MathVerse M6: Exploring Students’ Mathematical Critical-Thinking Performance in AR–Metaverse-Supported Learning
DOI:
https://doi.org/10.58524/oler.v6i4.1321Keywords:
Augmented Reality, Critical Thinking Sub-skills , Metaverse , M6 Learning Model , TPACKAbstract
Mathematical critical thinking involves distinct reasoning processes that are rarely evaluated separately in immersive technology-supported mathematics. This study aims to develop and formatively assess MathVerse M6 and describe overall and indicator-level change and exploratory phase-linked associations. An educational design research approach included 16 mathematics teachers in preliminary needs analysis and 118 Grade 9 students in a small trial (n = 28) and a large one-group pre–post-test trial (n = 90) across four schools in Cirebon, Indonesia. Three experts rated five artefacts, and classroom implementation and student responses were observed. Mean expert ratings were 3.48–3.82/4. The large-scale mean mathematics score increased from 48 to 82; mastery (score ≥75) increased from 0/90 to 75/90 (83.3%). Inference (+38 percentage points) and analysis (+35) showed the largest descriptive indicator changes; self-regulation (+18) showed the smallest. Previously reported phase and artefact correlations used only six and five aggregate pairs and remain exploratory. MathVerse M6 was judged suitable for trial and showed promising within-group changes, but the absence of a control group, clustered classes, single-item indicators, and inconsistent effect-size reporting preclude causal conclusions.
References
Alfaisal, R., Hashim, H., & Azizan, U. H. (2023). Metaverse system adoption in education: A systematic literature review. Journal of Computers in Education. https://doi.org/10.1007/s40692-022-00256-6
Bertrand, M. G., Sezer, H. B., & Namukasa, I. K. (2024). Exploring AR and VR tools in mathematics education through culturally responsive pedagogies. Digital Experiences in Mathematics Education, 10, 462–486. https://doi.org/10.1007/s40751-024-00152-x
Brianza, E., Schmid, M., Tondeur, J., & Petko, D. (2024). Is contextual knowledge a key component of expertise for teaching with technology? A systematic literature review. Computers and Education Open, 7, Article 100201. https://doi.org/10.1016/j.caeo.2024.100201
Bulut, M., & Borromeo Ferri, R. (2023). A systematic literature review on augmented reality in mathematics education. European Journal of Science and Mathematics Education, 11(3), 556–572. https://doi.org/10.30935/scimath/13124
Çakıroğlu, Ü., Güler, M., Dündar, M., & Coşkun, F. (2023). Virtual reality in realistic mathematics education to develop mathematical literacy skills. International Journal of Human–Computer Interaction, 40(17), 4661–4673. https://doi.org/10.1080/10447318.2023.2219960
Camilleri, M. A. (2024). Metaverse applications in education: A systematic review and a cost-benefit analysis. Interactive Technology and Smart Education, 21(2), 245–269. https://doi.org/10.1108/ITSE-01-2023-0017
Canbaz, B., & Yalçın, N. (2024). The effect of mathematics teaching with mobile augmented reality technology on secondary school students' attitudes and academic achievements. Participatory Educational Research, 11(4), 59–76. https://doi.org/10.17275/per.24.49.11.4
Çeken, B., & Taşkın, N. (2025). Examination of multimedia learning principles in augmented reality and virtual reality learning environments. Journal of Computer Assisted Learning, 41(1), Article e13097. https://doi.org/10.1111/jcal.13097
Chamola, V., Peelam, M. S., Mittal, U., Hassija, V., Singh, A., Pareek, R., Mangal, P., Sangwan, D., de Albuquerque, V. H. C., Mahmud, M., & Brown, D. J. (2025). Metaverse for education: Developments, challenges, and future direction. Computer Applications in Engineering Education, 33(3), Article e70018. https://doi.org/10.1002/cae.70018
Chang, H.-Y., Binali, T., Liang, J.-C., Chiou, G.-L., Cheng, K.-H., Lee, S. W.-Y., & Tsai, C.-C. (2022). Ten years of augmented reality in education: A meta-analysis of (quasi-) experimental studies to investigate the impact. Computers & Education, 191, Article 104641. https://doi.org/10.1016/j.compedu.2022.104641
Coban, M., Bolat, Y. I., & Goksu, I. (2022). The potential of immersive virtual reality to enhance learning: A meta-analysis. Educational Research Review, 36, Article 100452. https://doi.org/10.1016/j.edurev.2022.100452
De Felice, F., Petrillo, A., Iovine, G., Salzano, C., & Baffo, I. (2023). How does the metaverse shape education? A systematic literature review. Applied Sciences, 13(9), Article 5682. https://doi.org/10.3390/app13095682
Erşen, Z. B., & Alp, Y. (2024). A systematic review of augmented reality in mathematics education in the last decade. Malaysian Online Journal of Educational Technology, 12(1), 15–31. https://doi.org/10.52380/mojet.2024.12.1.476
Facione, P. A. (1990). Critical thinking: A statement of expert consensus for purposes of educational assessment and instruction (The Delphi Report). American Philosophical Association.
