Polyhedron International Journal in Mathematics Education

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 — Sun, 30 Nov 2025 00:00:00 +0700

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.

The Impact of augmented reality on the learning of polyhedral: an approach based on didactical engineering and instrumental genesis

Alberto Apreza Sies, Guillermina Sánchez Román, José Antonio Juárez-López — Sun, 30 Nov 2025 00:00:00 +0700

Despite the relevance of spatial skills in mathematics education, upper-secondary students face persistent difficulties, especially in the manipulation and conceptual understanding of three-dimensional objects. This study aims to design, implement, and analyze a didactic sequence mediated by Augmented Reality (AR) for the learning of polyhedral. The novelty lies in the analysis of the underlying cognitive processes through the framework of Instrumental Genesis, basing the design on the principles of Didactic Engineering. The research adopts a mixed-method and quasi-experimental approach. A pre-test and post-test were administered to a sample of fourth-semester upper-secondary students (n=12), complemented by an exhaustive qualitative analysis of the interaction with the GeoGebra 3D AR tool. Pre-test findings confirmed student weaknesses, showing only 25% success on measurement and dimensioning tasks. The post-intervention analysis demonstrated a significant and positive impact of the didactic sequence, evidenced by the total adaptation and instrumentalization of the AR tool. This resulted in a favorable evolution of cognitive schemes and a noticeable improvement in spatial visualization skills. The findings suggest that successful technological integration in 3D geometry must be guided by rigorous theoretical design and a detailed analysis of knowledge construction mediated by the instrument, providing empirical evidence for the implementation of AR in the mathematics classroom.

Enhancing mathematical disposition and learning outcomes through Team Games Tournament: A two-cycle action research on probability instruction in indonesian secondary education

Cintya Mayangsari, Abd Qohar, Nurul Faridha — Sun, 30 Nov 2025 00:00:00 +0700

Despite growing recognition of mathematical disposition's importance for long-term STEM success, traditional teacher-centered instruction often fails to develop students' affective engagement, leading to mathematics anxiety and diminished self-efficacy. Team Games Tournament (TGT) offers a promising cooperative learning approach, yet systematic investigation of its effects on both cognitive and affective outcomes remains limited. This two-cycle action research investigated TGT implementation effects on probability learning outcomes and mathematical disposition across four NCTM dimensions: attention to accuracy and precision, perseverance in facing challenges, reflection and evaluation abilities, and openness to diverse strategies. Thirty-four Grade 10 students in Aceh, Indonesia, participated in seven-week TGT instruction following Kemmis and McTaggart's spiral model. Data collection employed validated achievement tests (α = 0.82) and mathematical disposition questionnaires (α = 0.89) at three time points, supplemented by classroom observations and field notes. Paired t-tests, effect size calculations, and chi-square analyses examined changes across baseline, Cycle 1, and Cycle 2. TGT implementation produced substantial improvements in achievement (M = 67.3 to 87.7; Cohen's d = 2.35) and mastery rates (32.4% to 88.2%). Mathematical disposition improved markedly, with high-disposition students increasing from 12% to 70%. Iterative refinements in Cycle 2 generated additional significant gains (d = 0.79), demonstrating cumulative benefits of sustained implementation. Dimension-specific analysis revealed differential growth patterns, with tournament structures rapidly developing accuracy attention while strategic flexibility required sustained exposure. Well-designed TGT implementation simultaneously enhances cognitive achievement and cultivates productive mathematical dispositions essential for 21st-century competencies, offering scalable approaches for transforming mathematics instruction in contexts where students exhibit low engagement.

Bridging abstract to concrete: The SPLDV board as an innovative tool for teaching systems of linear equations

Chatra Arlinta Maurilla, Puguh Darmawan — Sun, 30 Nov 2025 00:00:00 +0700

This qualitative case study examines the effectiveness of the SPLDV Board, a color-coded manipulative tool, in teaching systems of linear equations with two variables to 37 mathematics education students. Through inquiry-based instruction and systematic questioning, the study analyzed students' conceptual understanding, procedural fluency, and engagement patterns. Results demonstrated that the SPLDV Board's visual scaffolding significantly improved students' ability to identify coefficients, execute cross-multiplication procedures, and understand underlying mathematical structures, with all participants achieving fluent responses to guiding questions. However, limitations emerged: the tool only works for systems with unique solutions and some students remained passive during instruction. Findings provide practical guidance for developing accessible manipulative materials that support both procedural and conceptual learning in algebra, with design principles transferable to other mathematical topics requiring multi-step problem-solving.

Development and validation of ethnomathematics-based worksheets integrating Sundanese Pupuh for enhancing number pattern learning in Indonesian secondary schools

Pitri Aulia Aulia, Rani Sugiarni, Camilo Andrés Rodríguez-Nieto — Sun, 30 Nov 2025 00:00:00 +0700

This study addresses the persistent challenge of low mathematical performance among Indonesian secondary students, particularly in learning number patterns, by developing culturally responsive teaching materials. Although Indonesia’s PISA performance has improved, students remain below the OECD average, with prior studies highlighting difficulties in pattern recognition, symbolic representation, and generalization. To address this issue, the study bridges abstract mathematical concepts with students’ cultural contexts through the development of ethnomathematics-based student worksheets integrating Sundanese Pupuh, a traditional literary art form characterized by structured numerical patterns in syllable counts and line arrangements. The research employed a Research and Development approach using the 4D model (Define, Design, Develop, Disseminate). The worksheets were designed to explicitly connect the inherent mathematical structures of Pupuh—guru wilangan and guru lagu—with formal number pattern concepts in the eighth-grade mathematics curriculum. The development process included needs analysis, alignment with Indonesia’s Merdeka Curriculum, and analysis of student characteristics. Expert validation conducted by mathematics education lecturers and prospective teachers resulted in a combined validity score of 90%, categorized as very valid. Practicality testing with eighth-grade students yielded a score of 92.6%, indicating high usability. This study contributes to mathematics education in three key ways: (1) introducing a novel pedagogical use of indigenous cultural heritage to support abstract mathematical learning, (2) providing empirically validated culturally responsive worksheets that address specific difficulties in number pattern learning, and (3) offering a replicable framework for integrating ethnomathematics into formal curricula. The findings suggest that culturally grounded instruction can enhance student engagement and conceptual understanding, with potential application to other cultural contexts.