Students’ Mathematical Reasoning Skills in Solving Mathematical Problems

Authors

  • Christine Iriane Gultom Universitas Sebelas Maret
  • Triyanto FKIP Matematika, Universitas Sebelas Maret, Surakarta, Indonesia
  • Dewi Retno Sari Saputro FMIPA Matematika, Universitas Sebelas Maret, Surakarta, Indonesia

DOI:

https://doi.org/10.23887/jpiundiksha.v11i3.42073

Keywords:

mathematical reasoning, mathematic problems, problems solving

Abstract

Mathematical material will be easily understood through reasoning and that reasoning skills can be trained through mathematics learning. However, there are still many students who do not have good reasoning skills. This study aims to analyses the mathematical reasoning skills of class XI students of Senior High School on trigonometry in solving mathematical problems. This research is a qualitative descriptive study. The participants of this study were 2 students, namely student 1 (S1) and student 2 (S2) who were selected by purposive sampling. The instruments used to explore this mathematical reasoning skill were written tests and interviews. Triangulation method was employed to validate the data. The results showed that S1 was able to meet the reasoning indicator in proposing conjectures, predicting the answers and the solution process, performing mathematical manipulation and concluding sentences at the end of a completion. S2 was able to meet the reasoning indicator in proposing conjectures and predicting the answers and the solution process. However, S2 was less capable in performing mathematical manipulation and less capable concluding sentences at the end of a completion.

References

Adamura, F., & Susanti, V. D. (2018). Penalaran Matematis Mahasiswa Dalam Memecahkan Masalah Analisis Real Berdasarkan Kemampuan Berpikir Intuitif. Journal of Mathematics and Mathematics Education, 8(2), 156–172. https://doi.org/10.20961/jmme.v8i2.25852.

Albay, E. M. (2019). Analyzing the effects of the problem solving approach to the performance and attitude of first year university students. Social Sciences & Humanities Open, 1(1), 100006. https://doi.org/10.1016/j.ssaho.2019.100006.

Aminah, & Kurniawati, K. R. A. (2018). Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Cerita. Jurnal Teori Dan Aplikasi Matematika, 2(2), 118–122. https://doi.org/10.31764/jtam.v2i2.713.

Christina, E. N., & Adirakasiwi, A. G. (2021). Analisis Kemampuan Pemecahan Masalah Tahapan Polya dalam Menyelesaikan Persamaan dan Pertidaksamaan Linear Satu Variabel. Jurnal Pembelajaran Matematika Inovatif, 4(2), 405–424. https://doi.org/10.22460/jpmi.v4i2.405-424.

Creswell, J. W. (2013). Qualitative Inquiry & Research Design: Choosing among Five Approaches (3rd ed). Sage.

Diniyah, A. N., Akbar, P., Nurjaman, A., & Bernard, M. (2018). Analisis Kemampuan Kemampuan Penalaran Dan Self Confidence Siswa Sma Dalam Materi Peluang. Journal On Education, 1(1), 14–21. https://doi.org/10.31004/joe.v1i1.5.

Djam’An, N., Bernard, & Sahid. (2021). Developing Students’ Creativity in Building City Mathematics through Project Based Learning. Journal of Physics: Conference Series, 1899(1), 267–274. https://doi.org/10.1088/1742-6596/1899/1/012147.

Effendi, L. A. (2012). Pembelajaran Matematika dengan Metode Penemuan Terbimbing Untuk Meningkatkan Kemampuan Representasi dan Pemecahan Masalah Matematis Siswa SMP. Jurnal Penelitian Pendidikan, 13(2), 1–10. http://jurnal.upi.edu/file/Leo_Adhar.pdf.

Fatimah, I., Sulandra, I. M., & Muhsetyo, G. (2019). Penalaran Matematis Siswa SMK dalam Memecahkan Masalah Perbandingan Trigonometri. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(8), 1043. https://doi.org/10.17977/jptpp.v4i8.12672.

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15, 105–123. https://doi.org/10.1007/s10763-017-9814-6.

Hidayah, I. R., Kusmayadi, T. A., & Fitriana, L. (2021). Minimum Competency Assessment (AKM): An Effort To Photograph Numeracy. Journal of Mathematics and Mathematics Education, 11(1), 14–20. https://doi.org/10.20961/jmme.v11i1.52742.

Izzah, K. H., & Azizah, M. (2019). Analisis Kemampuan Penalaran Siswa Dalam Pemecahan Masalah Matematika Siswa Kelas IV. Indonesian Journal Of Educational Research and Review, 2(2), 210. https://doi.org/10.23887/ijerr.v2i2.17629.

Kadarisma, G., Nurjaman, A., Sari, I. P., & Amelia, R. (2019). Gender and mathematical reasoning ability. Journal of Physics: Conference Series, 1157(4). https://doi.org/10.1088/1742-6596/1157/4/042109.

Kurniawati, L., Miftah, R., & Indriani, R. (2021). Improving students’ mathematical inductive reasoning ability through reflective learning Model. Journal of Physics: Conference Series, 1836(1). https://doi.org/10.1088/1742-6596/1836/1/012071.

Lara-Porras, A. M., Rueda-García, M. D. M., & Molina-Muñoz, D. (2019). Identifying the factors influencing mathematical literacy in several Spanish regions. South African Journal of Education, 39, 1–13. https://doi.org/10.15700/saje.v39ns2a1630.

Lemmer, M., Kriek, J., & Erasmus, B. (2020). Analysis of Students’ Conceptions of Basic Magnetism from a Complex Systems Perspective. Research in Science Education, 50(2), 375–392. https://doi.org/10.1007/s11165-018-9693-z.