Feng, S., Xu, X., Li, S., Li, Z., & Gibson, D. (2024). Is metaverse a buzzword in education? Insights from a systematic review. Educational Technology Research and Development, 72, 3349–3390. https://doi.org/10.1007/s11423-024-10398-2
Gómez-Rodríguez, V. (2026). From virtual worlds to real-world equity: A scoping review of the metaverse as computer-assisted learning for STEM competencies. Computers, 15(4), Article 229. https://doi.org/10.3390/computers15040229
Gonnermann-Müller, J., & Krüger, J. M. (2025). Unlocking augmented reality learning design based on evidence from empirical cognitive load studies: A systematic literature review. Journal of Computer Assisted Learning, 41(1), Article e13095. https://doi.org/10.1111/jcal.13095
Hamilton, D., McKechnie, J., Edgerton, E., & Wilson, C. (2021). Immersive virtual reality as a pedagogical tool in education: A systematic literature review of quantitative learning outcomes and experimental design. Journal of Computers in Education, 8, 1–32. https://doi.org/10.1007/s40692-020-00169-2
Hidajat, F. A. (2024). Augmented reality applications for mathematical creativity: A systematic review. Journal of Computers in Education, 11, 991–1040. https://doi.org/10.1007/s40692-023-00287-7
Hidayat, R., Samsudin, S., Wang, X., & Abd Rahman, S. N. (2026). Augmented reality in science, technology, engineering and mathematics education: A meta-analysis. Journal of Computer Assisted Learning, 42(1), Article e70164. https://doi.org/10.1002/jcal.70164
Hwang, G.-J., Chang, C.-Y., & Chang, S.-C. (2024). Promoting students' self-regulated learning with AI-incorporated metacognitive scaffolding in a flipped learning context. British Journal of Educational Technology, 55(1), 210–228. https://doi.org/10.1111/bjet.13384
Hwang, G.-J., Tu, Y.-F., & Chu, H.-C. (2023). Conceptions of the metaverse in higher education: A draw-a-picture analysis and surveys to investigate the perceptions of students with different motivation levels. Computers & Education, 203, Article 104868. https://doi.org/10.1016/j.compedu.2023.104868
İslim, Ö. F., Namlı, Ş., Sevim, N., Özçakır, B., & Lavicza, Z. (2024). Augmented reality in mathematics education: A systematic review. Participatory Educational Research, 11(4), 115–139. https://doi.org/10.17275/per.24.52.11.4
Istiqlal, M., Retnawati, H., Widihastuti, & Sari, D. K. (2026). Assessing students’ computational thinking ability based on mathematical reasoning. Jurnal Ilmiah Peuradeun, 14(2), 773–796. https://doi.org/10.26811/peuradeun.v14i2.1602
Kim, N. J., Belland, B. R., & Axelrod, D. (2024). Adaptive scaffolding, technology, and mathematics learning: A systematic review of the equity implications. Educational Technology Research and Development, 72(1), 89–118. https://doi.org/10.1007/s11423-023-10285-6
Koparan, T., Dinar, H., Koparan, E. T., & Haldan, Z. S. (2023). Integrating augmented reality into mathematics teaching and learning and examining its effectiveness. Thinking Skills and Creativity, 47, Article 101245. https://doi.org/10.1016/j.tsc.2023.101245
Ku, K. Y. L., Kong, Q., Song, Y., Hou, L., Deng, J., & Li, X. (2024). What predicts critical thinking performance? Investigating the role of prior knowledge, epistemological beliefs, and metacognitive self-regulation. Thinking Skills and Creativity, 51, Article 101481. https://doi.org/10.1016/j.tsc.2024.101481
Leppink, J. (2024). Cognitive load theory: Advances and contemporary perspectives. Educational Psychology Review, 36(1), Article 17. https://doi.org/10.1007/s10648-023-09817-6
Li, M., & Yu, Z. (2023). A systematic review on metaverse-based blended English learning. Frontiers in Psychology, 13, Article 1087508. https://doi.org/10.3389/fpsyg.2022.1087508
Maghaydah, S., Al-Emran, M., Maheshwari, P., & Al-Sharafi, M. A. (2024). Factors affecting metaverse adoption in education: A systematic review, adoption framework, and future research agenda. Heliyon, 10(7), Article e28602. https://doi.org/10.1016/j.heliyon.2024.e28602
