PROSPECTIVE TEACHERS REPRESENTATIONS IN PROBLEM SOLVING OF SPECIAL ANGLE TRIGONOMETRY FUNCTIONS BASED ON THE LEVEL OF ABILITY

Yayan Eryk Setiawan (1*)


(1) Universitas Islam Malang, Indonesia
(*) Corresponding Author


Abstract


One of the materials used as the basis for solving trigonometric function problems is special angle trigonometry. Prospective teachers' representation in problem-solving of trigonometric functions with special angles is thought to be influenced by prospective teachers' abilities. Therefore, this study aims to analyze the representations used by prospective teachers in problem-solving of special angle trigonometric function based on ability categories. This research is qualitative descriptive. The research subjects are prospective teachers of the mathematics education study program at a university in Malang. The data collected in this study are in the form of work results and observation. The research instrument consisted of the problem of the trigonometric function value of the special angle and the interview guide developed by the researcher. The analysis of prospective teacher work results was carried out by classifying the ability categories into low, medium, and high abilities. The work results of each of these categories are classified based on verbal, numeric, image, and algebraic representations. The analysis of the interview transcripts was carried out by coding the words or sentences which aims to determine prospective teachers' understanding of using representations. The results showed that prospective teachers with low ability use a lot of verbal representation, while prospective teachers with medium and high abilities use a lot of image representation in problem-solving of special angle trigonometric function. The implication of the results of this study is to teach special angle trigonometric function material based on appropriate representations.

Keywords


Prospective Teachers; Representation; Special Angle; Trigonometry

Full Text:

PDF

References


Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children's understanding and reasoning in multiplication. Educational Studies in Mathematics, 70, 217-241. https://doi.org/10.1007/s10649-008-9145-1

Bishop, J. (2000). Linear geometric number patterns : Middle school students' strategies. Mathematics Education Research Journal, 12, 107-126. https://doi.org/10.1007/BF03217079

Byers, P. (2010). Investigating trigonometric representations in the transition to college mathematics. College Quartely, 13(2), 1-10.

Byers, T. (2009). The basic intervention mathematics program for at-risk students. Australian Mathematics Teacher, 65(1), 6-11.

Cavanagh, M. (2008). Trigonometry from a different angle. Australian Mathematics Teacher, 64(1), 25-30.

Clark, L. M., Depiper, J. N., Frank, T. J., Nishio, M., Campbell, P. F., Smith, T. M., Griffin, M. J., Rust, A. H., Conant, D. L., & Choi, Y. (2014). Teacher characteristics associated with mathematics teachers’ beliefs and awareness of their students’ mathematical dispositions. Journal for Research in Mathematics Education, 45(2), 246-284. https://doi.org/10.5951/jresematheduc.45.2.0246

Cooper, J. L., & Alibali, M. W. (2012). Visual Representations in Mathematics Problem-Solving : Effects of Diagrams and Illustrations. In Proceeding of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Downing, D. (2009). Dictionary of mathematics terms. In Barron's Educational Series, Inc. (Third Edit ed., Vol. 51). Barron's Educational Series, Inc. https://doi.org/10.2307/3614426

Friedlander, A., & Tabach, M. (2001). Promoting multiple representations in algebra. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 173-185). National Council of Teachers of Mathematics.

Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 1-23). National Council of Teachers of Mathematics.

Hästö, P., Palkki, R., Tuomela, D., & Star, J. R. (2019). Relationship between mathematical flexibility and success in national examinations. European Journal of Science and Mathematics Education, 7(1), 1-13. https://doi.org/10.30935/scimath/9530

Jaelani, A. (2017). Kesalahan jawaban tes trigonometri mahasiswa pendidikan matematika semester pertama [Errors in the answers to trigonometry tests for first-semester mathematics education students]. Alphamath: Journal of Mathematics Education, 3(2), 1-13.

Joyner, J., & Reys, B. (2000). Principles and Standards for School Mathematics: What's in It for You? Teaching Children Mathematics TCM, 7(1), 26-29. https://doi.org/10.5951/tcm.7.1.0026

Kamber, D., & Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161-175. https://doi.org/10.1080/0020739X.2017.1357846

Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Taylor & Francis Group, LLC.

Kaput, J. J., Blanton, M. L., & Moreno, L. (2008). Algebra from a symbolization point of view. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 19-55). Taylor & Francis Group, LLC.

Lial, M. L., Hornsby, J., Schneider, D. I., & Daniels, C. J. (2016). Trigonometry (11 ed.). Pearson.

