Representation Obstacles in Semantic Processes for Geometric Problem Solving
DOI:
https://doi.org/10.33394/j-ps.v14i2.19751Keywords:
Representational obstacles, Semantic process, Geometric Problem solving, Inter-representational transformation, Mathematical representationAbstract
Mathematics is a fundamental subject in the curriculum, but many students still struggle when it comes to representing, interpreting, and connecting mathematical information in solving geometry problems. Previous research has generally addressed learning obstacles from conceptual, procedural, didactic, or epistemological perspectives, but has not specifically examined how representational obstacles emerge within the semantic process as students construct mathematical meaning. This study addresses this gap. The aim of this research is to describe the representational obstacles experienced by students during the semantic process of solving geometric problems. In this study, the semantic process is defined as a series of activities to construct meaning through reading, sorting information, identifying keywords, connecting concepts, constructing arguments, verifying solution steps, and drawing conclusions in the form of visual, symbolic, and verbal representations. The study employed an exploratory qualitative approach involving 51 students grouped into high, medium, and low ability levels. The basis for identifying representational obstacles was established through an analysis of geometric problem-solving test results, written work traces, and interviews across five semantic stages: sequencing, identification, argument formulation, verification, and conclusion, taking into account inaccuracies, incompleteness, or failures in inter-representational transformation. The research results indicate that high-ability subjects tend to experience visual, symbolic, and verbal obstacles in the early stages, whereas subjects with moderate and low abilities predominantly experience verbal and symbolic obstacles. In the verification stage, all groups exhibited relatively similar symbolic and verbal obstacles, indicating a common difficulty in formalizing and testing the validity of solutions. Theoretically, this study reinforces the understanding that representational obstacles are not only related to conceptual mastery but also to failures in the meaning-making process during the semantic stage. Practically, these findings provide a foundation for developing more targeted geometry learning strategies to strengthen inter-representational translation, mathematical argumentation, and solution validation.
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