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Observing Mathematical Properties in the Virtual World: An Exploratory Study of Online Independent Learning of Locus Concepts

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Abstract

In the post-pandemic world, metaverse technology has become a popular approach to facilitating students’ online learning experiences. Drawing on Kolb’s experiential learning theory, we created immersive scenes using CoSpaces Edu, a ‘mirror-world’ metaverse platform that enables students to observe mathematical properties virtually. We applied a quasi-experimental design and evaluated the effect of integrating these virtual experiences into our learning resources. Students in the control group used conventional resources created using GeoGebra, which allowed them to manipulate mathematical objects and observe the locus of moving points. For the experimental group, in addition to the GeoGebra resources, we incorporated scenes (e.g., scenarios featuring running dogs) via CoSpaces Edu, which enabled the students to observe mathematical properties virtually online. The post-test results demonstrated that the students in the experimental group (N = 28) performed better than those in the control group (N = 35). The virtual world, which offered immersive walk-through experiences and different perspectives, enhanced the students’ understanding of locus concepts. However, some students encountered technical issues during their online learning, which may have hindered their mathematical exploration. This study contributes to the application of experiential learning theory using metaverse tools, thus offering educators valuable insights into creating immersive environments for online mathematics instruction.

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References

  • Albus, P., Vogt, A., & Seufert, T. (2021). Signaling in virtual reality influences learning outcome and cognitive load. Computers & Education, 166, 104154.

    Article  Google Scholar 

  • Bhatia, S., Björling, E. A., & Budhiraja, T. (2021). Exploring web-based VR for participatory robot design. In C. Bethel & A. Paiva (Eds.), Proceedings of Companion of the 2021 ACM/IEEE International Conference on Human-Robot Interaction (pp. 109–112). ACM. https://doi.org/10.1145/3434074.3447139

  • Bock, C. G., & Dimmel, J. K. (2021). Digital representations without physical analogues: A study of body-based interactions with an apparently unbounded spatial diagram. Digital Experiences in Mathematics Education, 7(2), 193–221.

    Article  Google Scholar 

  • Bozkurt, A., Jung, I., **ao, J., Vladimirschi, V., Schuwer, R., Egorov, G., Lambert, S. R., Al-Freih, M., Pete, J., Olcott Jr., D., Rodes, V., Aranciaga, I., Bali, M., Alvarez Jr., A. V., Roberts, J., Pazurek, A., Raffaghelli, J. E., Panagiotou, N., de Coëtlogon, P., ... & Paskevicius, M. (2020). A global outlook to the interruption of education due to COVID-19 pandemic: Navigating in a time of uncertainty and crisis. Asian Journal of Distance Education, 15(1), 1–126.

  • Bugler, D., Marple, S., Burr, E., Chen-Gaddini, M., & Finkelstein, N. (2017). How teachers judge the quality of instructional materials. WestEd. https://www.wested.org/wp-content/uploads/2017/03/resource-selecting-instructional-materials-brief-1-quality.pdf

  • Cao, Y., Zhang, S., Chan, M. C. E., & Kang, Y. (2021). Post-pandemic reflections: Lessons from Chinese mathematics teachers about online mathematics instruction. Asia Pacific Education Review, 22, 157–168.

    Article  Google Scholar 

  • Cowin, J. B. (2020). Digital worlds and transformative learning: Google Expeditions, Google Arts and Culture, and the Merge Cube. International Research and Review, 10(1), 42–53.

    Google Scholar 

  • Curriculum Development Council. (2017). Supplement to mathematics education key learning area curriculum guide: Learning content of senior secondary mathematics. Education Bureau.

    Google Scholar 

  • Dimmel, J., & Bock, C. (2017). HandWaver: A gesture-based virtual mathematical making environment. In G. Aldon & J. Trgalová (Eds.), Proceedings of the 13th International Conference on Technology in Mathematics Teaching (pp. 323–330). The Ecole Normale Supérieure de Lyon and the University Lyon 1. https://ictmt13.sciencesconf.org/140840/DimmelBock2017_Final.pdf

  • Eldh, A. C., Årestedt, L., & Berterö, C. (2020). Quotations in qualitative studies: Reflections on constituents, custom, and purpose. International Journal of Qualitative Methods, 19, 1–6.

