Penalaran Matematis Siswa SMK dalam Memecahkan Masalah Perbandingan Trigonometri

I’im Fatimah, I Made Sulandra, Gatot Muhsetyo

Abstract


Abstract: The reasoning abilities of Vocational students are still low. This qualitative study describes student’s mathematical reasoning in solving problems based on Polya's steps. The subjects were three students, high (ST), medium (SS), and low (SR). Research was conducted by analyzing the work results subjects and interviews. Research shows that Understanding problems, subjects analysed problem:ST, SS, SR revealed problem information; ST was relevant in representing triangles, SS, SR; ST identified tangen, SS, SR sine rule. Planning, subjects connected the trigonometric comparison. Implementing plans, subjects applied strategies:ST used procedure by setting the solution step and the correct calculation, SS, SR incorrect; ST, SS reviewed strategies by checking the calculation/formulas, SR not. Looking back, subjects reflected the solution:ST, SS did not write the conclusion and considered the fairness of the solution, SR not.

Abstrak: Kemampuan penalaran siswa SMK masih rendah. Penelitian kualitatif ini mendeskripsikan penalaran matematis siswa dalam memecahkan masalah, berdasarkan langkah Polya.Subjek penelitian tiga siswa yaitu berkemampuan tinggi (ST), sedang (SS), dan rendah (SR). Penelitian dilakukan dengan menganalisis hasil pekerjaan siswa dan wawancara. Penelitian menunjukkan bahwa saat memahami masalah, ketiga subjek menganalisis masalah ST, SS, SR mengungkapkan informasi masalah; ST relevan dalam merepresentasikan segitiga, SS, SR tidak; ST mengidentifikasi konsep trigonometri tangen, SS, SR aturan sinus. Ketika merencanakan,ketiga subjek mengoneksikan perbandingan trigonometri.Ketika melaksanakan rencana, ketiga subjek menerapkan strategi: ST menggunakan prosedur dengan mengatur langkah solusi terarah dan perhitungan tepat, SS, SR tidak tepat; ST, SS meninjau strategi dengan mengecek perhitungan/rumus,SR tidak.Ketika memeriksa kembali, ketiga subjek merefleksikan solusi: ST, SS tidak menuliskan kesimpulan; ST, SS mempertimbangkan kewajaran solusi, SR tidak.

Keywords


mathematical reasoning; solve the problem; trigonometric comparison; penalaran matematis; memecahkan masalah; perbandingan trigonometri

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References


Durmus, S. (2004). Matematikte Öğrenme Güçlüklerinin Saptanmasi Üzerine bir Çalişma. Kastamonu Eğitim Dergisi, 125.

Hodgson, T. R. (1995). Connections as Problem-Solving Tools. Connecting Mathematics across the Curriculum, 13–21.

Krulik, S., Rudnick, J. A., & Milou, E. (2003). Teaching Mathematics in Middle School: A Practical Guide. Allyn and Bacon.

Lithner, J. (2008). A Research Framework for Creative and Imitative Reasoning. Educational Studies in Mathematics, 67(3), 255–276.

Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers Promoting Student Mathematical Reasoning. Investigations in Mathematics Learning, 7(2), 1–20.

Musdhalifah, U. (2013). Analisis Kesalahan Siswa Kelas VII dalam Memecahkan Masalah Non Rutin yang Terkait dengan Bilangan Bulat Berdasarkan Tingkat Kemampuan Matematika di SMPN 31 Surabaya. MATHEdunesa, 2(3).

Musser, G., Burger, W., & Peterson, B. (2011). Mathematics for Elementary Teacher a Contemporary Approach. Danvers, MA: PreMedia Global.

Musser, G. L., & Burger, W. F. (1991). Mathematics for Elementary Teachers: A Contemporary Approach. MacMillan Publishing Company.

Mustangin, M. (2015). Representasi Konsep dan Peranannya dalam Pembelajaran Matematika di Sekolah. JPM: Jurnal Pendidikan Matematika, 1(1), 15–21.

NCTM. (2010). Why Is Teaching with Problem Solving Important to Student Learning?

Nurhajati, N. (2014). Pengaruh Penerapan Pendekatan Konstruktivisme dengan Model Pembelajaran Kooperatif Berbantuan Program Cabri 3D terhadap Kemampuan Penalaran dan Koneksi Matematis Siswa SMA di Kota Tasikmalaya. Jurnal Pendidikan dan Keguruan, 1(1).

Safrida, L. N., As’ari, A. R., & Sisworo. (2016). Pengembangan Perangkat Pembelajaran Berbasis Problem Solving Polya untuk Meningkatkan Kemampuan Penalaran Matematis Siswa Materi Peluang Kelas XI SMA. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 1(4), 583–591.

Saglam, Z., Sevim, M., Yurtseven, T., Oguz, T., Yildirim, Y., & Saglam, A. (2007). Matematik 10. Sinif Ders Kitabi. Istanbul: Rotamat Basim.

Shadiq, F., Mustajab, M., & Amini, N. (2011). Penerapan Teori Belajar dalam Pembelajaran Matematika di SD. Yogyakarta.

Suriasumantri, J. (2001). Filsafat Ilmu. Jakarta: Pustaka Sinar Harapan.

Tatar, E., Okur, M., & Tuna, A. (2008). A Study to Determine Learning Difficulties in Secondary Mathematics Education. Kastamonu Education Journal, 16(2), 507–516.

Tuna, A. (2013). A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian. World Journal of Education, 3(4), 1–9.

Widodo, S. A. (2013). Analisis Kesalahan Dalam Pemecahan Masalah Divergensi Tipe Membuktikan pada Mahasiswa Matematika. Jurnal Pendidikan dan Pengajaran, 46(2).




DOI: http://dx.doi.org/10.17977/jptpp.v4i8.12672

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JPtpp is accredited “Rank 2” as a scientific journal under the decree of the Directorate General of Research Enhancement and Development, Ministry of Research, Technology, and Higher Education, dated October 24, 2018, No: 30/E/KPT/2018, effective for five years from Volume 3 Issue 1, 2018 until Volume 7 Issue 8, 2022.


Jurnal Pendidikan: Teori, Penelitian, & Pengembangan

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