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All Journal Riemann : Research of Mathematics and Mathematics Education
Silfia Hayuningrat
Universitas Pendidikan Indonesia
Education Mathematics

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Didactic Obstacles in Trigonometric Ratios: Insights into Students’ Mathematical Understanding Silfia Hayuningrat; Didi Suryadi; Imam Rofiki
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.166

Abstract

This study examines the relationship between the knowledge prescribed in the school curriculum, the knowledge enacted by mathematics teachers, and the knowledge constructed by students in learning trigonometric ratios through the perspective of Didactic Transposition Theory. A qualitative intrinsic case study was conducted with one mathematics teacher and 22 tenth-grade students in an Indonesian senior high school. Data were collected from curriculum documents, teaching notes, classroom observations, interviews, and two tests designed to capture students’ conceptual understanding. The data were analyzed using document analysis, content analysis, and descriptive analysis. The findings show that although students’ understanding of trigonometric ratios improved during instruction, the enacted classroom practices mainly emphasized trigonometric ratios as fixed relationships among the sides of right triangles. Consequently, students tended to interpret sine, cosine, and tangent primarily as geometric ratios rather than as functions of angles. This emphasis limited students’ ability to connect geometric reasoning with functional interpretations of trigonometric relationships. These results highlight the importance of strengthening instructional coherence in curriculum implementation so that classroom teaching better supports the development of both geometric and functional understanding of trigonometry.
How Cognitive Styles Shape Creative Mathematical Thinking Dian Septi Nur Afifah; Grafika Saraswati; Silfia Hayuningrat
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.192

Abstract

Creative thinking is widely recognized as a core component of higher-order thinking in mathematics education; however, its development among Indonesian students remains a persistent challenge, as reflected in large-scale international assessments such as PISA 2018. Differences in students’ cognitive styles particularly reflective, impulsive, and slow-inaccurate styles are assumed to shape cognitive processing and mathematical problem-solving performance, yet empirical evidence remains limited. This study aims to examine students’ creative thinking ability in mathematical problem solving from the perspective of these cognitive styles. Employing a qualitative descriptive approach, the participants were eighth-grade students from SMP Negeri 2 Sumbergempol Tulungagung, classified using the Matching Familiar Figure Test (MFFT). Data were obtained through problem-solving tests and semi-structured interviews and analyzed through methodological triangulation. The findings indicate that students with reflective cognitive styles exhibit a high level of creative thinking, characterized by fluency, flexibility, and originality. In contrast, students with impulsive and slow-inaccurate cognitive styles demonstrate moderate creative performance, predominantly reflected in elaborative responses. These results highlight the need for differentiated instructional strategies that align with students’ cognitive characteristics. The study contributes to the growing body of literature on cognitive style-based instruction and offers pedagogical insights for fostering creative thinking in mathematics classrooms.
Co-Authors Dian Septi Nur Afifah Didi Suryadi Grafika Saraswati Imam Rofiki