IDENTIFYING STUDENTS’ DIFFICULTIES IN UNDERSTANDING AND APPLYING PYTHAGOREAN THEOREM WITH AN ONTO-SEMIOTIC APPROACH

  • Rudi Rudi SPS Pendidikan Matematika Universitas Pendidikan Indonesia, LPMP Sulawesi Selatan
    (ID)
  • Didi Suryadi Universitas Pendidikan Indonesia
    (ID)
  • Rizky Rosjanuardi Universitas Pendidikan Indonesia
    (ID)

Abstract

Abstract:

This research is conducted to obtain a description of students’ difficulties in understanding and applying Pythagorean theorem based on the onto-semiotic approach. This research applies a qualitative approach with phenomenology interpretation design. Research data were collected using test and interview methods. The research result was deducted from students' answer sheets and interviews. Participants involved in this study were as many as 25 students of UPI Lab School Junior High School Bandung, who had learned Pythagorean theorem, 4 of which also participated in the interview. It showed that students found it complicated to comprehend definition, describe symbols or notations of mathematical objects, and interpret mathematical objects. Meanwhile, in solving problems related to the application of the Pythagorean theorem, students could describe procedure, algorithm, and technique in solving questions well.

Abstrak:

Penelitian ini bertujuan untuk mendapatkan gambaran kesulitan siswa dalam memahami dan menerapkan Teorema Pythagoras menggunakan pendekatan onto-semiotika. Penelitian ini menggunakan pendekatan kualitatif dengan desain interpretasi fenomenologi. Metode pengumpulan data, yaitu tes dan wawancara. Partisipan penelitian yang dilibatkan dalam uji kemampuan siswa adalah 25 orang siswa SMP Lab School UPI Bandung yang pernah belajar materi teorema Pythagoras, 4 orang dari 25 orang siswa tersebut dilibatkan dalam wawancara. Hasil penelitian menunjukkan bahwa siswa mengalami kesulitan dalam memahami definisi, mendeskripsikan simbol atau notasi dari objek matematika, serta kesulitan dalam memaknai objek matematika, sedangkan dalam menyelesaikan permasalahan penerapan teorema Pythagoras, siswa mampu mendeskripsikan prosedur, algoritma, dan teknik penyelesaikan masalah dengan baik.

Downloads

Download data is not yet available.

References

Ahmady, G., & Ruhi, N. N. (2016). Impact of promoting whole-class discussions in geometry instruction on students' reasoning ability. International Journal of Humanities and Cultural Studies (IJHCS) ISSN 2356-5926, 1(1), 2079-2092. Retrieved from http://www.ijhcs.com /index.php/ijhcs/ article/view/1792.

Alfian, H., Sugiatno, & Hamdani. (2016). Mengatasi hambatan pemahaman konseptual matematis dengan pendekatan antisipasi didaktis materi dalil Pythagoras di SMP. Jurnal Pendidikan dan Pembelajaran Khatulistiwa, 6(1), 1-16. Retrieved from https://jurnal.untan.ac.id/index. php/jpdpb/article/view/18108.

Al-Khateeb, M. A. (2016). The extent of mathematics teacher's awareness of their students' misconceptions in learning geometrical concepts in the intermediate education stage. European Scientific Journal, ESJ, 12(31), 357-372. https://doi.org/ 10.19044/esj.2016.v12n31p357.

Amin, M. E. I. A., Juniati, D., & Sulaiman, R. (2018). Onto semiotic approach to analyze students' understanding of algebra based on math ability. In AIP Conference Proceedings, 2014(1), 020077. AIP Publishing. https://aip. scitation.org/doi/pdf/10.1063/1.5054481.

Anggraini, G. R., & Ariyanto, A. (2017). Analisis kesulitan pemahaman konsep pada materi Pythagoras di kelas VIII SMP Negeri 3 Kartasura. Paper Presented at Prosiding SEMPOA (Seminar Nasional, Pameran Alat Peraga, dan Olimpiade Matematika) 3 2017. http://hdl.handle.net/ 11617/8795.

