Exploring Derivatives by Means of GeoGebra

Puspita Sari, Aris Hadiyan, Dwi Antari

Abstract


The paper aims to explain how GeoGebra can be used in a differential calculus course to explore the Derivative concepts by providing dynamic-visualizations of the concept. Design research methodology was used in this research by designing an instructional design (hypothetical learning trajectories) in the first phase and conducting the teaching experiment in the second phase. The data collected during the experiment consist of video recordings of the classroom activities, observations, interviews, and students written work. In the third phase of the design research, the data were analyzed retrospectively by comparing the actual learning process and the hypothetical learning trajectory. The results show that the dynamic feature of GeoGebra offers the possibility of zooming in on a graph corresponds to taking infinitesimal when a secant line transforms into a tangent line. This builds a foundation for the understanding of the definition of derivative intuitively.

Keywords


Geogebra; derivatives; calculus; design research

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References


Ahuja, O.P., Lim-Teo, Suat-Khoh and Lee, Peng Yee. (1998). Mathematics Teachers’ Perspective of Their Students’ Learning in Traditional Calculus and Its Teaching Strategies. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 2(2), 89-108.

Amiel, T., Reeves, T. C. (2008). Design-Based Research and Educational Technology: Rethinking Technology and the Research Agenda. Educational Technology and Society, 11(4), 29-40.

Cobb, P., Stephan, M., McClain, K., and Gravemeijer, K. (2001). Participating in Classroom Mathematical Practice. The Journal of the Learning Science, 10(1 & 2), 113-163.

Cobb, P., Confrey, J., diSessa, A., and Lehrer, R. (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9-13.

Diković, L. (2009). Applications GeoGebra into Teaching Some Topics of Mathematics at the College Level. ComSIS, 6(2), 191-203.

Edelson. D. C. (2002). Design Research: What We Learn When We Engage in Design. The Journal of The Learning Sciences, 11(1), 105-121.

Gravemeijer, K., and Cobb, P. (2006). Design Research from a Learning Design Perspective, Educational Design Research. London and New York: Routledge,

Gravemeijer, K., and Doorman, M. (1999). Context Problems in Realistic Mathematics Education: a Calculus Course as an Example. Educational Studies in Mathematics, 39(1-3), 111-129.

Haciomeroglu, E. S., and Andreasen, J.B. (2013). Exploring Calculus with Dynamic Mathematics Software. Mathematics and Computer Education, 47(1), 6-18.

Haciomeroglu, E. S., Aspinwall, L., Presmeg, N.C. and Knott, L. (2009). Visual and Analytic Thinking in Calculus. The Mathematics Teacher, 103(2), 140-145.

Haciomeroglu, E. S., Aspinwall, L. and Presmeg, N. (2010). Contrasting Cases of Calculus Students' Understanding of Derivative Graphs. Mathematical Thinking and Learning, 12(2), 152-176.

Hohenwarter, M., Hohenwarter, J., Kreis, Y., and Lavicza, Z. (2008). Teaching and Learning Calculus with Free Dynamic Mathematics Software GeoGebra, TSG 16: Research and development in the teaching and learning of calculus, ICME 11, Monterrey, Mexico.

Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational Studies in Mathematics, 48(2–3), 137–174.

Lee, P. Y. (2006). Teaching Secondary School Mathematics. Singapore: Mc Graw Hill.

Özmantar, M. F., Akkoc, H., Bingolbali, E., Demir, S., and Ergene, B. (2010). Pre-Service Mathematics Teachers’ Use of Multiple Representations in Technology-Rich Environments. Eurasia Journal of Mathematics, Science & Technology Education, 6(1), 19-36.

Rasmussen, C., Marrongelle, K., and Borba, M.C. (2014). Research on calculus: what do we know and where do we need to go. ZDM, 46(4), 507-515.

Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26(2), 114-145.

Struik, D. J. (Ed.). (1969). A source book in mathematics, 1200–1800. Cambridge: Harvard University Press.

Tall, D.O. (2009). Dynamic mathematics and the blending of knowledge structures in calculus. ZDM, 41(4), 481-492.

Varberg, D., Purcell, E., and Rigdon, S. (2006). Calculus 9th Edition. New York: Pearson.

Weigand, G. H. (2014). A Discrete Approach to the Concept of Derivative. ZDM, 46(4), 603-619.

Zimmerman, W. (1991). Visual Thinking in Calculus. In W. Zimmermann and S. Cunningham (Editors), Visualization in Teaching and Learning Mathematics (pp. 127-138). Washington, DC: Mathematical Association of America.




DOI: http://dx.doi.org/10.12928/ijeme.v2i1.8670

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