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http://dx.doi.org/10.7468/jksmed.2013.17.1.063

Toward Students' Full Understanding of Trigonometric Ratios  

Yi, Jung-A (Department of Mathematics Education, Graduate School, Seoul National University)
Yoo, Jae-Geun (Department of Mathematics Education, Graduate School, Seoul National University)
Lee, Kyeong Hwa (Department of Mathematics Education, Seoul National University)
Publication Information
Research in Mathematical Education / v.17, no.1, 2013 , pp. 63-78 More about this Journal
Abstract
Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.
Keywords
trigonometric ratios; mathematical term; mathematics teaching; students' understanding;
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1 Kim, Y. G. (2009). An analysis on the level of using the Mathematical language by 12th Graders and a High School-based on the Analysis Part of Mathematics. Dissertation of M. Ed. Degree. Cheongju, Chungbuk: Korea National University of Education.
2 Ko, J. H. (1998). An analysis of the linguistic aspects of school mathematics. Dissertation of Master degree. Seoul: Seoul National University.
3 Lee, H. J. (2010). Both comparison and analysis about a mathematics textbook between Korea and Singapore. Dissertation of M. Ed. degree. Daegu: Kyungpook National University.
4 Maor, E. (1998). Trigonometric delights. Princeton, NJ: Princeton University Press. ME 1999b.01028
5 Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaboration the Pirie-Kieren Theory. J. Math. Behav. 27(1), 64-85. ME 2009b.00106   DOI   ScienceOn
6 Massa, M. R.; Romero, F.& Guevara, I. (2006). Teaching mathematics through history: Some trigonometric concepts. In: M. Kokowski (Ed.), The Global and the local: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS, Craow, Poland; September 6-9, 2006.
7 Ministry of Education, Science and Technology (MEST) (2011). Mathematics Curriculum. Seoul, Korea: MEST.
8 Park, K. S. (2003). A semantic investigation on high school mathematics terms in Korea — centered on terms of Chinese characters. J. Educational Research in Mathematics. 8(3), 227-246.
9 Pirie, S. & Kieren, T. (1989). A recursive theory of mathematical understanding. Lear.Math. 9(3), 7-11. ME 1991c.00883
10 Cavanagh, M. (2008). Trigonometry from a different angle. Aust. Math. Teach. 64(1), 25-30. ME 2008e.00342
11 Choi, J. Y. (2011). A study on students' understanding of concepts through mathematical terms. Seoul National University: Dissertation of Master degree.
12 Pirie, S. & Kieren, T. (1995). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educ. Stud. Math. 26(2-3), 165-190. ME 1995d.02089   DOI   ScienceOn
13 Rhew, H. C., Rhew, S. L., Han, H. J., Kang, S. M., Je, S. Y., Kim, M. S., Cheon, T. S. & Kim, M. J. (2011). Middle School Mathematics Textbook, Grade 3. Seoul, Korea: Mirae and Culture.
14 Weber, K.(2006). Students' Understanding of Trigonometric Functions. Math.Edu.Res.J. 17(3), 91-112. ME 2006c.01808
15 Song, E. Y. (2008). A Study on the teaching of the concept on trigonometric function. Dissertation of Master degree. Seoul: Seoul National University.
16 Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul, Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12.
17 UCSMP (1992). Functions, Statistics, and Trigonometry: Teacher's Edition. Glenview, IL: Scott, Foresman and Company.
18 Yi, J.; Yoo, J. & Lee, K. (2012). Toward Students' full Understanding of Trigonometric Ratios. In: J. Cho, S. Lee & Y. Choe (Eds.), Proceedings of KSME 2012 Fall Conference on Mathematics Education at Korea National University of Education, Cheongju, Chungbuk 363-791, Korea; November 2-3, 2012 (pp.361-375).
19 Crossfield, D., Shepherd, C., Stein R., & Williams, G. (2009). Trigonometry. Historical Modules Project (Funded by the National Science Foundation). Washington, DC: Mathematical Association of America. Available from: http://www.coursehero.com/file/2894685/Trigonometry/
20 Conzales Astudillo, M. T.; Codes, M.; Delgado, M. L. & Monterrubio, M. C. (2012). Growth in the understanding of the concept of infinite numerical series: A glance through Pirie and Kieren Theory (Paper: TSG 13-2). In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 2660-2667). Seoul, Korea: ICME-12.
21 Freudenthal, H. (1978). Weeding and sowing: preface to a science of mathematics education. Dordrecht, Netherlands: Reidel. 233-242. ME 1979b.00145
22 Katz, V. J. (1997). Some Ideas on the Use of History in the Teaching of Mathematics. Learn. Math. 17(1), 62-63. ME 1998b.00701
23 Kim, S. H. & Lee, C. H. (2003). Mathematical language levels of middle school students. J. Educational Research in Mathematics. 8(2), 123-141.