Arifin, M. (2018). Profil implementasi elpsa framework dalam meningkatkan pemahaman konsep siswa tentang teorema Pythagoras. In ELPSA Conference II, 1(1). Retrieved from http://elpsa.org/proceeding/index. php/ec18/article/view/55.

Anwar, R. B., & Rahmawati, D. (2017). Symbolic and verbal representation process of student in solving mathematics problem based Polya's stages. International Education Studies, 10(10), 20-28. https://doi.org/ 10.5539/ies.v10n10p20.

Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational studies in mathematics, 85(2), 221-239. Retrieved from https://link.springer.com/article/10.1007/s10649-013-9507-1.

Celik, A. O., & Guzel, E. B. (2017). Mathematics teachers' knowledge of student thinking and its evidences in their instruction. Journal on Mathematics Education, 8(2), 199-210. http:/doi.org/10.22342/jme.8.2. 4144.199-210.

Cresswell, J. W. (2014). Penelitian kualitatif & desain riset. Yogyakarta: Pustaka Pelajar.

Dundar, S. (2015). Mathematics teacher-candidates performance in solving problem with different representation style: The trigonometry example. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1379-1397. https://doi.org/10.12973/eurasia. 2015.1396a.

Etikan, I., Musa, S. A., & Alkassim, R. S. (2016). Comparison of convenience sampling and purposive sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1-4. https://doi.org/10.11648/j.ajtas.20160501.11.

Font, V., Godino, J. D., & D'Amore, B. (2007). An onto-semiotic approach to representations in mathematics education. For the learning of mathematics, 27(2), 2-14. Retrieved from http://www.dm.unibo.it/ rsddm/it articoli/damore/17%20%202007% 20FLM.pdf

Godino, J. D., Batanero, C., & Roa, R. (2005) 'An onto-semiotic analysis of combinatorial problems and the solving processes by university students,' Educational Studies in Mathematics, 60(1). https://doi.org/ 10.1007/s10649-005-5893-3.

Godino, J., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. Zentralblatt für Didaktik der Mathematik, 39, 127–135. https://doi.org/10.1007/s11858-006- 0004-1.

Guner, N. (2018). How to teach the pythagorean theorem: An analysis of lesson plans. Ankara University Journal of Faculty of Educational Sciences, 51(1), 119-141. https://doi.org/10.30964/auebfd.405041.

Ham, V. D. A. K., & Heinze, A. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students' achievement in mathematics. Studies in Educational Evaluation, 59, 133-140. https://doi.org/10.1016/j.stueduc.2018.07.005.

Hutapea, M. L., Suryadi, D., & Nurlaelah, E. (2015). Analysis of students' epistemological obstacles on the subject of pythagorean theorem. Jurnal Pengajaran MIPA, 20(1), 1-10. http://doi.org/10.18269/jpmipa. v20i1.555.

Ishartono, N., Nurcahyo, A., & Setyono, I. D. (2019). Guided discovery: An alternative teaching method to reduce students' rote learning behavior in studying geometric transformation. Journal of Physics: Conference Series, 1265(1), 012019. IOP Publishing. Retrieved from https:// iopscience.iop.org/article/10.1088/1742-6596/1265/1/012019/meta.

Iori, M. (2017). Objects, signs, and representations in the semio-cognitive analysis of the processes involved in teaching and learning mathematics: A Duvalian perspective. Educational Studies in Mathematics, 94(3), 275-291. https://doi.org/10.1007/s10649-016-9726-3.

Li, Y., Zhang, M., Chen, Y., Deng, Z., Zhu, X., & Yan, S. (2018). Children's non-symbolic and symbolic numerical representations and their associations with mathematical ability. Frontiers in Psychology, 9, 1035. https:// doi.org/10.3389/fpsyg.2018.01035.

