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Students’ Ways of Understanding and Ways of Thinking in Solving Trigonometric Problems
Abstract
Berpikir matematis sangat penting sebagai cara untuk mempelajari matematika. Menurut teori Harel istilah berpikir matematis tingkat lanjut berakar pada dua elemen pengetahuan: cara memahami (WoU) dan cara berpikir (WoT). Cara memahami mengacu pada bagaimana siswa menginterpretasikan suatu konsep tertentu dan hubungan antar konsep, memberikan solusi terhadap masalah, dan membenarkan apakah suatu keyakinan benar atau tidak, sedangkan cara berpikir adalah proses mental yang menghasilkan pemahaman siswa terhadap suatu hal. Tujuan dari penelitian ini adalah untuk menggambarkan cara siswa memahami dan berpikir dalam menyelesaikan masalah matematika yang terkait dengan trigonometri. Penelitian ini dilakukan di sebuah sekolah menengah atas di Jakarta Selatan, Indonesia. Subjek penelitian adalah siswa kelas 11 yang telah mempelajari tentang trigonometri. Data dikumpulkan dari instrumen tes yang terdiri dari tiga masalah matematika terkait trigonometri dan hasil wawancara. Analisis data dilakukan dengan tiga tahap, yaitu teknik reduksi, penyajian, dan penarikan simpulan. Hasil penelitian ini menunjukkan bahwa cara memahami dan cara berpikir siswa saling memengaruhi. Jadi, dalam masalah trigonometri ini, cara berpikir siswa memengaruhi pemahaman siswa terhadap konsep, dan sebaliknya pemahaman siswa terhadap konsep memengaruhi cara berpikir mereka.
Mathematical thinking is essential as a way of learning mathematics. According to Harel’s theory in defining the term advanced mathematical thinking, it is rooted in two pieces of knowledge: ways of understanding (WoU) and ways of thinking (WoT). Ways of understanding refer to how students interpret a particular concept and the relationship between concepts, give solutions to a problem, and justify whether a belief is true or not, while ways of thinking are a mental process that results in students’ understanding of a particular thing. The purpose of this research is to describe students’ ways of understanding and ways of thinking in solving mathematical problems related to trigonometry. The research was conducted at a senior high school in Jakarta Selatan, Indonesia. The subjects of the research were the students grade 11 who has learned trigonometry. The data were collected from the test instruments consisting of three mathematical problems related to trigonometry and interview transcript. The data analysis used in this research are reduction techniques, presentation, and drawing conclusions. The result of this research showed that students’ ways of understanding and ways of thinking influenced each other. So, in this trigonometry problem, students’ ways of thinking influence the students’ understanding of the concepts, and likewise students’ understanding of the concepts affects their ways of thinking.
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DOI: http://doi.org/10.25273/jipm.v12i2.18833
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