Mannan, A. M. K., Bajuri, M. R., Abdul Rahim, S. S., & Abdullah, N. A. (2026). How do digital tools support metacognition in mathematics learning? A systematic review of research on GeoGebra and problem-solving. Educational Research Review, 52, Article 100827. https://doi.org/10.1016/j.edurev.2026.100827
Maulida, A. S., Wahyudin, Turmudi, & Nurlaelah, E. (2024). The effect of experiential learning and directed instruction assisted by augmented reality on students' self-regulated learning. Infinity Journal, 13(2), 553–568. https://doi.org/10.22460/infinity.v13i2.p553-568
Miller, M. D., Kong, A., & Oh, J. (2024). Edu-metaverse design: Perspectives of undergraduate learners. Computers & Education: X Reality, 5, Article 100079. https://doi.org/10.1016/j.cexr.2024.100079
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054. https://doi.org/10.1111/j.1467-9620.2006.00684.x
Mishra, P., Warr, M., & Islam, R. (2023). TPACK in the age of ChatGPT and generative AI. Journal of Digital Learning in Teacher Education, 39(4), 235–251. https://doi.org/10.1080/21532974.2023.2247480
Nieveen, N., & Folmer, E. (2013). Formative evaluation in educational design research. In T. Plomp & N. Nieveen (Eds.), Educational design research (pp. 152–169). SLO Netherlands Institute for Curriculum Development.
Onu, P., Pradhan, A., & Mbohwa, C. (2024). Potential to use metaverse for future teaching and learning. Education and Information Technologies, 29, 8893–8924. https://doi.org/10.1007/s10639-023-12167-9
Pereles, A., Ortega-Ruipérez, B., & Lázaro, M. (2024). The power of metacognitive strategies to enhance critical thinking in online learning. Journal of Technology and Science Education, 14(3), 831–843. https://doi.org/10.3926/jotse.2721
Plomp, T. (2013). Educational design research: An introduction. In T. Plomp & N. Nieveen (Eds.), Educational design research (pp. 11–50). SLO Netherlands Institute for Curriculum Development.
Poupard, M., Larrue, F., Sauzéon, H., & Tricot, A. (2025). A systematic review of immersive technologies for education: Learning performance, cognitive load and intrinsic motivation. British Journal of Educational Technology, 56(1), 5–41. https://doi.org/10.1111/bjet.13503
Pradana, M., & Elisa, H. P. (2023). Metaverse in education: A systematic literature review. Cogent Social Sciences, 9(2), Article 2252656. https://doi.org/10.1080/23311886.2023.2252656
Ramadoni, & Adnan, M. (2026). Cross-national effects of a gamified algebra learning intervention: A mixed-design analysis of country and gender differences in Indonesia and Malaysia. Eurasia Journal of Mathematics, Science and Technology Education, 22(5), Article em2829. https://doi.org/10.29333/ejmste/16199
Risdianto, E., Wachidi, W., Riyanto, R., Fathurochman, I., Yanto, M., & Asmara, A. (2022). Feasibility test of learning media with blended learning model and augmented reality-assisted MOOCs. Jurnal Ilmiah Peuradeun, 10(1), 149–164. https://doi.org/10.26811/peuradeun.v10i1.626
Romero-Saritama, J. M., Espinosa-Tapia, S., & Palacios-Rodríguez, A. (2025). Using WhatsApp in distance education: Assessing the impact on academic interaction and influencing factors. Social Sciences, 14(3), Article 183. https://doi.org/10.3390/socsci14030183
Sakr, A., & Abdullah, T. (2024). Virtual, augmented reality and learning analytics impact on learners, and educators: A systematic review. Education and Information Technologies, 29, 19913–19962. https://doi.org/10.1007/s10639-024-12602-5
Schmid, M., Brianza, E., Mok, S. Y., & Petko, D. (2024). Running in circles: A systematic review of reviews on technological pedagogical content knowledge (TPACK). Computers & Education, 214, Article 105024. https://doi.org/10.1016/j.compedu.2024.105024
Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd ed.). SAGE.
