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http://dx.doi.org/10.7468/jksmed.2014.18.1.31

Investigating Arithmetic Mean, Harmonic Mean, and Average Speed through Dynamic Visual Representations  

Vui, Tran (College of Education, Hue University)
Publication Information
Research in Mathematical Education / v.18, no.1, 2014 , pp. 31-40 More about this Journal
Abstract
Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.
Keywords
Dynamic visual representations; arithmetic mean; harmonic mean; average speed;
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1 Tran, V. (2006b). Helping students develop and extend their capacity to do purposeful mathematical works. Tsukuba Journal of Educational Study in Mathematics25, 279-287. http://www.criced.tsukuba.ac.jp/math/apec2006/Tsukuba_Journal_25.pdf
2 Tran, V. et al. (2007). Design dynamic models for teaching and learning high school mathematics with the Geometer's Sketchpad.Hanoi, Vietnam:Educational Publishing House, MOET.
3 Confrey, J. & Smith, E. (1991). A framework for functions: Prototypes, multiple representations and transformations. In: R. G. Underhill (Ed.), Proceedings of the 13th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 57-63). Blacksburg, VA: Virginia Polytechnic Institute and State University.
4 Meyer, M. (2007).From discoveries to verifications - theoretical framework and inferential analyses of classroom interaction, Germany: TU Dortmund. http://tsg.icme11.org/document/get/633
5 Meyer, M. (2010), Abduction-A logical view for investigating and initiating processes of discovering mathematical coherences, Educ. Stud.Math.74(2),185-205. ME 2010f.00587   DOI
6 MOET (2009).Regulation on professional standards for teachers at junior and senior secondary schools.Circular No. 30/2009/TT-MOET.Hanoi, Vietnam: Ministry of Education and Training (MOET).
7 Montgomery, H. (1988). Mental models and problem solving: Three challenges to a theory of restructuring and insight. Scandinavian Journal of Psychology29, 85-94.   DOI
8 Sierpinska, A. (1992). On understanding the notion of function. In: E. Dubinsky & G. Harel (Ed.), The concept of function: Aspects of epistemology and pedagogy (pp. 25-58). Washington, DC: Mathematical Association of America. ME 19930f.03532
9 Suh, J. & Moyer, P. S. (2007).Developing students' representational fluency using virtual and physical algebra balances.J. Comput. Math. Sci. Teach.26(2), 155-173. ME 2009a.00343
10 Tran, V. (2006a).Using lesson study as a tool to develop profession of mathematics teachers. Journal of Education, Vietnam, No. 151 (Vol. 1-12/2006), pp. 18-20.
11 Arcavi, A. (2003).The role of visual representations in the learning of mathematics.Educ. Stud. Math.52(3), 215-241. ME 2003d.02928   DOI