Muhammad Ilyas
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Cokroaminoto Palopo

Published : 2 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 2 Documents
Search

Fifth-Grade Students’ Conceptual Understanding of Fractions: A Qualitative Study Sherly Purwasih Oley; Muhammad Ilyas; Taufiq Taufiq; Patmaniar Patmaniar
Kognitif: Jurnal Riset HOTS Pendidikan Matematika Vol. 6 No. 3 (2026): July - September 2026
Publisher : Education and Talent Development Center Indonesia (ETDC Indonesia)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51574/kognitif.v6i3.5861

Abstract

Understanding fraction concepts is a fundamental foundation for mathematics learning at the elementary school level; however, students often struggle to connect symbols, visual representations, the characteristics of fraction forms, and operations in contextual problems. This study aimed to describe fifth-grade students' understanding of fraction concepts at UPT SD Negeri 041 Padang. A qualitative descriptive design was employed, involving three participants purposively selected to represent high, moderate, and low mathematics ability categories. Data were collected through a fraction concept understanding test consisting of five essay items and task-based interviews. The test instrument and interview guide were validated by two experts using Aiken's V index, yielding average values of 0.875 and 0.861, respectively. Data were analyzed interactively through data reduction, data display, and conclusion drawing and verification. The credibility of the findings was maintained through method triangulation among written responses, interviews, and field notes. The results revealed three patterns of understanding. Students with stronger understanding were able to explain equivalent fractions, classify mixed fractions, distinguish common fractions from whole numbers, represent fractions visually, and systematically apply fraction operations in contextual problems. Students with partial understanding could verbally explain basic concepts but were inconsistent in classifying fraction forms and translating symbols into visual representations. Students with lower understanding tended to rely on surface features, such as visual similarity or the presence of specific numbers, without fully grasping the quantitative relationship among numerator, denominator, and fraction value. These findings underscore the need for fraction assessment to evaluate students' answers, reasoning, representations, and strategies in an integrated manner. Fraction instruction should connect concrete objects, visual representations, symbols, and contextual problems, while encouraging students to explain and verify their problem-solving strategies.
Analysis of Elementary School Students' Creative Thinking in Solving Mathematical Problems Based on Level of Mathematical Understanding Ismail Nur; Muhammad Ilyas; Taufiq Taufiq; Patmaniar Patmaniar
Kognitif: Jurnal Riset HOTS Pendidikan Matematika Vol. 6 No. 3 (2026): July - September 2026
Publisher : Education and Talent Development Center Indonesia (ETDC Indonesia)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51574/kognitif.v6i3.5863

Abstract

Creative thinking is an essential mathematics competency, supporting idea generation, strategy selection, and non-routine problem solving. At the elementary level, it must be developed systematically so students move beyond routine procedures toward flexible, logical, reflective thinking. This study describes sixth-grade students' creative thinking in solving data-handling problems by level of mathematical understanding. Using a qualitative descriptive approach, three sixth-grade students at UPT SD Negeri 099 Masamba were purposively selected for high, moderate, and low understanding levels. Data were collected through a creative-thinking test and semi-structured interviews, analyzed using fluency, flexibility, originality, and elaboration indicators. Credibility was strengthened through triangulation of written responses and interviews; data were processed through reduction, display, verification, and conclusion drawing. The high-ability student displayed all four indicators strongly and consistently, proposing alternative strategies, adjusting solution steps, developing logical plans, and re-checking solutions. The moderate-ability student showed all indicators but was inconsistent in exploring ideas, developing solutions, and evaluating answers. The low-ability student showed limitations in independently generating strategies, developing solutions, and explaining reasoning in detail. These findings show that understanding level relates to differences in students' creative-thinking characteristics in problem solving. Instruction should therefore give students room to explore strategies, explain reasoning, and reflect on solutions.