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All Journal Union: Jurnal Ilmiah Pendidikan Matematika Jurnal Didactical Mathematics
Syifa Ismayanti
Universitas Majalengka
Education Mathematics

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Structural Alignment in Students’ Reasoning on Rational Inequalities: A Comenian Hermeneutic Analysis Syifa Ismayanti; Mohamad Gilar Jatisunda; Laelasari
Jurnal Didactical Mathematics Vol. 8 No. 1 (2026): April 2026
Publisher : Program Studi Pendidikan Matematika, Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/dm.v8i1.17710

Abstract

This study investigates students’ reasoning in rational inequalities through a structural–hermeneutic framework interpreted within Comenian epistemology. Rather than examining procedural accuracy alone, the study explores the degree to which students’ reasoning aligns with the intrinsic structural order of rational expressions. 32 students completed 3 rational inequality tasks with increasing relational complexity. Written responses and follow-up interviews were analysed sequentially through structural segmentation, coherence analysis, and epistemic interpretation. Across tasks, three stable configurations emerged: coherent rational alignment, procedural performance without integration, and fragmented structural reasoning. Students demonstrating coherent alignment engaged domain restrictions as structural boundaries, interpreted zeros as relational thresholds, and conducted interval-based sign analysis relationally rather than mechanically. Procedural performance without integration reflected operational competence but limited articulation of structural coherence. Fragmented reasoning revealed a breakdown of relational unity, including the decomposition of rational expressions into independent linear components and the omission of discontinuity. As symbolic and relational complexity increased—particularly in tasks requiring quadratic transformation—structural coherence decreased while fragmentation increased. The findings suggest that difficulty with rational inequalities lies not solely in algebraic manipulation but in sustaining epistemic alignment among the recognition of discontinuities, symbolic transformation, and the interpretation of relational signs. Theoretically, the study reframes rational inequality reasoning as a problem of epistemic formation rather than procedural mastery. Within a Comenian perspective, mathematical understanding emerges when cognition conforms to intrinsic structural order. The results highlight the importance of instructional approaches that foreground relational coherence and structural unity in algebraic reasoning.
Innovative teaching modules utilizing discovery learning to strengthen mathematical problem-solving skills Syifa Ismayanti; Iik Nurhikmayati; Mohamad Gilar Jatisunda
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 1 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i1.18981

Abstract

This research aims to strengthen students' mathematical problem-solving skills by creating teaching modules based on the Discovery Learning approach. Because traditional teaching approaches often fail to engage students effectively, the development of this module is essential. In our research, we use research and development (R&D) techniques with 4D models up to the Development stage, which concentrates on module design and testing. Based on the findings of the validity test, media experts got a score of 73%, while material experts got a score of 87%. The criteria used include relevance, completeness, ease of understanding, suitability for discovery learning, and problem-solving skills. Meanwhile, practicality received an average score of 93.5% from teachers and students. Therefore, modules can be considered legitimate and useful, and are expected to improve student engagement and problem-solving skills. Through this research, it is hoped to significantly advance mathematics education with the creation of more creative teaching strategies. The findings provide a foundation for future studies to refine and expand Discovery Learning-based instructional materials in mathematics education.
Co-Authors Iik Nurhikmayati Laelasari Mohamad Gilar Jatisunda Mohamad Gilar Jatisunda