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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 Mustikaningsih, Dian; 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.
Effectiveness of ChatGPT-integrated discovery learning on mathematical literacy in three-variable linear equation systems: A quasi-experimental study Monike, Rismun Sufia; Sudirman, Sudirman; Kandaga, Thesa; Rodríguez-Nieto, Camilo Andrés
International Journal of Didactic Mathematics in Distance Education Vol. 3 No. 1 (2026): ijdmde (in Progress)
Publisher : Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/ijdmde.v3i1.13157

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This quasi-experimental study investigated the effectiveness of ChatGPT-integrated discovery learning on high school students' mathematical literacy in three-variable linear equation systems, while examining the moderating role of self-efficacy. Eighty tenth-grade students from a public high school in Indonesia were assigned to either an experimental group receiving ChatGPT-supported discovery learning instruction or a control group receiving conventional instruction, with mathematical literacy assessed through problem-solving tests and self-efficacy measured using validated questionnaires. Statistical analyses using non-parametric tests, including Wilcoxon Signed Rank Test, Mann-Whitney U Test, and Rank-Based ANCOVA, revealed that the experimental group achieved significantly higher post-test scores (M=79.25, SD=8.42) compared to the control group (M=65.30, SD=9.18), yielding a large effect size (d=1.24, p<.001) that substantially exceeded typical outcomes reported in meta-analyses of computer-assisted mathematics instruction. Contrary to established theoretical frameworks positing strong relationships between self-efficacy and mathematics achievement, this study found that self-efficacy neither significantly predicted mathematical literacy (F=3.171, p=.083, η²=.077) nor interacted with the learning model, suggesting that ChatGPT's pedagogical benefits operated uniformly across students with varying confidence levels. These findings suggest that ChatGPT functioned as adaptive conversational scaffolding that provided immediate formative feedback, facilitated metacognitive engagement through dialogic prompting, and generated multiple mathematical representations to support conceptual understanding. The null self-efficacy effect may indicate that robust AI scaffolding serves as an external compensatory mechanism that equalizes learning opportunities by reducing students' dependence on internal confidence judgments, thereby contributing novel theoretical insights into the conditional nature of motivational constructs in AI-mediated learning environments and offering practical implications for implementing conversational AI in mathematics education.
Phenomenological exploration of low conceptual understanding in mathematical story problem-solving among Indonesian Junior High School Students Rauhun, Siti; Indrawati, Indrawati; Samsul, Bahri; Sudirman, Sudirman; Olivero-Acuña, Ronaldo Rafael
International Journal of Mathematics and Sciences Education Vol. 3 No. 2 (2025): Ijmsed
Publisher : Nashir Al-Kutub Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59965/ijmsed.v3i2.186

Abstract

Mathematical story problems present persistent challenges for students worldwide, yet little research explores how students with low conceptual understanding subjectively experience these difficulties. This phenomenological study investigated the lived experiences of 15 Indonesian Grade VIII students (ages 13-15) with low conceptual understanding in mathematical story problem-solving. Using open-ended questionnaires and reflexive thematic analysis, we explored students’ perceptions and challenges in a private junior high school in West Lombok Regency, Indonesia. Three interconnected themes emerged: (1) Internal Psychological Barriers—mathematics anxiety, fixed mindset beliefs, and internalized failure attributions; (2) Cognitive and Linguistic Challenges—difficulties in text comprehension, mathematical representation, strategic knowledge, and multi-step reasoning; and (3) Glimpses of Interest—unexpected positive affective responses to story contexts despite struggles. Findings reveal that low conceptual understanding is not a unitary cognitive deficit but a complex, multi-dimensional phenomenon involving cognitive, affective, linguistic, and motivational dimensions. Students experience multiple, compounding obstacles while carrying emotional burdens that further impede learning. By centering student voice, this study illuminates subjective realities that quantitative achievement data alone cannot capture. Implications suggest effective interventions must comprehensively address conceptual skills, affective barriers, linguistic demands, and motivation simultaneously. For Indonesian contexts, findings call for reconsidering traditional approaches prioritizing procedural fluency over conceptual understanding and student wellbeing. This research advances phenomenological methodology in mathematics education and provides actionable insights for developing responsive, equity-oriented instruction.
Connection ethnomathematics and ethnomodeling in the bocah sukerta traditional ceremony, Indonesia Sudirman, Sudirman; Bonyah, Ebenezer; Dejarlo, Jenisus O.; Runisah, Runisah; Nandang, Nandang; Rosyadi, Rosyadi; Taufan, Mochammad; Ibrahim, Anzzal
Journal of Education and Learning (EduLearn) Vol 20, No 2: May 2026
Publisher : Intelektual Pustaka Media Utama