Maor, E. (2019). The Pythagorean theorem: A 4,000-year history. Princeton University Press. Retrieved from https://books.google.co.id.

Miles, M. B., Huberman, A. M., & Saldana, J. (2018). Qualitative data analysis: A methods sourcebook, 4th Edition. Retrieved from https:// books.google. co.id.

Misbakhudin, M. (2018). Kemampuan representasi matematis siswa dalam menyelesaikan masalah teorema pythagoras ditinjau dari perbedaan gender kelas VIII di SMP Negeri 1 Ngadiluwih tahun ajaran 2017/2018. Thesis. Retrieved from http://repo.iain-tulungagung.ac.id/8877/7/ Bab%20IV .pdf.

Montiel, M., Wilhelmi, M. R., Vidakovic, D., & Elstak, I. (2009). Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educational Studies in Mathematics, 72(2), 139. https://doi.org/ 10.1007/s10649-009-9184-2.

Murphy, P. K., Alexander, P. A., Greene, J. A., & Hennessey, M. N. (2004). Examining epistemic frames in conceptual change research: Implications for learning and instruction. Asia Pacific Education Review, 13(3), 475-486. https://doi.org/10.1007/s12564-011-9199-0.

Niko, N., Wahyuni, R., & Nurhayati, N. (2018). Analisis kemampuan multi representasi matematis ditinjau dari motivasi belajar siswa pada materi teorema Phytagoras kelas IX SMP Negeri 12 Singkawang. Journal Of Educational Review and Research, 1(2), 92-99. Retrieved from https:// journal.stkipsingkawang.ac.idindex.php/JERR/article/view/1676.

Ojose, B. (2015). Students' misconceptions in mathematics: analysis of remedies and what research says. Ohio Journal of School Mathematics, 72, 30-34. Retrieved from https://kb.osu.edu/bitstream/handle/1811/78927/ OJSM_72_Fall2015_30.pdf?sequence=1.

Pino-Fan, L. R., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/eurasia.20151403a.

Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94. https://doi.org/10.1007/s10857-016-9349-8.

Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education (TOCE), 18(1), 1-24. https://doi.org/10.1145/ 3077618.

Robbia, D. F. (2013). Desain didaktis model problem solving pokok bahasan teorema pythagoras pada pembelajaran matematika untuk meningkatkan kompetensi matematis siswa. Thesis. Retrieved from http://reposi-tory.upi.edu/287.

Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students' mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014, 1-10. https://doi.org/10.5899/2014/metr-00051.

Sbaragli, S., Arrigo, G., D'Amore, B., Fandiño-Pinilla, M. I., Frapolli, A., Frigerio, D., & Villa, O. (2011). Epistemological and didactic obstacles: The influence of teachers' beliefs on the conceptual education of students. Mediterranean Journal for Research in Mathematics Education, 10, 61-102. Retrieved from http://repository.supsi.ch/3384/1/Sbaragli %20Arrigo%20et%20alpdf.

Villegas, J. L., Castro, E., & Gutierrez, J. (2009). Representation in problem solving: a case study with optimization problem. Electronic Journal of Research in Education Psychology, 17(7), 279-308. Retrieved from http://repositorio.ual.es/bitstream/handle/10835/713/Art_17_297_eng.pdf?sequence=1.

Zuya, H. E. (2014). Mathematics teachers" responses to students" misconceptions in algebra, International Journal of Research in Education Methodology, 6,(2), 830-836. Council for Educative Research. Retrieved from https://dspa-ce.unijos.edu.ng/jspui/bitstream/123456789/2450 /1/3880-Article%20Text-4405-2-10-20180104.pdf.

Zuya, E. H., & Kwalat, S. K. (2015). Teacher's knowledge of students about geometry. International Journal of Learning, Teaching and Educational Research, 13(3), 100-114. Retrieved from http://mail.ijlter.org/index.php /ijlter/ article/view/ 438.

Published
2020-06-29
Section
Vol. 8 No. 1
Abstract viewed = 2049 times