ANALISIS KESALAHAN MAHASISWA BERDASARKAN PROSEDUR NEWMAN DALAM MENYELESAIKAN SOAL ALJABAR LINEAR DASAR
DOI: https://doi.org/10.30605/9en8es65
Analisis kesalahan, Prosedur Newman, Aljabar linear, Vektor, Kesejajaran bidang
Abstract
Aljabar linear merupakan mata kuliah dasar bagi mahasiswa matematika, tetapi kesalahan pada materi determinan, vektor, dan bidang masih sering terjadi. Penelitian ini bertujuan mendeskripsikan jenis dan proporsi kesalahan mahasiswa dalam menyelesaikan soal Ujian Akhir Semester Aljabar Linear Dasar berdasarkan prosedur Newman. Penelitian menggunakan pendekatan deskriptif kualitatif yang didukung penghitungan persentase. Data berupa lembar jawaban tertulis 40 mahasiswa pada empat butir soal yang mencakup determinan matriks, komponen vektor, norma dan vektor satuan berlawanan arah, serta kesejajaran bidang. Setiap unit jawaban yang mengandung kesalahan dikodekan ke salah satu dari lima kategori Newman, yaitu membaca, memahami, transformasi, keterampilan proses, dan penulisan jawaban akhir. Hasil menunjukkan bahwa 17 dari 40 mahasiswa (42,5%) melakukan setidaknya satu kesalahan, dengan 32 unit jawaban yang mengandung kesalahan dari 320 unit jawaban (10,0%). Kesalahan transformasi paling dominan (50,0%), diikuti keterampilan proses (25,0%), pemahaman (15,6%), penulisan jawaban akhir (6,3%), dan membaca (3,1%). Kesalahan terbanyak terdapat pada penentuan vektor satuan berlawanan arah (20,0%) dan pemeriksaan kesejajaran bidang yang konstantanya berbeda (17,5%). Kesalahan tersebut umumnya berupa membalik arah vektor, tidak menyajikan vektor yang berlawanan arah, serta memasukkan konstanta ke dalam vektor normal. Selain itu, hanya satu mahasiswa yang menyebut keberimpitan pada pasangan bidang yang berimpit. Temuan ini menunjukkan perlunya penguatan pemaknaan geometris pada pembelajaran vektor dan bidang.
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