ANALYSIS OF STUDENTS’ MATHEMATICAL REPRESENTATION ERRORS IN SOLVING CIRCLE PROBLEMS

Abstract

Mathematical representation plays an important role in solving geometry problems because students need to coordinate information across different forms of representation. This study aims to describe the characteristics and patterns of students’ mathematical representation errors in solving circle problems. A descriptive qualitative approach was employed with 23 Mathematics Education students from one class. Data were collected through an essay test involving visual, symbolic, and verbal representations and analyzed to identify error characteristics and relationships among representations. The results revealed five main types of errors: visual representation errors; visual-to-symbolic transformation errors; errors in constructing and manipulating symbolic representations; errors in selecting appropriate concepts or symbolic representations; and verbal representation errors. The findings further indicate that, in several responses, errors continued across representations, particularly when inaccurate interpretation of geometric information was carried over into symbolic representations and verbal explanations. These findings suggest that effective problem solving in circle topics depends not only on the accuracy of individual representations but also on students’ ability to coordinate information across representations. Therefore, analytic geometry instruction should explicitly engage students in constructing, translating, and examining relationships among visual, symbolic, and verbal representations.