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All Journal Range : Jurnal Pendidikan Matematika Polyhedron International Journal in Mathematics Education
Dian Mustikaningsih
Universitas Terbuka
Education Mathematics

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Enhancing mathematical communication and learning independence through learning cycle 6E model with dynamic geometry software: A study of vocational high school students Dian Mustikaningsih; Yumiati Yumiati; Sudirman Sudirman
Polyhedron International Journal in Mathematics Education Vol. 3 No. 2 (2025): pijme
Publisher : Nashir Al-Kutub Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59965/pijme.v3i2.262

Abstract

Mathematical communication ability and learning independence are essential 21st-century competencies that remain underdeveloped in vocational mathematics education, where students often perceive mathematics as irrelevant to their careers. This quasi-experimental study investigated the effectiveness of integrating the Learning Cycle 6E model with Dynamic Geometry Software (GeoGebra) in improving these competencies among vocational high school students. Sixty-nine tenth-grade students from the Marketing Skills Program were assigned to experimental (n=35) and control (n=34) groups through random sampling. The experimental group received instruction using the six-phase Learning Cycle 6E model (engage, explore, explain, elaborate, evaluate, extend) integrated with GeoGebra, while the control group received conventional expository instruction. Data were collected through mathematical communication tests and learning independence questionnaires administered as pretest and posttest. Normalized gain (N-Gain) analysis was employed to measure improvement effectiveness. Results demonstrated that the experimental group achieved significantly higher improvement in mathematical communication ability (N-Gain = 0.62) compared to the control group (N-Gain = 0.44), representing a 40.9% advantage. Similarly, learning independence improved significantly more in the experimental group (N-Gain = 0.51) versus the control group (N-Gain = 0.26), nearly doubling the control group's gain. Statistical analyses confirmed both differences were significant (p < 0.05) with large effect sizes. These findings provide empirical evidence that integrating constructivist pedagogy with dynamic technology effectively enhances both cognitive and metacognitive competencies in vocational mathematics education, offering a practical framework for revitalizing mathematics instruction to meet contemporary educational demands and career-relevant applications.
Integrating Dynamic Geometry Software into the 6E Instructional Model to Enhance Students’ Mathematical Communication Skills and Learning Autonomy Dian Mustikaningsih; Yumiati Yumiati; Sudirman Sudirman; Camilo Andrés Rodríguez-Nieto
RANGE: Jurnal Pendidikan Matematika Vol. 8 No. 1 (2026): Range Juli 2026
Publisher : Pendidikan Matematika UNIMOR

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/jpm.v8i1.10412

Abstract

The integration of technology into mathematics instruction is increasingly acknowledged as a means to foster 21st-century competencies, particularly mathematical communication and independent learning. This study investigates the effects of the 6E instructional model combined with Dynamic Geometry Software (DGS) on these two aspects. A quasi-experimental design was conducted with tenth-grade students from a vocational school in Sukoharjo, Central Java. The sample included 35 students in the experimental group and 34 students in the control group, selected randomly. Mathematical communication was measured using essay-based pre- and post-tests, while learning autonomy was assessed through questionnaires administered before and after the intervention. Normality and homogeneity tests using Kolmogorov–Smirnov and Levene’s confirmed the assumptions for parametric analysis. Data were analyzed using the Independent Sample T-test. Results indicated that significance values for both mathematical communication and learning autonomy were below 0.05, showing statistically significant differences between groups. The experimental group achieved an average post-test score of 82.40, higher than the control group’s 74.24, indicating improved mathematical communication under the 6E model with DGS integration. Similarly, the experimental group’s average final questionnaire score of 105.11 exceeded the control group’s 90.38, reflecting greater learning autonomy. These findings demonstrate that embedding GeoGebra within the 6E instructional model substantially enhances students’ ability to articulate mathematical ideas and promotes independent learning. The study provides empirical support for technology-enhanced learning designs in mathematics education, highlighting their potential to strengthen key competencies and contribute to more effective instructional practices.
Co-Authors Camilo Andrés Rodríguez-Nieto Sudirman Yumiati