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http://dx.doi.org/10.7468/jksmee.2020.34.3.393

Comparison of Trigonometry in Mathematics Textbooks in Korea, Australia, and Finland  

Choi, Eun (Hansol Middle School)
Kwon, Oh Nam (Seoul National University)
Publication Information
Communications of Mathematical Education / v.34, no.3, 2020 , pp. 393-419 More about this Journal
Abstract
Trigonometry allows us to recognize the usefulness of mathematics through connection with real life and other disciplines, and lays the foundation for the concept of higher mathematics through connection with trigonometric functions. Since international comparisons on the trigonometry area of textbooks can give implications to trigonometry teaching and learning in Korea, this study attempted to compare trigonometry in textbooks in Korea, Australia and Finland. In this study, through the horizontal and vertical analysis presented by Charalambous et al.(2010), the objectives of the curriculum, content system, achievement standards, learning timing of trigonometry content, learning paths, and context of problems were analyzed. The order of learning in which the three countries expanded size of angle was similar, and there was a difference in the introduction of trigonometric functions and the continuity of grades dealing with trigonometry. In the learning path of textbooks on the definition method of trigonometric ratios, the unit circle method was developed from the triangle method to the trigonometric function. However, in Korea, after the explanation using the quadrant in middle school, the general angle and trigonometric functions were studied without expanding the angle. As a result of analyzing the context of the problem, the proportion of problems without context was the highest in all three countries, and the rate of camouflage context problem was twice as high in Korea as in Australia or Finland. Through this, the author suggest to include the unit circle method in the learning path in Korea, to present a problem that can emphasize the real-life context, to utilize technological tools, and to reconsider the ways and areas of the curriculum that deal with trigonometry.
Keywords
trigonometry; textbook analysis; comparative study;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Kim, S. H. (2016). A study of the relationship between 9th grade students' concept images and their understanding of trigonometric ratios and problem-solving strategies. Master thesis, Ewha Womans University.
2 Noh, J. H. (2016). Analyzing Contexts Used in Textbook Problems -A Case of Precalculus-, Communications of Mathematical Education, 30(3), 295-308.   DOI
3 Ryu, H., Sunwoo, H., Shin, B., Cho, J., Lee, B., Kim, Y., Im, M., Han, M., Nam, S., Kim, M., & Jung, S (2018). Hich School Mathematics I. Seoul: Chunjae
4 Lew, H., Sunwoo, H., Shin, B., Jeong, D., Sul, J., Jang, Y., & Park, S(2020). Middle School Mathematics 3. Seoul: Chunjae
5 Park, K. (1998). A Study on How to Use Calculators in Elementary Mathematics Education in Korea, Journal of Educational Research in Mathematics, 8(1), 237-249.
6 Pang, J., Lee, J., Lee, S. M., Park, Y., Kim, S. K., Choi, I.., & Sun, W. (2015) A comparative analysis of school mathematics curricula in Korea, China, Japan, and USA, Journal of the Korean School Mathematics Society, 18(3), 311-334.
7 Song, E. (2008). A study on the teaching of the concept of trigonometric function, Master thesis, Seoul National University.
8 Shin, Y. et al. (2011). Research report on the mathematics curriculum according to the 2009 revised curriculum. Korean Foundation for the Advancement of Science and Creativity Research Report 2011-11.
9 Shin, J. S. (2011). A Comparative study of mathematics curriculum in Finland, Education of Primary School Mathematics, 14(3), 225-236.   DOI
10 Yoo, J. (2014) A historical analysis on trigonometric functions, Journal of Education Research in Mathematics, 24(4), 607-622.
11 Lee, S. W., & Bang, S. (2004). The effect of the trigonometric ratio unit on the trigonometric function unit, Communications of Mathematical Education, 18(2), 187-208.
12 Choi, J. (2018). A Comparative Study on Calculator in Mathematics Educations Between Korea and Singapore, Journal of the Korean School Mathematics Society, 21(3), 227-245.   DOI
13 Ko, H., Chang, K., & Lee, G. (2016). A Comparative Analysis of the Middle School Mathematics Curriculum in Korea and Australian, Journal of Educational Research in Mathematics, 26(2), 309-331.
14 Ministry of Education (2015). Mathematics Curriculum, Ministry of education notice 2015-74[supplement 8].
15 Kim, M. & Kim, G. (2013) The analysis of mathematical tasks in the high school mathematics, School Mathematics, 15(1), 37-59.
