Patterns of Fifth-Grade Students’ Difficulties in Solving Fraction Problems Across Mathematical Ability Levels
Abstract
Fractions remain a challenging topic in elementary mathematics because successful problem solving requires students to coordinate problem comprehension, conceptual understanding, procedural knowledge, and mathematical representation. This study aimed to analyze the patterns of fifth-grade students’ difficulties in solving fraction problems across different mathematical ability levels. A descriptive qualitative design was employed involving 30 fifth-grade students at SD Negeri 8 Baubau, Indonesia. Data were collected through a 10-item open-ended fraction test administered to all participants and semi-structured interviews with three students representing high-, medium-, and low-ability levels. The data were analyzed through data reduction, data display, comparison of written responses and interview evidence, and conclusion drawing. The results showed that 20.00% of students were classified as high ability, 36.67% as medium ability, and 43.33% as low ability. Three major patterns of difficulty were identified: understanding fraction problems, performing fraction operations, and mathematical problem solving. High-ability students generally understood the problems and selected appropriate operations but still made minor procedural and accuracy-related errors. Medium-ability students demonstrated partial conceptual understanding accompanied by unstable procedural knowledge, particularly in converting fraction forms, finding common denominators, and selecting appropriate operations. Low-ability students showed the most complex pattern, involving interconnected difficulties in understanding problem situations, representing quantitative relationships, performing fraction operations, and organizing complete solution procedures. These findings indicate that fraction difficulties differ qualitatively across ability levels; therefore, instruction should be differentiated by emphasizing accuracy and verification for high-ability students, conceptual–procedural connections for medium-ability students, and integrated comprehension–representation–procedure scaffolding for low-ability students.