Maknun, C. L., Rosjanuardi, R., & Jupri, A. (2019). From ratios of right triangle to unit circle: An introduction to trigonometric functions. Journal of Physics: Conference Series, 1157(2), 022124. https://doi.org/10.1088/1742-6596/1157/2/022124

Mustangin, & Setiawan, Y. E. (2021). Pemahaman konsep mahasiswa semester satu pada mata kuliah trigonometri [The conceptual understanding of first semester students in trigonometry courses]. Jurnal Elemen, 7(1), 98-116. https://doi.org/10.29408/jel.v7i1.2773

Nabie, M. J., Akayuure, P., Ibrahim-Bariham, U. A., & Sofo, S. (2018). Trigonometric concepts: Pre-service teachers' perceptions and knowledge. Journal on Mathematics Education, 9(2), 169-182. https://doi.org/10.22342/jme.9.2.5261.169-182

Nejad, M. J. (2016). Undergraduate students' perception of transformation of sinusoidal functions. In Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson.

Özsoy, G. (2018). Pre-service teachers’ use of visual representations. International Electronic Journal of Elementary Education, 11(1), 49-54. https://doi.org/10.26822/iejee.2018143960

Perkins, D. N., Jay, E., & Tishman, S. (1993). Beyond abilities: A dispositional theory of thinking. Merrill-Palmer Quarterly, 39(1), 1-21. http://www.jstor.org/stable/23087298

Ron, S. (2001). From IQ to IC: A dispositional view of intelligence. Roeper Riview, 23(3), 1-23.

Scher, D., & Goldenberg, E. P. (2001). A multirepresentational journey through the law of cosines. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 117-128). National Council of Teachers of Mathematics.

Setiawan, Y. E. (2020). Analisis kemampuan siswa dalam pembuktian kesebangunan dua segitiga [Analysis of students' abilities in proving the similarity of two triangles]. Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam, 8(1), 23-38. https://doi.org/10.24256/jpmipa.v8i1.800

Setiawan, Y. E. (2020). Analisis kesalahan siswa dalam menggeneralisasi pola linier. Jurnal Nasional Pendidikan Matematika, 4(2), 180-194. https://doi.org/10.33603/jnpm.v4i2.3386

Setiawan, Y. E. (2020). Analisis kesalahan siswa dalam menilai kebenaran suatu pernyataan [Analysis of student errors in assessing the truth of a statement]. Jurnal Didaktik Matematika, 7(1), 13-31. https://doi.org/10.24815/jdm.v7i1.14495

Setiawan, Y. E. (2020). Disposisi Berpikir [Thinking Disposition]. CV. Al-Mukmin Yes.

Setiawan, Y. E. (2020). Proses berpikir siswa dalam memperbaiki kesalahan generalisasi pola linier [Students' thinking process in correcting linear pattern generalization errors]. Mosharafa: Jurnal Pendidikan Matematika, 9(3), 371-382. https://doi.org/10.31980/mosharafa.v9i3.751

Setiawan, Y. E. (2020). The thinking process of students using trial and error strategies in generalizing linear patterns. Numerical: Jurnal Matematika dan Pendidikan Matematika, 4(1), 1-12. https://doi.org/10.25217/numerical.v4i1.839

Setiawan, Y. E. (2021). Analisis kesalahan mahasiswa semester pertama dalam menentukan nilai fungsi trigonometri sudut istimewa [Analysis of first-semester student errors in determining the value of special angle trigonometric functions]. Supremum Journal of Mathematics Education, 5(1), 110-121. https://doi.org/10.35706/sjme.v5i1.4531

Setiawan, Y. E., Purwanto, Parta, I. N., & Sisworo. (2020). Generalization strategy of linear patterns from field-dependent cognitive style. Journal on Mathematics Education, 11(1), 77-94. https://doi.org/10.22342/jme.11.1.9134.77-94

Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International journal of STEM education, 2, 1-16. https://doi.org/10.1186/s40594-015-0029-5

Tishman, S., & Andrade, A. (1995). Thinking dispositions : A review of current theories, practices, and issues. Harvard University Graduate School of Education.

Tishman, S., Jay, E., & Perkins, D. N. (1993). Teaching thinking dispositions : From transmission to enculturation. Theory Into Practice, 32(3), 147-153. https://doi.org/10.1080/00405849309543590

Trigueros, M., & Martínez-planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73, 3-19. https://doi.org/10.1007/s10649-009-9201-5

Tuna, A. (2013). A conceptual analysis of the knowledge of prospective mathematics teachers about degree and radian. Word Journal of Education, 3(4), 1-9. https://doi.org/10.5430/wje.v3n4p1

Usman, M. a. H., & Hussaini, M. M. (2017). Analysis of students’ error in learning of trigonometry among senior secondary school students in Zaria Metropolis, Nigeria. IOSR Journal of Mathematics, 13(2), 01-04. https://doi.org/10.9790/5728-1302040104

Wongapiwatkul, P., & Laosinchai, P. (2011). Enhancing conceptual understanding of trigonometry using earth geometry and the great circle. Australian Senior Mathematics Journal, 25(1), 54-64.




DOI: https://doi.org/10.22460/infinity.v11i1.p55-76

Article Metrics

Abstract view : 216 times
PDF - 101 times

Refbacks

  • There are currently no refbacks.




Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.