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/edulearn.v20i2.21872

Abstract

This research aims to identify and reveal the connection between ethnomathematics and ethnomodeling in Indonesia’s bocah sukerta traditional ceremony. An ethnographic design was used to reveal the research objectives. The participants involved in this research were the ceremony leader and bocah sukerta. Next, the data obtained from interviews and observations were analyzed using the content analysis method. The research results reveal that the ethnomathematics connection is reflected in weighting activities (weighing objects, calculating total weight, making comparisons, and balancing weights) and the shape of the scales (the basic shape represents 2D geometry, and the frame shape represents 3D geometry). This research also concludes that the ethnomodeling connection produces mathematical understanding, especially in arithmetic operations, weight measurements, weight conversions, mathematical equations, basic statistics, Cartesian coordinates, the center point of a square, and determining a pyramid’s distance, length, and area. Furthermore, this research concludes that the relationship between ethnomathematics and ethnomodeling in the bocah sukerta traditional ceremony can be used to construct didactic designs for square material volumes and rectangular pyramids.
Analysis of Students' Mathematical Reasoning in Triangles by Learning Style Preferences Rakha Pradestya; Sudirman Sudirman; Ardi Dwi Susandi
Journal of Instructional Mathematics Vol. 5 No. 2 (2024): Mathematics Education: Psychology, Teaching, Curriculum, and Technology
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v5i2.2120

Abstract

This study analyzes students' mathematical reasoning abilities concerning triangles and special lines, considering their individual learning styles. The qualitative case study was conducted at Khalifah Boarding Junior High School, involving three grade VIII students representing visual, auditory, and kinesthetic learning styles. The selection of these students was based on their learning style preferences identified through a questionnaire. Data collection included mathematical ability tests and interviews, which were then analyzed by triangulating answer sheet observations and interview findings. Initial data revealed a distribution of 50% visual learners, 42% auditory learners, and 8% kinesthetic learners. Subjects were purposively selected based on the highest scores in each learning style group. The subjects demonstrated differences in understanding and approaching problem-solving, influenced by their learning styles. This study highlights specific challenges and recommendations for each subject, emphasizing the importance of a tailored learning approach to improve mathematical understanding and problem-solving skills. The research underscores the significance of recognizing and accommodating diverse learning styles to optimize students' academic achievements in mathematics.
Design of 6E-Instructional Model Assisted by GeoGebra Media in Improving Students' Mathematical Visual Spatial Ability on the Topic of Prism Natan Prasetya; Maximus Gorky Sembiring; Sudirman Sudirman
Journal of Instructional Mathematics Vol. 6 No. 1 (2025): Contemporary Perspectives on Mathematics Teaching, Learning, and Technology
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v6i1.2341

Abstract

Students’ mathematical visual-spatial ability is crucial for understanding geometry. However, its suboptimal level calls for quality learning. The purpose of this study was to test the quality of the Geogebra-assisted 6E-Instructional Model (6E-IM) on students' spatial visual ability; test the effect of Geogebra-assisted 6E-IM on spatial visual ability; and describe students' spatial visual ability after receiving the Geogebra-assisted 6E-IM model. This study used an embedded design. The Geogebra-assisted 6E-IM model (independent variable) was measured through interviews, while spatial visual ability (dependent variable) was assessed using questionnaires. The results showed that the geometry learning instrument with the 6E-IM learning model assisted by Geogebra was in the very good category with a score of 92%, and positively affected students' visual-spatial abilities. Description of students' spatial visual ability involving 2 students in each category, in the high category, met all indicators of spatial visual ability; students with moderate spatial visual ability met two indicators of spatial visual ability; and students with low spatial visual ability met one indicator of spatial visual ability. The results of this study are expected to be Geogebra integrated 6E-IM Design can be used by teachers to improve students' visual spatial abilities.
Development of Problem-Based E-Worksheet Assisted by GeoGebra to Improve Numeracy Literacy and Student Learning Activeness in Junior High School Dyana Astuti; Yumiati; Sudirman
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 10 No 1 (2025): July
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v10i1.6944

