Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple

Dann G. Mallet

doi:10.29333/iejme/173

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Dann G. Mallet

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Abstract

A number of different representational methods exist for presenting the theory of linear equations and associated solution spaces. Discussed in this paper are the findings of a case study where first year undergraduate students were exposed to a new (to the department) method of teaching linear systems which used visual, algebraic and data-based representations constructed using the computer algebra system Maple. Positive and negative impacts on the students are discussed as they apply to representational translation and perceived learning.

Keywords

Computer Algebra System
Multiple Representations
Linear Algebra
Maple

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 2, Issue 1, January 2007, 16-31

https://doi.org/10.29333/iejme/173

Publication date: 02 Feb 2007

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Article Downloads: 2510

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References

Ainley, J., Barton, B., Jones, K., Pfannkuch, M. and Thomas, M. (2002). Is what you see what you get? Representations, metaphors and tools in mathematics didactics. In, J. Novotna (ed.) European Research in Mathematics Education II. Proceedings of the Second Conference of the European Society for Research in Mathematics Education. Prague, Czech Republic, Charles University Press, 128-138.
Ainsworth, S.E. (1999). A functional taxonomy of multiple representations, Computers and Education, 33(2/3), 131- 152.
Ainsworth, S. and Van Labeke, N. (2002). Using a multi-representational design framework to develop and evaluate a dynamic simulation environment. Paper presented at Dynamic Information and Visualisation Workshop, Tuebingen, July 2002. Retrieved May 21, 2006, from http://www.psychology.nottingham.ac.uk/staff/Shaaron.Ainsworth/div.pdf.
Cretchley, P., Harman, C., Ellerton, N. and Fogarty, G. (2000). MATLAB in early undergraduate mathematics: An Investigation into the effects of scientific software on learning. Math. Educ. Res. J., 12, 219-233.
Hazari, S. (2004). Applying instructional design theories to improve efficacy of technology – Assisted presentations. Journal of Instruction Delivery Systems, 18(2), 24-33.
Klincsik, M. (2003). Teaching spline approximation techniques using Maple. ZDM, 35(2), 30-35.
Kordaki, M. (2005). The role of multiple representation systems in the enhancement of the learner model in open learning computer environments. In Proceedings from 3rd International Conference on Multimedia and Information and Communication Technologies in Education.
Lin, P. and Hsieh, C. (1993). Parameter Effects and Solving Linear Equations in Dynamic, Linked, Multiple Representation Environments. The Mathematics Educator, 4(1), 25-33.
Lindner, W. (2003). CAS-Supported multiple representations in elementary linear algebra. ZDM, 35(2), 36-42.
Mackie, D. (2002). Using computer algebra to encourage a deep learning approach to calculus. In Proceedings from 2nd International Conference on the Teaching of Mathematics (at the undergraduate level). Retrieved April 15, 2006, from http://server.math.uoc.gr/~ictm2/Proceedings/pap415.pdf.
Moyer, P.S., Bolyard, J.J. and Spikell, M.A. (2002, February). What are virtual manipulatives? Teaching Children Mathematics, 372-377.
Queensland Board of Senior Secondary School Studies (2000). Mathematics C Senior Syllabus 2001. Retrieved August 23 2006, from http://www.qsa.qld.edu.au/yrs11_12/subjects/maths_c/syllabus.pdf.
Romberg, T.A., Fennema, E. and Carpenter, T. (1993). Integrating Research on Graphical Representations of Functions. NJ: Erlbaum Inc.
Sankey, M.D. (2005). Multimodal design and the neomillennial learner. In Proceedings from OLT 2005 Conference, QUT, Brisbane, 251-259.
Tonkes, E.J., Loch, B.I. and Stace, A.W. (2005). An innovative learning model for computation in first year mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 751-759.
Yerushalmy, M. (2005). Functions of interactive visual representations in interactive mathematical textbooks. International Journal of Computers for Mathematical Learning, 10, 217-249.

How to cite this article

APA

Mallet, D. G. (2007). Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple. International Electronic Journal of Mathematics Education, 2(1), 16-31. https://doi.org/10.29333/iejme/173

Vancouver

Mallet DG. Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple. INT ELECT J MATH ED. 2007;2(1):16-31. https://doi.org/10.29333/iejme/173

AMA

Mallet DG. Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple. INT ELECT J MATH ED. 2007;2(1), 16-31. https://doi.org/10.29333/iejme/173

Chicago

Mallet, Dann G.. "Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple". International Electronic Journal of Mathematics Education 2007 2 no. 1 (2007): 16-31. https://doi.org/10.29333/iejme/173

Harvard

MLA

Mallet, Dann G. "Multiple Representations for Systems of Linear Equations Via the Computer Algebra System Maple". International Electronic Journal of Mathematics Education, vol. 2, no. 1, 2007, pp. 16-31. https://doi.org/10.29333/iejme/173