    Article  Google Scholar 

  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). Sage.

    Google Scholar 

  • Fromm, J., Radianti, J., Wehking, C., Stieglitz, S., Majchrzak, T. A., & vom Brocke, J. (2021). More than experience? On the unique opportunities of virtual reality to afford a holistic experiential learning cycle. The Internet and Higher Education, 50, 100804.

    Article  Google Scholar 

  • Ghosheh Wahbeh, D., Burgos, D., & Affouneh, S. (2023). Adopting the GHOSHEH model to create innovative open educational resources based on Rogers’ process for diffusion of innovations. Sustainability, 15, 5427.

    Article  Google Scholar 

  • Hew, K. F., Huang, W., Du, J., & Jia, C. (2021). Using chatbots in flipped learning online sessions: Perceived usefulness and ease of use. In R. Li, S. K. S. Cheung, C. Iwasaki, L. F. Kwok, & M. Kageto (Eds.), Blended learning: Re-thinking and re-defining the learning process (pp. 164–175). Springer.

    Chapter  Google Scholar 

  • HKEAA. (2021). Mathematics (Compulsory Part): 2021 HKDSE Question Papers (with Marking Schemes and Comments on Candidates’ Performance). Hong Kong Examinations and Assessment Authority.

    Google Scholar 

  • Huang, R., Tlili, A., Chang, T. W., Zhang, X., Nascimbeni, F., & Burgos, D. (2020). Disrupted classes, undisrupted learning during COVID-19 outbreak in China: Application of open educational practices and resources. Smart Learning Environments, 7, Article 19.

    Article  Google Scholar 

  • Hwang, G. J., & Chien, S. Y. (2022). Definition, roles, and potential research issues of the metaverse in education: An artificial intelligence perspective. Computers and Education: Artificial Intelligence, 3, 100082.

    Google Scholar 

  • Jiang, M. Y. C., Jong, M. S. Y., Lau, W. W. F., Chai, C. S., Liu, K. S. X., & Park, M. (2022). A sco** review on flipped classroom approach in language education: Challenges, implications and an interaction model. Computer Assisted Language Learning, 35(5–6), 1218–1249.

    Article  Google Scholar 

  • Jost, P., Cobb, S., & Hämmerle, I. (2020). Reality-based interaction affecting mental workload in virtual reality mental arithmetic training. Behaviour & Information Technology, 39(10), 1062–1078.

    Article  Google Scholar 

  • Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development. Prentice-Hall.

    Google Scholar 

  • Kye, B., Han, N., Kim, E., Park, Y., & Jo, S. (2021). Educational applications of metaverse: Possibilities and limitations. Journal of Educational Evaluation for Health Professions, 18, 32.

    Article  Google Scholar 

  • Lee, H., & Hwang, Y. (2022). Technology-enhanced education through VR-making and metaverse-linking to foster teacher readiness and sustainable learning. Sustainability, 14, 4786.

    Article  Google Scholar 

  • Lo, C. K. (2023). Strategies for enhancing online flipped learning: A systematic review of empirical studies during the COVID-19 pandemic. Interactive Learning Environments. https://doi.org/10.1080/10494820.2023.2184392

  • Lo, C. K., & Hew, K. F. (2021). Develo** a flipped learning approach to support student engagement: A design‐based research of secondary school mathematics teaching. Journal of Computer Assisted Learning, 37(1), 142–157.

  • Lo, C. K., Cheung, K. L., Chan, H. R., & Chau, C. L. E. (2023). Develo** flipped learning resources to support secondary school mathematics teaching during the COVID-19 pandemic. Interactive Learning Environments, 31(8), 4787–4805.

