Learning Obstacles in Senior High School Students' Conceptual Understanding of Translation
DOI:
https://doi.org/10.35706/sjme.v10i2.13614Keywords:
Learning Obstacle, Conceptual Understanding Ability, Translation, Geometric Transformation, Mathematics LearningAbstract
Students’ difficulties in understanding translation indicate that learning problems in geometric transformation are not limited to procedural errors but are also related to obstacles in constructing and applying conceptual knowledge. This study aimed to analyze learning obstacles associated with senior high school students’ conceptual understanding of translation using ontogenic, epistemological, and didactical obstacles as the analytical framework. The study employed a qualitative phenomenological approach as the initial phase of Didactical Design Research (DDR), focusing on the identification of learning obstacles before the development of a didactical design. The participants were 29 eleventh-grade students from a senior high school in Bandung, Indonesia, selected purposively based on variations in their solution and error patterns. Data were collected through four open-ended conceptual understanding test items, semi-structured interviews with selected students and a mathematics teacher, and documentation. Data analysis followed the stages of data reduction, data display, and conclusion drawing, while credibility was strengthened through triangulation of written responses, student interviews, and teacher interviews. The findings showed that students’ conceptual understanding of translation remained limited across all indicators. The highest achievement was found in selecting and applying appropriate procedures or operations (41%), followed by representing concepts in various mathematical forms (34%), restating concepts (28%), and applying concepts or algorithms in problem-solving (14%). The analysis identified ontogenic instrumental obstacles related to insufficient mastery of Cartesian coordinates as prerequisite knowledge and epistemological obstacles related to students’ limited ability to use translation concepts flexibly across visual, symbolic, procedural, and contextual representations. Epistemological obstacles appeared more dominant, whereas didactical obstacles could not be adequately identified from the available data. These findings provide an empirical basis for developing didactical designs that connect prerequisite knowledge, multiple representations, conceptual meaning, and contextual problem-solving.
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