Exploration of Vocational Students’ Mathematical Understanding: A Case Study on Trigonometric Ratios

Irmawati Liliana Kusuma Dewi; Cita Dwi Rosita; Muchamad Subali Noto; Farhan Ferdiansyah

doi:10.31980/mosharafa.v14i3.1901

Authors

Irmawati Liliana Kusuma Dewi Universitas Swadaya Gunung Jati
Cita Dwi Rosita Universitas Swadaya Gunung Jati
Muchamad Subali Noto Universitas Swadaya Gunung Jati
Farhan Ferdiansyah Universitas Swadaya Gunung Jati

DOI:

https://doi.org/10.31980/mosharafa.v14i3.1901

Keywords:

Mathematical Understanding, Trigonometry, Pemahaman Matematis, Siswa SMK, Studi Kasus Kualitatif, Trigonometri, Vocational High School Students, Qualitative Case Study

Abstract

Penelitian bertujuan mengeksplorasi kemampuan pemahaman matematis siswa Sekolah Menengah Kejuruan (SMK) pada materi perbandingan trigonometri. Penelitian menggunakan pendekatan kualitatif dengan metode studi kasus. Subjek penelitian yaitu tiga siswa SMK yang mewakili kategori kemampuan tinggi, sedang, dan rendah, dipilih secara purposive. Data dikumpulkan melalui tes dan wawancara semi-terstruktur. Hasil penelitian menunjukkan adanya profil pemahaman matematis yang berbeda pada setiap kategori kemampuan. Siswa berkemampuan tinggi mampu mengidentifikasi konsep trigonometri, menggunakan berbagai representasi, serta mengaitkan perbandingan trigonometri dengan bentuk simbolik dan kontekstual, meskipun masih ditemukan kelemahan pada penguasaan materi prasyarat aljabar. Siswa berkemampuan sedang umumnya mampu menyelesaikan soal rutin dan representasional, namun mengalami kebingungan konseptual dalam menentukan sudut acuan dan menafsirkan perbandingan trigonometri pada situasi non-rutin. Adapun siswa berkemampuan rendah menunjukkan pemahaman yang terfragmentasi, ditandai dengan kesulitan mengidentifikasi konsep yang relevan, menghubungkan informasi soal cerita dengan representasi segitiga siku-siku, serta menjelaskan alasan penyelesaian. Temuan ini mengindikasikan bahwa kesulitan siswa pada materi trigonometri tidak semata-mata bersifat prosedural, tetapi berkaitan erat dengan lemahnya pemahaman konseptual dan penguasaan materi prasyarat.

This study aims to explore vocational high school students’ mathematical understanding of trigonometric ratios. A qualitative case study approach was employed. The participants were three vocational students representing high, medium, and low achievement levels, purposively selected. Data were collected through test and semi-structured interviews. The results reveal distinctive profiles of mathematical understanding. High-achieving students were able to identify trigonometric concepts, use multiple representations, and flexibly relate trigonometric ratios to symbolic and contextual forms, although minor weaknesses in prerequisite algebraic knowledge were still evident. Medium-achieving students generally succeeded in routine and representational tasks but experienced conceptual confusion in determining reference angles and interpreting trigonometric ratios in non-routine situations. In contrast, low-achieving students exhibited fragmented understanding, characterized by difficulties in identifying relevant concepts, connecting word problem information to right triangle representations, and explaining their reasoning processes. These findings indicate that students’ difficulties in trigonometry are not merely procedural but are strongly related to conceptual understanding and prerequisite knowledge.

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