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Journal : Journal on Mathematics Education

Level of students' proportional reasoning in solving mathematical problems Sari, Riska Novia; Rosjanuardi, Rizky; Isharyadi, Ratri; Nurhayati, Aat
Journal on Mathematics Education Vol. 15 No. 4 (2024): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v15i4.pp1095-1114

Abstract

This study aimed to evaluate the level of proportional reasoning among middle school students in their ability to solve mathematical problems involving proportions. Proportional reasoning is essential for understanding and mastering various mathematical concepts, serving as a fundamental skill for higher-level mathematics. A qualitative case study design was employed, involving 28 eighth-grade students from a school in Bandung, Indonesia. The participants were assessed using a set of proportion-related problems, including numerical comparison, non-proportional (additive), direct proportion, and inverse proportion tasks. The analysis focused on categorizing the students' problem-solving strategies into distinct levels of proportional reasoning, ranging from non-proportional to formal proportional reasoning. Additionally, three students representing high, moderate, and low mathematical performance were selected for in-depth interviews to explore their reasoning processes when addressing proportion problems. Data analysis included administering tests, reviewing students' problem-solving strategies, conducting in-depth interviews, and evaluating their proportional reasoning abilities. The findings revealed that students with high and moderate mathematical performance exhibited proportional reasoning levels ranging from 0 to 3, whereas low-performing students displayed levels ranging from 0 to 2. Moreover, students generally faced difficulties distinguishing between proportional and non-proportional problems. Even when correct answers were provided, many lacked a deep understanding of direct and inverse proportion concepts. The study also discusses several implications for enhancing students' proportional reasoning skills.
Exploring three-dimensional geometry using praxeological analysis: Indonesian textbook insights Isharyadi, Ratri; Nurjanah
Journal on Mathematics Education Vol. 16 No. 1 (2025): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v16i1.pp343-364

Abstract

The integration of three-dimensional geometry in secondary mathematics education plays a crucial role in developing students' spatial reasoning and problem-solving skills. However, textbooks often present limitations in structuring tasks, techniques, and justifications, which may lead to learning obstacles. Despite the importance of well-designed instructional materials, there is a lack of comprehensive studies analyzing Indonesian mathematics textbooks using both the praxeological framework and the learning obstacles perspective in didactic situations. Addressing this gap, this study examines a Grade XII mathematics textbook in Indonesia, focusing on three-dimensional geometry through a structured content analysis. The analysis categorizes tasks based on praxeological components, including types of tasks, solution techniques, technological justifications, and supporting theories, while also identifying potential learning obstacles related to the clarity of visual representations and contextual problem diversity. The findings reveal that the textbook includes 10 types of tasks, solved using 6 techniques, supported by 7 forms of technological reasoning, all grounded in three-dimensional geometry concepts. The presentation of tasks is systematically structured and balances conceptual and procedural aspects, minimizing significant didactic obstacles. However, epistemological obstacles were identified, primarily due to limited visualizations and a lack of diverse contextual tasks, which may hinder students’ flexibility in applying three-dimensional geometry concepts. These findings highlight the need for improved task design and enhanced visual representations to foster deeper conceptual understanding and adaptability in problem-solving. This study contributes to mathematics education research by providing empirical insights into textbook design and its impact on students' learning processes, offering recommendations for more effective instructional material development.