Analisis Kesalahan Pemodelan Matematika Siswa SMK dalam Menyelesaikan Masalah Kontekstual Ditinjau dari Kemampuan Matematika

Abstract

The low mathematical modeling ability of vocational high school students is an issue that needs special attention, especially regarding the errors that occur at each stage of mathematical modeling. This study aims to describe the mathematical modeling errors of high, medium, and low-ability vocational high school students in solving contextual problems on arithmetic sequences and series. This study is a descriptive study with a qualitative approach conducted in the even semester of the 2025/2026 academic year. The research subjects consisted of three 10th grade vocational high school students, each representing high, medium, and low mathematical abilities, selected based on the results of a mathematical ability test using purposive sampling techniques. Data were collected through mathematics ability tests, problem-solving assignments, and in-depth interviews. Data analysis used seven indicators of mathematical modeling stage errors adapted from Blum and Kaiser, Ndii, Lutvaidah, and Masfiyah and Shodikin. The results of the study show that high-ability student demonstrate excellent mastery of almost all stages of modeling and do not make procedural errors. However, at the stage of making modeling assumptions, they have not yet demonstrated an explicit conceptual understanding of the limitations of mathematical models. Student with average abilities completed all stages with correct models and final answers without substantive errors, but their conceptual understanding of modeling assumptions was not yet fully in-depth. Low-ability student made errors in several indicators, particularly in the use of variables, making assumptions, and accuracy in calculations, although they were still able to determine the month of target achievement. These findings indicate that differences in ability levels affect the depth of conceptual understanding and the systematic nature of students' mathematical modeling processes.