Abstract

This research aims to develop a problem-based electronic worksheet (E-Worksheet) assisted by GeoGebra to enhance students' numeracy literacy and learning activeness in junior high school. The development procedure follows the ADDIE model, including analysis, design, development, implementation, and evaluation stages. Validation by experts shows the E-Worksheet is very feasible to use, with an average validation score of 4.46 out of 5. Practicality is confirmed through positive responses from teachers and students, scoring above 4.5. Effectiveness testing through a quasi-experimental design indicates a significant improvement in students’ numeracy literacy and learning activeness when using the developed E-Worksheet compared to the control group. These findings suggest that the developed E-Worksheet can be a valuable learning resource to improve mathematical literacy and student engagement in learning.
The Effectiveness of Differentiated E-LKPD Using Liveworksheets on Junior High School Students’ Statistical Literacy in Data Presentation Sari Muliawanti; Endang Wahyuningrum; Sudirman Sudirman
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 10 No 3 (2026): January
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v10i3.7638

Abstract

Indonesian students’ low statistical literacy, as revealed by PISA 2022 with only 18% achieving Mathematics competency at level 2, presents an urgent educational challenge. The dominant use of printed teaching materials limits students’ digital learning experiences with varying levels of initial understanding. This study developed differentiated E-LKPD (Electronic Student Worksheets) using Liveworksheets on Data Presentation topics through Research and Development with ADDIE model. Participants were 7th grade students of SMP Gunungjati 1 Purwokerto in the 2024/2025 academic year. Data collection instruments included interview instruments, needs analysis questionnaires, validation questionnaires, student response questionnaires, and statistical literacy tests. The product achieved very high validity based on Aiken’s index for content (0.91), media (0.94), and language (0.90). Practicality received 86% with very practical criteria. The product’s effectiveness showed statistical literacy improvement with N-Gain of 0.60 (moderate). The differentiated E-LKPD using Liveworksheets proved valid, practical, and effective in enhancing statistical literacy skills of junior high school students. This digital, interactive approach successfully accommodates diverse student readiness levels, providing an innovative solution for personalized mathematics learning that bridges the gap between traditional instruction and students’ digital learning needs.
Students' mathematical critical thinking skill: An exploration case study when using argumentation-based learning Ardi Dwi Susandi; Sudirman Sudirman
Journal of Advanced Sciences and Mathematics Education Vol. 5 No. 1 (2025): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v%vi%i.547

Abstract

Background: Critical thinking skills are essential in addressing the learning challenges faced by students in the 21st century. To foster these skills effectively, it is necessary to adopt specific instructional approaches that enhance students’ mathematical critical thinking within the classroom setting.Aims: This study aims to investigate students’ critical thinking abilities in mathematics during the implementation of the Argumentation-Based Learning Process (ABLP) in classroom instruction.Methods: A qualitative case study design was employed, involving 30 eighth-grade students from an A-accredited school in Indonesia. Data sources included ABLP-based worksheets, audio recordings of student group discussions, and interview transcripts. The collected data were analyzed using a triangulation strategy to ensure accuracy, and peer reviews were conducted to validate the findings. The analysis focused on identifying indicators of critical thinking skills at each stage of the ABLP model.Results: The results show that students demonstrated various levels of critical thinking throughout the ABLP stages. However, not all students consistently met the predetermined indicators at each stage of the process. Despite these variations, the findings suggest that ABLP can be an effective pedagogical approach to foster students’ critical thinking in mathematics.Conclusion: This study concludes that ABLP offers meaningful opportunities for students to develop critical mathematical thinking and should be considered as a strategy in mathematics instruction.
Geometry from coastal life: A grounded theory of primary students’ 3D geometry understanding in Northern Coastal West Java Endang Wahyuningrum; Sudirman Sudirman; Camilo Andrés Rodríguez-Nieto
Journal of Advanced Sciences and Mathematics Education Vol. 5 No. 2 (2025): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v5i2.813

