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, 2025)
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.