ANALYSIS OF STUDENTS' PROCEDURAL ERRORS IN SOLVING GEOMETRIC TRANSFORMATION PROBLEMS BASED ON PROCEDURAL FLUENCY

Abstract

This study aims to analyze students' procedural errors in solving geometric transformation problems based on Kilpatrick's (2001) indicators of procedural fluency, which include accuracy, efficiency, and flexibility. The approach used is qualitative descriptive with quantitative data support. The research subjects were 32 tenth-grade students at a private high school in Medan who had studied geometric transformation material. Data collection was conducted through a 5-question essay test analyzed using a scoring rubric for each indicator of procedural fluency. The results showed that the average student procedural fluency ability was in the low category with a score of 0.84 on a 4.00 scale. A total of 64.29% of students were in the very low category, 25% in the low category, 7.14% in the moderate category, and only 3.57% in the high category. The flexibility indicator was the weakest, with an average score of 0.39 (very low), while accuracy and efficiency were 0.95 (low) each. The dominant errors in accuracy included errors in basic concepts (78.6%), formula substitution (67.9%), and algebraic operations (64.3%). In terms of efficiency, students tended to repeat steps (71.4%) and use overly long procedures (67.9%). Regarding flexibility, 96.4% of students used only one method of solution, and 89.3% were unable to write down the transformation matrix. These findings indicate the need for instruction that places greater emphasis on procedural flexibility and reinforces conceptual understanding.

ABSTRAK

Penelitian ini bertujuan untuk menganalisis kesalahan prosedural siswa dalam menyelesaikan masalah transformasi geometri berdasarkan indikator kelancaran prosedural dari Kilpatrick (2001), yaitu akurasi, efisiensi, dan fleksibilitas. Pendekatan yang digunakan adalah deskriptif kualitatif dengan dukungan data kuantitatif. Subjek penelitian adalah 32 siswa kelas X di salah satu SMA swasta di Medan yang telah mempelajari materi transformasi geometri. Pengumpulan data dilakukan melalui tes esai sebanyak 5 soal yang dianalisis menggunakan rubrik penilaian untuk setiap indikator kelancaran prosedural. Hasil penelitian menunjukkan bahwa rata-rata kemampuan kelancaran prosedural siswa berada pada kategori rendah dengan skor 0,84 dari skala 4,00. Sebanyak 64,29% siswa berada pada kategori sangat rendah, 25% pada kategori rendah, 7,14% pada kategori sedang, dan hanya 3,57% pada kategori tinggi. Indikator fleksibilitas merupakan yang terlemah dengan rata-rata skor 0,39 (sangat rendah), sedangkan akurasi dan efisiensi masing-masing sebesar 0,95 (rendah). Kesalahan dominan pada akurasi meliputi kesalahan konsep dasar (78,6%), substitusi rumus (67,9%), dan operasi aljabar (64,3%). Pada efisiensi, siswa cenderung mengulang langkah (71,4%) dan menggunakan prosedur yang terlalu panjang (67,9%). Pada fleksibilitas, 96,4% siswa hanya menggunakan satu metode penyelesaian dan 89,3% tidak dapat menuliskan matriks transformasi. Temuan ini menunjukkan perlunya pembelajaran yang lebih menekankan pada fleksibilitas prosedural dan memperkuat pemahaman konseptual.