Browse > Article
http://dx.doi.org/10.7468/jksmee.2011.25.1.063

Exploring a Teaching Method of Limits of Functions with Embodied Visualization of CAS Graphing Calculators  

Cho, Cheong-Soo (Department of Mathematics Education, Yeungnam University)
Publication Information
Communications of Mathematical Education / v.25, no.1, 2011 , pp. 63-78 More about this Journal
Abstract
The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.
Keywords
limit of function; CAS graphing calculators; visualization; APOS theory;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.   DOI   ScienceOn
2 Vinner, S. (1991). The role of definitions in the teaching and learning mathematics. In D. Tall(Eds.), Advanced mathematical thinking(pp. 65-81). Dordrecht: Kluwer Academic Publishers.
3 Williams, S. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22, 219-236.   DOI   ScienceOn
4 Wood, N. G. (1992). Mathematical analysis: A comparison of students development and historical development. Unpublished doctoral dissertation, Cambridge University, U.K.
5 Pinto, M. M. F. (1998). Students' understanding of real analysis. Unpublished doctoral dissertation, Warwick University, U.K.
6 Smith D. A., & Moore, L. C. (1996). Calculus: Modeling and application. Boston: Houghton Mifflin.
7 Tall, D. (1980). Mathematical intuition, with special reference to limiting processes. Proceedings of the Fourth International Conference for the Psychology of Mathematics Education, 170-176.
8 Tall, D. (1993). Real mathematics, rational computers and complex people. Proceedings of the fifth annual International Conference on Technology in College Mathematics Teaching(pp. 243-258). Reading, MA: Addison-Wesley.
9 Tall, D. (2002). Natural and formal infinities. Educational Studies in Mathematics, 48, 199-238.
10 Tall, D. (2001). Cognitive development in advanced mathematics using technology. Mathematics Education Research Journal, 12, 196-218.
11 Tall, D., Smith, D., & Piez, C. (2008). Technology and calculus. In M. K. Heid & G. W. Blume(Eds.), Research on technology and the teaching and learning of mathematics: Volume 1(pp. 207-258). Charlotte, NC: Information Age Publishing.
12 윌리엄 던햄 (2004). 수학의 천재들(조정수 번역.). 서울: 경문사. (원본출판 1990)
13 Artigue, M. (1991). Analysis. In D. Tall(Ed.), Advanced mathematical thinking(pp. 167-198). Kluwer Academic Publishers.
14 Cornu. B. (1991). Limits. In D. Tall(Ed.), Advanced mathematical thinking(pp. 153-166). Kluwer Academic Publishers.
15 Monaghan, J. D. (1986). Adolescents' understanding of limits and infinity. Unpublished doctoral dissertation, Warwick University, U.K.
16 Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process scheme. Journal of Mathematical Behavior, 15, 167-192.   DOI   ScienceOn
17 Dubinsky, Ed., Weller, K., Mcdonale, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis: Part 1. Educational Studies in Mathematics, 58, 335-359.   DOI   ScienceOn
18 Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.