Analysis of errors produced by NCV-level 2 students when solving linear equations with fractional coefficients

There is growing concern and awareness of the low levels of mathematics achievement in the Technical Vocational Education and Training (TVET) sector. Students perform particularly poorly in algebra related activities. This study focuses on National Certificate Vocational (NCV) Level 2 students and the common errors they make when solving linear equations with fraction coefficients and the causes of these errors. Teachers should understand the conceptual difficulties students face when working with algebra and try to find ways to support their development. This is a qualitative case study that seeks to understand how students think and communicate when solving linear equations interpreted through the lens of Sfard’s (2008) commognitive theory. The research question is why do NCV Level 2 students perform poorly when solving linear equations with fractional coefficients. It involves the use of student errors to understand their cognitive and discursive processes. Data were collected from a written test containing twelve linear equations (with and without fractions) completed by all students and individual interviews with a select group of students, based on their errors, to probe their algebraic reasoning. Data analysis included: identifying incorrect responses, classifying error types, categorising error patterns, and interpreting the explanations of students through the commognitive lens. The findings show that the students had difficulty with conceptual, procedural, and operational errors, as well as inverse operations, fractional coefficients, and the concept of equality. The study contributes to growing research on mathematics learning in the TVET field and highlights what student discourse can show about their reasoning practices and misconceptions. Mathematics lecturers must encourage more algebraic discourse and interactions in classrooms to make use of different representations and teaching strategies, and promote error-based learning approaches. These findings have important consequences for teaching practice, curriculum, and teacher professional development which is aimed at building student conceptual understanding and problem-solving skills in algebra. One of recommendations for future research would be to have a larger and more diverse sample of NCV Level 2 mathematics students to better understand how students’ educational backgrounds might influence their conceptual understanding of linear equations with fraction coefficients