Abstract

Background: Although three-dimensional (3D) geometry is an essential component of the elementary school mathematics curriculum, research exploring how students develop spatial understanding of 3D geometric objects in authentic learning contexts remains limited. Furthermore, the challenge of bridging visual, verbal, and manipulative representations persists as a major gap in the literature.Aims: This study aims to address this gap by examining the process through which elementary students develop conceptual understanding of 3D geometry using a grounded theory approach.Method: The study was conducted at a public elementary school in Indramayu Regency, West Java, Indonesia. A total of 26 students (20 female and 6 male, aged 11–12) voluntarily participated. Data were collected through 3D geometric visualization tests and in-depth interviews focusing on students' thought processes in imagining, comparing, and manipulating spatial forms. Data analysis followed the three stages of grounded theory methodology: open coding, axial coding, and selective coding, to construct a theory grounded in empirical data.Results: The findings reveal that students’ understanding of 3D volume is still in a transitional stage, moving from concrete experiences to formal mathematical representations. Familiar local contexts alone were found insufficient to bridge spatial understanding without adequate visual and pedagogical support. Major obstacles included conceptual misconceptions, procedural errors, limited visualization skills, and reliance on teacher assistance.Conclusion: The core category, “multiple representations as a bridge to spatial understanding,” underscores the importance of integrating concrete visualization, verbal description, and mathematical symbolism in geometry instruction. This study suggests that teachers should design instructional strategies that systematically combine visual media, concrete manipulatives, and verbal approaches. Such integration is crucial to ensure that local contexts effectively serve as a bridge between real-world experiences and abstract mathematical understanding.
Co-Authors Abubakar, Abdulhalim Aloisius Loka Son Alsulami, Naif Mastoor Andrés Rodríguez-Nieto, Camilo Andriani, Mela Angelia, Inge Ardi Dwi Susandi Arie Purwa Kusuma Baltaeva, Umida Bambang Avip Priatna Martadiputra cakrawala Bayu Jaya Tama Bete, Hendrika Bongani Dhlamini, Zwelithini Bonyah, Ebenezer Camilo Andrés Rodríguez-Nieto Camilo Andrés Rodríguez-Nieto Camilo Andrés Rodríguez-Nieto Damayanti Lestari, Wiwit Dayat Mardiana Dejarlo, Jenisus O. Denni Ismunandar Didik Triyono Dyana Astuti Eko Hartono, Eko Endang Wahyuningrum Erlinda, Rosni Fiki Alghadari Fitriyani Fitriyani García-García, Javier Ginashantika, Evana Gorky Sembiring, Maximus Gunadi, Farid Himphinit, Musakkid Ibrahim, Anzzal Indrawati Indrawati Isnawan, Muhamad Galang Jackson Pasini Mairing, Jackson Pasini Jarnawi Afgani Dahlan Javier García-García Jenisus Dejarlo Jusniani, Nia Kartini Kartini Kartono Kartono Karunia Tumba Sanda Pakabu Khairunnisa, Ika Aulia Khalid, Nursyahidah binti Lily Aulin Assya Linawati Linawati Lukman Nulhakim Luthfiyati Nurafifah Mela Andriani Mery Noviyanti Monike, Rismun Sufia Mustapa, Noviana mustikaningsih, Dian Nandang Nandang Nandang Nasir Nasir Natan Prasetya Nizlel Huda O. Dejarlo, Jenisus Olivero-Acuña, Ronaldo Rafael Pochulu, Marcel David Prasetya, Natan Puspitasari, Kristanti Ambar Rakha Pradestya Rasilah, Rasilah Rauhun, Siti Rizkiah Nurul Fitriani Rodríguez-Nieto, Camilo Andrés Ronaldus Ariyanto Jelahu Rosyadi Rosyadi, Rosyadi Runisah, Runisah Samsul, Bahri Sari Muliawanti Sembiring, Gorky Sembiring, Maximus Gorky Sendi Ramdhani Singh Chauhan, Alok Siti Aisyah Siti Anisa Sri Adi Widodo Susandi, Ardi Syafa&#039;at Ariful Huda Syarah, Erie Siti Taufan, Mochammad Thesa Kandaga Thesa Kandaga Topik Ilham ULFHA RACHMAWATI Yaya Sukjaya Kusumah Yossa Giovani Vianto Yumiati Yumiati