Pre-service mathematics teachers' relational understanding in solving special cases of systems of linear equations in two variables - David Pratama; Septiani Yugni Maudy; Warissara Audjam (UNION : Jurnal Ilmiah Pendidikan Matematika, 2026)
This study aims to describe the profile of Pre-service Mathematics Teachers' relational understanding in solving special cases of Systems of Linear Equations in Two Variables (SLETV) and to identify the factors underlying the emergence of cognitive impasse during the solving process. Using a qualitative method with a case study approach, the research was conducted on two final-year students at a state university in Karawang through whiteboard observations and unstructured clinical interviews during a comprehensive examination. The findings reveal that while students are proficient in solving routine problems with a single solution, they face a complete standstill when variables are entirely eliminated, such as in 0 = 0 or 0 = c results. Students tend to memorize technical steps without understanding the logical meaning behind the "disappearing variables". The primary factors for this confusion are low sensitivity to mathematical symbols and a reliance on mechanical self-learning from digital media. Although limited to two participants, this study highlights that pre-service teacher who only master technical procedures risk avoiding deeper conceptual teaching in future classrooms. This study concludes that a strong dominance of procedural fluency without relational understanding leads to cognitive impasse when students encounter non-typical algebraic structures. The contribution of this study lies in providing empirical evidence on the gap between procedural mastery and conceptual meaning-making among pre-service teachers, as well as offering critical insights for teacher education programs to design instruction that strengthens symbol sense, relational understanding, and pedagogical readiness in teaching non-routine mathematical cases.