino R. & Furinghetti F. (1998) The computer in mathematics teaching: scenes from classroom, in D. Tinsley & D.C. Johnson (Eds.), Information and communication technologies in school mathematics (pp. 131–139). London: Chapman & Hall.
Flynn P. (2001) Examining mathematics with CAS: Issues and possibilities, in C. Vale, J. Horwood & J. Roumeliotis (Eds.), A mathematical odyssey, Proceedings of the 38th annual conference of the MAV (pp. 285–298). Melbourne: Mathematical Association of Victoria.
Flynn P. (2003) Adapting “Problems to prove” for CAS-permitted examinations, The International Journal of Computer Algebra in Mathematics Education 10(3), 103–121.
Forster P. (1997) Teaching through technology, Australian Senior Mathematics Journal 11(1), 54–61.
Forster P. & Mueller U. (2000) Diversity and difficulties with graphics calculator usage, in the 1999 calculus tertiary entrance examinations in Western Australia, Australian Senior Mathematics Journal 14(1), 4–15.
Heid M.K. (1988) Resequencing skills and concepts in applied calculus using the computer as a tool, Journal for Research in Mathematics Education 19(1), 3–25.
Heid M.K., Sheets C. & Matras M.A. (1990) Computer enhanced algebra: New roles and challenges for teachers and students, in T. Cooney (Ed.), Teaching and learning mathematics in the 1990s, NCTM 1990 Year Book. Reston, VA: NCTM, 194–204.
Keller B., Russell C. & Thompson H. (1999) A large-scale study clarifying the roles of the TI-92 and instructional format on student success in calculus, The International Journal of Computer Algebra in Mathematics Education 6(3), 191–207.
Kendal M. & Stacey K. (1999) Varieties of teacher privileging for teaching calculus with computer algebra systems, International Journal of Computer Algebra in Mathematics Education 6(4), 233–247.
Kendal M. & Stacey K. (2001) The impact of teacher privileging on learning differentiation with technology, The International Journal of Computers for Mathematical Learning 6, 143–163.
Kendal M. (2002) Teaching and learning introductory differential calculus, Unpublished doctoral thesis. Australia: The University of Melbourne. Available: (http://thesis.lib.unimelb.edu.au/).
Kendal M. & Stacey K. (2002) Teachers in transition: Moving towards CAS-supported classrooms, Zentralblatt für Didacktik der Mathematik 34(5), 196–203.
Kutzler B. (2003) CAS as pedagogical tools for teaching and learning mathematics, in J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R.M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics (pp. 53–71). Reston: National Council of Teachers of Mathematics.
Lagrange J.B., Artigue M., Laborde C. & Trouche L. (2003) Technology and Mathematics Education: a Multidimensional Study of the Evolution of Research and Innovation, in A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick & F.K.S. Leung (Eds), Second International Handbook of Mathematics Education (Vol. 1, pp. 239–271). Kluwer Academic Publishers.
Lumb S, Monaghan J. & Mulligan S. (2000) Issues arising when teachers make extensive use of computer algebra, The International Journal of Computer Algebra in Mathematics Education (7)4, 223–240.
McCrae B., Asp G. & Kendal M. (1999) Learning calculus with supercalculators, in J. Truran & K. Truran (Eds.), Making the difference, Proceedings of the 22nd annual conference of The Mathematical Educational Research Group of Australasia (pp. 359–364). Adelaide: MERGA.
Monaghan J. (1997) Teaching and learning in a computer algebra environment: Some issues relevant to sixth-form teachers in the 1990’s, The International Journal of Computer Algebra in Mathematics Education 4(3), 207–220.
Monaghan J. (2001) Teachers’ classroom interactions in ICT-based mathematics lessons, in M. Van den Heuvel-Panhuizen (Ed.), Proceedings of PME 25 (Vol. 1, pp. 383–390). Utrecht: Freudenthal Institut.
National Council for Educational Technology (1994) The A-level curriculum of the future — The impact of computer algebra systems. Coventry: NCET.
Oldknow A. & Taylor R. (2000) Teaching mathematics with ICT. London and New York: Continuum.
Palmiter J.R. (1991) Effects of computer algebra systems on concept and skill acquisition in calculus, Journal for Research in Mathematics Education 22(2), 151–156.
Pierce R. & Stacey K. (2001a) Reflections on the changing pedagogical use of computer algebra systems: Assistance for doing or learning mathematics? Journal for Computers in Mathematics and Science Teaching 20(2), 141–159.
Pierce R. & Stacey K. (2001b) Observations on students’ responses to learning in a computer environment, Mathematics Education Research Journal 13(1), 28–46.
Repo S. (1994) Understanding and reflective abstraction: learning the concept of derivative in a computer environment, International DERIVE Journal 1(1), 97–113.
Schneider E. (1999) La TI-92 dans l’enseignement des mathématiques, des enseignant(e)s découvrent la didactique des mathématiques, in D. Guin (Ed.), Calculatrices symboliques et géométriques dans l’enseignement des mathématiques, Actes du colloque francophone européen (pp. 49–60). Montpellier: IREM, Université Montpellier II.
Schneider E. (2000) Teacher experiences with the use of CAS in a mathematics classroom, International Journal of Computer Algebra in Mathematics Education 7(2), 119–141.
Simmt E. (1997) Graphing calculators in high school mathematics, International Journal of Computers in Mathematics and Science Teaching 16(2/3), 269–289.
Stacey K., Asp G. & McCrae B. (2000a) Goals for a CAS-active senior mathematics curriculum, in M. Thomas (Ed.), TIME 2000, Conference proceedings at an International Conference on Technology in Mathematics Education, 11th–14th December (pp. 244–252). Auckland: The University of Auckland.
Stacey K., McCrae B., Chick H., Asp G. & Leigh-Lancaster D. (2000b) Research-led policy change for technologically-active senior mathematics assessment, in J. Bana & A. Chapman (Eds.), Mathematics Education Beyond 2000, Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia (pp. 572–579). Fremantle: MERGA.
Tharp M.L., Fitzsimmons, J.A. & Brown Ayers, R.L. (1997) Negotiating a technological shift: Teacher perception of the implementation of graphing calculators, Journal of Computers in Mathematics and Science Teaching 16(4), 551–575.
Thomas M., Tyrrell J. & Bullock J. (1995) Using computers in the mathematics classroom: The role of the teacher, Mathematics Education Research Journal 8(1), 38–57.
Victorian Curriculum and Assessment Authority (Accessed 3 Sep 2003). Available: (http://www.vcaa.vic.edu.au/vce/studies/MATHS/).
Voigt J. (1994) Negotiation of mathematical meaning and learning mathematics, Educational Studies in Mathematics 26, 275–298.
Zbiek R.M. (2001) Influences on Mathematics Teachers’ Transitional Journeys in Teaching with CAS, CAME Meeting. Utrecht: (http://ltsn.mathstore.ac.uk/came).
Zbiek R. M. (2003) Computer algebra systems in secondary schools mathematics education, in J. Fey, A. Cuoco, C. Kieran, L. McMullin & R.M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics (pp. 197–216). Reston: National Council of Teachers of Mathematics.
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Kendal, M., Stacey, K., Pierce, R. (2005). The Influence of a Computer Algebra Environment on Teachers’ Practice. In: Guin, D., Ruthven, K., Trouche, L. (eds) The Didactical Challenge of Symbolic Calculators. Mathematics Education Library, vol 36. Springer, Boston, MA. https://doi.org/10.1007/0-387-23435-7_5
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