Lestary, R., Subanji, & Rahardi, R. (2019). An analysis of students’ mathematical reasoning ability in statistic problem solving based on structure of the observed learning outcome taxonomy. Journal of Physics: Conference Series, 1320(1). https://doi.org/10.1088/1742-6596/1320/1/012055.

Mayer, I. (2015). Qualitative research with a focus on qualitative data analysis. International Journal of Sales, Retailing & Marketing, 4(9), 53–67. https://www.circleinternational.co.uk/wp-content/uploads/2021/01/IJSRM4-9.pdf#page=57.

Musdhalifah, U., Sutinah, & Kurniasari, I. (2013). Analisis Kesalahan Siswa Kelas VII dalam Memecahkan Masalah Non Rutin yang Terkait dengan Bilangan Bulat Berdasarkan Tingkat Kemampuan matematika di SMP N 31 Surabaya. Jurnal Mahasiswa Universitas Negeri Surabaya, 1(1), 1–6. https://jurnalmahasiswa.unesa.ac.id/index.php/3/article/view/3905.

Musser, G. L., Peterson, B. E., & Burger, W. F. (2011). Mathematics For Elementary Teachers. National Council of Teachers of Mathematics.

Mustangin, M. (2015). Representasi Konsep Dan Peranannya Dalam Pembelajaran Matematika Di Sekolah. JPM : Jurnal Pendidikan Matematika, 1(1), 15. https://doi.org/10.33474/jpm.v1i1.405.

Novitasari, P., Usodo, B., & Fitriana, L. (2021). Visual, Symbolic, and Verbal Mathematics Representation Abilities in Junior High School’s Students. IOP Conference Series: Earth and Environmental Science, 1808(1). https://doi.org/10.1088/1742-6596/1808/1/012046.

Prajono, R., Rahmat, Maryanti, E., & Salim. (2021). Kemampuan Penalaran Matematis Siswa Ditinjau dari Gender. JNPM (Jurnal Nasional Pendidikan Matematika), 5(2), 208–218. https://doi.org/10.33603/jnpm.v5i2.3641.

Pratiwi, I. (2019). Efek Program Pisa Terhadap Kurikulum Di Indonesia. Jurnal Pendidikan Dan Kebudayaan, 4(1), 51. https://doi.org/10.24832/jpnk.v4i1.1157.

Rahmawati, D., & Permata, L. D. (2018). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Program Linear Dengan Prosedur Newman. Jurnal Elektronik Pembelajaran Matematika, 5(2), 173–185. https://jurnal.uns.ac.id/jpm/article/view/26050.

Sadieda, L. U. (2019). Kemampuan argumentasi mahasiswa melalui model berpikir induktif dengan metode probing-prompting learning. Pythagoras: Jurnal Pendidikan Matematika, 14(1), 23–32. https://doi.org/10.21831/pg.v14i1.24038.

Shadiq, F., & Mustajab, N. A. (2011). Penerapan Teori Belajar dalam Pembelajaran Matematika di SD. Pusat Pengembangan dan Pemberdayaan Pendidik dan Tenaga Kependidikan Matematika.

Smieskova, E. (2017). Communication Students’ Skills as a Tool of Development Creativity and Motivation in Geometry. Universal Journal of Educational Research, 5(1), 31–35. https://doi.org/10.13189/ujer.2017.050104.

Sumarsih, S., Budiyono, B., & Indriati, D. (2018). Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking. Journal of Physics: Conference Series, 1008(1). https://doi.org/10.1088/1742-6596/1008/1/012078.

Sumartini, T. S. (2015). Peningkatan Kemampuan Penalaran Matematis Siswa Melalui Pembelajaran Berbasis Masalah. Jurnal Pendidikan Matematika, 5(1), 1–10. https://journal.institutpendidikan.ac.id/index.php/mosharafa/article/view/mv4n1_1.

Supriadi, N., Man, Y. L., Pirma, F. O., Lestari, N. L., Sugiharta, I., & Netriwati. (2021). Mathematical reasoning ability in linear equations with two variables: The impact of flipped classroom. IOP Conference Series: Earth and Environmental Science, 1796(1). https://doi.org/10.1088/1742-6596/1796/1/012022.

Umbara, U., & Suryadi, D. (2019). Re-Interpretation of Mathematical Literacy Based on The Teacher’s Perspective. International Journal of Instruction, 12(4), 789–806. https://doi.org/10.29333/iji.2019.12450a.

Usman, M. 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(02), 01–04. https://doi.org/10.9790/5728-1302040104.

Wahyuni, E. S., Susanto, & Hadi, A. F. (2019). Profile of the student’s mathematical reasoning ability in solving geometry problem. Journal of Physics: Conference Series, 1211(1). https://doi.org/10.1088/1742-6596/1211/1/012079.

Wahyuni, N. S., & Widayanti, E. (2020). Students’ Errors Analysis in Finishing A Problem Solving Test Based on Newman Procedures in Trigonometry Materials. IndoMath: Indonesia Mathematics Education, 3(2), 78–87. https://doi.org/10.30738/indomath.v3i2.7213.

Wati, M. K., & Sujadi, A. A. (2017). Analisis Kesalahan Dalam Menyelesaikan Masalah Matematika Dengan Menggunakan Langkah Polya Siswa Kelas Vii Smp. Jurnal PRISMA Universitas Suryakancana, 6(1), 9–16. https://doi.org/10.35194/jp.v6i1.24.

Wijaya, C. B. (2018). Analisis Kemampuan Representasi Matematis Siswa Dalam Menyelesaikan Soal Lingkaran Pada Kelas VII-B Mts Assyafi’iyah Gondang. Suska Journal of Mathematics Education, 4(2), 115–124. https://doi.org/10.24014/sjme.v4i2.5234.

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Published

2022-09-04

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