Soebagyo, J., Usman, H., & Tambak, S. (2023). Digital divide and technology integration in Indonesian mathematics classrooms: A nationwide survey. Journal on Mathematics Education, 14(4), 611–632. https://doi.org/10.22342/jme.v14i4.pp611-632
Susandi, A. D., Sa'dijah, C., As'ari, A. R., & Susiswo. (2022). Developing the M6 learning model to improve mathematical critical thinking skills. Pedagogika, 145(1), 182–204. https://doi.org/10.15823/p.2022.145.11
Susandi, A. D., Sa’dijah, C., & Susiswo, S. (2026). Improving critical thinking skills in mathematics: Implementation of the M6 learning model. Pedagogical Research, 11(3), Article em0271. https://doi.org/10.29333/pr/18773
Umam, K., & Susandi, A. D. (2022). Critical thinking skills: Error identifications on students with APOS theory. International Journal of Evaluation and Research in Education, 11(1), 182–192. https://doi.org/10.11591/ijere.v11i1.22048
Vegas, S. O., & Djukri. (2021). The effect of problem-based learning on the critical thinking skill of the students. Jurnal Ilmiah Peuradeun, 9(1), 221–240. https://doi.org/10.26811/peuradeun.v9i1.411
Walkington, C., Nathan, M. J., Hunnicutt, J., Washington, J., & Zhou, M. (2024). New kinds of embodied interactions that arise in augmented reality dynamic geometry software. The Journal of Mathematical Behavior, 75, Article 101175. https://doi.org/10.1016/j.jmathb.2024.101175
Walkington, C., Nathan, M. J., Washington, J., Hunnicutt, J., Darwin, T., Daughrity, L., & Schenck, K. (2025). Comparing learning geometry using a tablet to head-mounted display augmented reality: How and when dimensionality matters. Education and Information Technologies, 30, 5397–5426. https://doi.org/10.1007/s10639-024-13008-z
Walkington, C., Washington-Henderson, J., Hunnicutt, J., & Nathan, M. J. (2026). The impact of different collaboration formats on mathematical problem-solving in augmented reality. Computers & Education, 242, Article 105491. https://doi.org/10.1016/j.compedu.2025.105491
Wang, Q., & Abdullah, A. H. (2024). Enhancing students' critical thinking through mathematics in higher education: A systematic review. SAGE Open, 14(3), 1–15. https://doi.org/10.1177/21582440241274007
Wang, X., Liu, Q., Pang, H., Lv, Z., Sun, D., Chen, W., & Cheng, B. (2023). What matters in the design of game-based learning for mathematics? A meta-analysis on learning achievement and motivation in China. Computers & Education, 195, Article 104718. https://doi.org/10.1016/j.compedu.2023.104718
Wang, Y., Wang, H., Wang, S., Wind, S. A., & Gill, C. (2024). A systematic review and meta-analysis of self-determination-theory-based interventions in the education context. Learning and Motivation, 87, Article 102015. https://doi.org/10.1016/j.lmot.2024.102015
Won, M., Ungu, D. A. K., Matovu, H., Treagust, D. F., Tsai, C.-C., Park, J., Mocerino, M., & Tasker, R. (2023). Diverse approaches to learning with immersive virtual reality identified from a systematic review. Computers & Education, 195, Article 104701. https://doi.org/10.1016/j.compedu.2022.104701
Wu, J., Jiang, H., Long, L., & Zhang, X. (2024). Effects of AR mathematical picture books on primary school students' geometric thinking, cognitive load and flow experience. Education and Information Technologies, 29, 24627–24652. https://doi.org/10.1007/s10639-024-12768-y
Xie, J., Al-Shaibani, G. K. S., Zhao, J., & Talib, O. (2025). The current status and contributing factors of the metaverse adoption in education: A systematic review. Contemporary Educational Technology, 17(4), Article ep593. https://doi.org/10.30935/cedtech/17301
Zapata-Rodríguez, M., Ramos-Galarza, C., Valencia-Aragón, K., & Guachi, L. (2024). Enhancing mathematics learning with 3D augmented reality escape room. International Journal of Educational Research Open, 7, Article 100389. https://doi.org/10.1016/j.ijedro.2024.100389
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