Intan Sari Rufiana, Slamet Arifin, Fierda Nursitasari Amaliya, Mohammad Yusuf Randy
Mathematical reasoning is essential for primary school students, particularly when tackling controversial math problems. However, many students struggle with these challenges, which can impede their mathematical development. This study investigates and describes the levels of mathematical reasoning among elementary students confronted with controversial problems, thereby advancing the understanding of their reasoning processes. Employing a descriptive qualitative research design grounded in a constructivist framework, we selected six students through snowball sampling, categorizing them into three reasoning levels: initial, exploratory, and clarifying. Data were collected through written tests featuring controversial math problems and semi-structured interviews. The tests assessed students' reasoning and identified contradictions in their answers, while interviews provided insights into their thought processes. Findings reveal distinct reasoning patterns: initial level students show basic understanding but struggle with deeper reasoning, leading to contradictions; exploratory level students recognize contradictions but lack the conceptual understanding for complete solutions; clarifying level students effectively identify and explain contradictions, demonstrating a solid grasp of mathematical concepts. This study contributes to the field by highlighting the varying reasoning processes of elementary students in the context of controversial problems. It underscores the need for targeted instructional strategies tailored to each reasoning level, which can enhance students' mathematical reasoning skills and problem-solving abilities. By addressing these specific needs, educators can foster a more effective learning environment that promotes deeper engagement with mathematics. © 2025 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Malang, Indonesia
