Elementary Students’ Mathematical Reasoning Abilities in Solving Non-Routine Fraction Story Problems

Abstract

English

Fraction is an important part of elementary mathematics, yet they often cause difficulties because students may have trouble interpreting fraction concepts and applying them in unfamiliar situations. These difficulties can also affect students’ reason when solving non-routine word problems. This study describes the mathematical reasoning demonstrated by elementary school students when solving non-routine problems involving fractions. A descriptive qualitative approach was used with six fifth-grade students from Public Elementary School 109 Palembang. The participants were purposively selected to represent high, medium, and low levels of mathematical ability. Data was collected through three non-routine essay problems designed to examine three aspects of mathematical reasoning: making conjectures, performing mathematical manipulation, and drawing logical conclusions. Students’ writing was analyzed alongside interview data to examine how they interpreted information, conducted mathematical procedures, and justified their answers. The finding indicates that students showed various levels of reasoning across the three aspects. Making conjectures was the most challenging aspect, particularly when students had to identify relevant information and determine an appropriate initial strategy. In contrast, drawing logical conclusions was more frequently demonstrated, although some conclusions were not adequately supported by the preceding reasoning. The findings suggest that difficulties in solving fraction problems were not limited to procedural errors but were also related to students’ conceptual understanding and interpretation of the problem context. These results highlight the need for fraction instruction that gives students greater opportunities to explain, justify, and evaluate their mathematical reasoning.

Indonesian

Pecahan merupakan salah satu materi penting dalam pembelajaran matematika karena mendukung perkembangan kemampuan penalaran matematis siswa. Namun, materi pecahan sering dianggap sulit dan kerap menimbulkan miskonsepsi pada siswa sekolah dasar. Penelitian ini bertujuan untuk mendeskripsikan kemampuan penalaran matematis siswa dalam menyelesaikan soal cerita pecahan non-rutin. Penelitian ini menggunakan metode kualitatif dengan pendekatan deskriptif. Partisipan penelitian terdiri dari enam siswa kelas V di SD Negeri 109 Palembang. Data dikumpulkan melalui tes tertulis kemampuan penalaran matematis dan wawancara semi-terstruktur. Hasil penelitian menunjukkan bahwa kemampuan penalaran matematis siswa dalam menyelesaikan soal pecahan non-rutin masih perlu ditingkatkan, terutama pada penyelesaian operasi pecahan campuran dan soal kontekstual. Indikator menarik kesimpulan secara logis paling sering muncul karena siswa sudah terbiasa memberikan kesimpulan pada jawaban mereka, sedangkan indikator membuat dugaan paling jarang muncul karena siswa belum terbiasa mengidentifikasi dan menuliskan informasi yang relevan dalam menyelesaikan masalah matematika. Temuan ini menunjukkan pentingnya memberikan aktivitas pembelajaran yang kontekstual dan berorientasi pada penalaran untuk mendukung pemahaman konsep pecahan serta meningkatkan kemampuan penalaran matematis siswa.

Keywords

• descriptive qualitative
• elementary school students
• fractions
• mathematical reasoning
• non-routine word problems