Students’ Translation Between Mathematical Representations in Solving Geometric Transformation Problems: A Qualitative Study

Abstract

Mathematical representation ability is essential for students to understand mathematical concepts and solve problems by connecting different forms of representation. This research aims to analyze student translation abilities between mathematical representations in solving geometric transformation problems. A descriptive qualitative approach was employed involving 34 eleventh-grade students of Kesatrian 1 Senior High School, Semarang, who were selected through purposive sampling. Data were collected using a mathematical representation ability test and semi-structured interviews. Based on the test results, 8 students were classified as having high mathematical representation ability, 14 as moderate, and 12 as low. Three representative students, one from each category, were selected for in-depth analysis and interviews. The findings indicate that students with high ability could effectively translate verbal information into visual and symbolic representations and connect the three forms consistently. Students with moderate ability could identify and represent most information visually but experienced difficulties applying symbolic procedures, particularly when translating between sequential transformation steps. Students with low ability experienced difficulties identifying relevant information, constructing visual representations, and selecting appropriate symbolic procedures. Overall, effective translation between mathematical representations is associated with students’ ability to understand and solve geometric transformation problems.