16 Kim, W., Cho, M., Bang, G., Yoon, J., Shin, J. H., Im, S., Kim, D., Kang, S., Kim, K., Park, H., Shim, J., Oh, H., Lee, D., Lee, S., J. & Jung, J (2018). High School Mathematics I. Seoul: Visang
17 Kim, W, Cho, M., Bang, K., Kim, D., Kang, S., Bae, S., Ji, E., & Kim, Y. (2018). Middle School Mathematics 3. Seoul: Visang
18 Chong, Y.., Chang, K.., Kim, G., Kwon, N., Kim, J., Seo, D., ...&.Tak, B. J. (2016). A comparative study of mathematics curriculum among the United States, Singapore, England, Japan, Australia and Korea, Journal of Educational Research in Mathematics, 26(3), 371-402.
19 Choi, Y. & Cho, M. (2011). A study on the content anaytic comparison of Korean and Finnish high school mathe textbooks, Korean Journal of Teacher Education, 27(1), 61-82.
20 Australian Curriculum, Assessment and Reporting Authority. (2013). The Australian curriculum : Mathematics Curriculum F-10. Retrieved from http://www.australiancurriculum.edu.au/ 2020.7.26
21 Brown, S. A. (2005). The trigonometric connection: Students' understanding of sine and cosine. Doctoral dissertation. Illinois State University.
22 Fi, C. D. (2003). Preservice secondary school mathematics teachers' knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. Doctoral dissertation. Iowa University.
23 Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical thinking and learning, 12(2), 117-151.   DOI
24 De Lange, J. (1995). Assessment: No change without problems. In Tomas A. Romberg(Eds.), Reform in school mathematics and authentic assessment, 87-172. The USA: SUNY Press.
25 Demir, O. (2012). Students' concept development and understanding of sine and cosine functions: A new theoretical and educational approach. Doctoral dissertation. Universite van Amsterdam.
26 Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219.   DOI
27 Hähkioniemi, Juhala, Juutinen, Louhikallio-Fomin, Luoma-aho, Raittila, Tikka. (2016). Juuri 3 - MAA3 : geometria. Helsingissa : Kustannusosakeyhtio Otava.
28 Hong, D. & Choi, K. (2014). A comparison of Korean and American secondary school textbooks: the case of quadratic equations. Educational Studies in Mathematics, 85(2), 241-263.   DOI
29 Kendal, M., & Stacey, K. (1996). Trigonometry: Comparing ratio and unit circle methods. In Technology in Mathematics Education. Proceedings of the 19th Annual Conference of the Mathematics education Research group of Australasia, 322-329.
30 Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world, situated, and school contexts. Educational Studies in Mathematics, 63(3), 283-301.   DOI
31 Laurinolli, T., Lindroos-Heinanen, R., Luoma-aho, E., Timo sankilampi, Selenius, R., Talvitie, K., & Vaha-Vahe, O. (2009). Laskutaito 9. Lee, J. Y. translation (2014). Finnish Middle School Mathematics 9. Solbitgil.
32 Mesa, V., & Goldstein, B. (2017). Conceptions of Angles, Trigonometric Functions, and Inverse Trigonometric Functions in College Textbooks. International Journal of Research in Undergraduate Mathematics Education, 3(2), 338-354.   DOI
33 Moore, K. C. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83(2), 225-245.   DOI
34 Peter Brown, Michael Evans, Garth Gaudry, David Hunt, Robert McLaren, Bill Pender, Brian Woolacott. (2011). ICE-EM Mathematics Australian Curriculum 2nd Edition Year 9 Book 2. Cambridge University Press.
35 The Finnish National Board of Education(2016b). National Core Curriculum for Upper secondary education 2014. Helsinki: The Finnish National Board of Education.
36 Peter Brown, Michael Evans, Garth Gaudry, David Hunt, Robert McLaren, Bill Pender, Brian Woolacott. (2017). ICE-EM Mathematics Australian Curriculum 3rd Edition Year 10 & 10A. Cambridge University Press.
37 Shin, J., & Lee, S. J. (2018). The alignment of student fraction learning with textbooks in Korea and the United States. The Journal of Mathematical Behavior, 51, 129-149.   DOI
38 Stein, M. K., Remillard, J. T., & Smith, M. S.(2007) How curriculum influences student learning. Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age.
39 Stinner, A. (1995). Contextual settings, science stories, and large context problems: Toward a more humanistic science education. Science Education, 79(5), 555-581.   DOI
40 The Finnish National Board of Education(2016a). National Core Curriculum for Basic education 2014. Helsinki: The Finnish National Board of Education.
41 Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. Proceedings of the annual meeting of the International Group for the Psychology of Mathematics Education, 1, 31-49.
42 Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics education. Netherlands.
43 Weber, K. (2005). Students' understanding of trigonometric functions. Mathematics Education Research Journal, 17(3), 91-112.   DOI
44 Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational studies in Mathematics, 89(1), 41-65.   DOI