Structural Alignment in Students’ Reasoning on Rational Inequalities: A Comenian Hermeneutic Analysis

Syifa Ismayanti; Mohamad Gilar Jatisunda; Laelasari

doi:10.31949/dm.v8i1.17710

Authors

Syifa Ismayanti Universitas Majalengka, Indonesia
Mohamad Gilar Jatisunda Mathematics Education, Universitas Majalengka, Majalengka, Indonesia, Indonesia https://orcid.org/0000-0001-8860-0462
Laelasari Mathematics Education, Universitas Swadaya Gunung Jati, Cirebon, Indonesia, Indonesia https://orcid.org/0000-0003-3985-2916

DOI:

https://doi.org/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.

Keywords:

Rational inequalities, Comenian epistemology, Structural reasoning, Epistemic alignment, Hermeneutic analysis

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