Analysis of Students’ Learning Obstacles in Solving SLETV Problems and the Development of a Hypothetical Didactical Design Based on Contextual Problems

Abstract

This study aims to identify students’ learning obstacles in the topic of Systems of Linear Equations in Two Variables (SLETV) and to develop a hypothetical didactical design based on contextual problems. The method used is descriptive qualitative within the framework of Didactical Design Research (DDR) at the prospective analysis stage. The research subjects were 34 tenth grade students at a public high school in Bandung, selected through purposive sampling. Data were collected via contextual essay tests and semi-structured interviews, then analyzed using the Miles and Huberman model. The results of the study indicate that all three types of learning obstacles were found simultaneously. Epistemological obstacles were the most dominant, manifested in the understanding of nominal variables, incomplete solutions, and failure to transfer knowledge across contexts. Didactical obstacles were identified in students’ inability to provide mathematical arguments, while ontogenical obstacles were evident in errors in algebraic operations and the lack of logical sequence in solution steps. Based on these findings, a hypothetical didactical design was developed in the form of a six-stage worksheet based on an online game context, supplemented with Pedagogical Didactical Anticipation (PDA) at each stage. This design addresses each obstacle through variable scaffolding, argumentative validation situations, and context-based institutionalization.