Error analysis of vocational students in solving linear equation problems

Abstract

Difficulties in understanding algebraic concepts often lead vocational high school students to make systematic errors in solving linear-equation problems. This study analyzes the types and causes of students’ errors in solving One-Variable Linear Equations (PLSV) and Two-Variable Linear Equation Systems (SPLDV). A qualitative descriptive design was used with purposive sampling involving 25 tenth-grade Fashion Design students at SMKN 6 Palembang who had completed introductory algebra units. Instruments consisted of six problem-solving items on PLSV and SPLDV; their content validity was established through expert review and pilot testing, followed by item refinement. Data were analyzed using Miles and Huberman’s interactive model with a predefined coding scheme developed from literature-based error categories. The analysis included error identification, code assignment, category confirmation through coder agreement checks, data display, and conclusion drawing. Five dominant error types emerged: (1) equation-manipulation errors rooted in procedural “transposing” without conceptual grounding, (2) misapplication of the distributive property and negative signs, (3) modeling errors when translating word problems, (4) integer-operation errors, and (5) failure to connect results to context. The findings show intertwined conceptual and procedural difficulties. Practical implications include structured learning sequences in which teachers first build conceptual schemas through visual representations, then guide students in modeling real-world scenarios using modeling templates, and finally implement reflective routines such as error-analysis sheets and justification prompts to consolidate understanding and reduce algebraic errors.