  • Morris, T. H. (2020). Experiential learning – A systematic review and revision of Kolb’s model. Interactive Learning Environments, 28(8), 1064–1077.

    Article  Google Scholar 

  • Ng, D. T. K. (2022). What is the metaverse? Definitions, technologies and the community of inquiry. Australasian Journal of Educational Technology, 38(4), 190–205.

  • Ng, D. T. K., Ng, R. C. W., & Chu, S. K. W. (2023). Engaging students in virtual tours to learn language and digital literacy. Journal of Computers in Education, 10(3), 575–602.

  • Nili, A., Tate, M., Barros, A., & Johnstone, D. (2020). An approach for selecting and using a method of inter-coder reliability in information management research. International Journal of Information Management, 54, 102154.

    Article  Google Scholar 

  • Papadakis, S., Zourmpakis, A. I., & Kalogiannakis, M. (2023). Analyzing the impact of a gamification approach on primary students’ motivation and learning in science education. In M. E. Auer, W. Pachatz, & T. Rüütmann (Eds.), Learning in the age of digital and green transition. ICL 2022. Lecture notes in networks and systems (Vol. 633, pp. 701–711). Cham: Springer. https://doi.org/10.1007/978-3-031-26876-2_66

  • ** Por, F., Tsong Chau, K., Leng Chew, B., & Leong, Y. K. (2020). Think e-reader: Pedagogy-led open educational resources for metacognitive comprehension skills. In N. Baba Rahim (Ed.), Multidisciplinary research as agent of change for industrial revolution 4.0 (Vol. 81, pp. 419–430). European Publisher.

  • Radović, S., Radojičić, M., Veljković, K., & Marić, M. (2020). Examining the effects of GeoGebra applets on mathematics learning using interactive mathematics textbook. Interactive Learning Environments, 28(1), 32–49.

    Article  Google Scholar 

  • Roy, K., & Verma, P. (2020). Effectiveness of peer assisted learning strategies in solving mathematical word problems. Indian Journal of Mental Health, 7(4), 364–369.

    Google Scholar 

  • Schott, C., & Marshall, S. (2018). Virtual reality and situated experiential education: A conceptualization and exploratory trial. Journal of Computer Assisted Learning, 34(6), 843–852.

    Article  Google Scholar 

  • Stern, J., & Piper, B. (2019). Resetting targets: Examining large effect sizes and disappointing benchmark progress. RTI Press.

    Book  Google Scholar 

  • Stracke, C. M., Sharma, R. C., Bozkurt, A., Burgos, D., Swiatek Cassafieres, C., Inamorato dos Santos, A., Mason, J., Ossiannilsson, E., Santos-Hermosa, E., Shon, J. G., Wan, M., Agbu, J.-F. O., Farrow, R., Karakaya, Ö., Nerantzi, C., Ramírez-Montoya, M. S., Conole, G., Truong, V., & Cox, G. (2022). Impact of COVID-19 on formal education: An international review of practices and potentials of open education at a distance. International Review of Research in Open and Distributed Learning, 23(4), 1–18.

  • Szeto, E. (2015). Community of Inquiry as an instructional approach: What effects of teaching, social and cognitive presences are there in blended synchronous learning and teaching? Computers & Education, 81, 191–201.

    Article  Google Scholar 

  • Tlili, A., Huang, R., Chang, T. W., Nascimbeni, F., & Burgos, D. (2019). Open educational resources and practices in China: A systematic literature review. Sustainability, 11, 4867.

    Article  Google Scholar 

  • Trudeau, A. A. (2020). Virtual reality: Opening doorways to experiential learning for students. In Proceedings of 2020 Seventh International Conference on Information Technology Trends (ITT) (pp. 80–82). IEEE. https://doi.org/10.1109/ITT51279.2020.9320874

  • Turgut, M. (2022). Reinventing geometric linear transformations in a dynamic geometry environment: Multimodal analysis of student reasoning. International Journal of Science and Mathematics Education, 20, 1203–1223.

    Article  Google Scholar 

  • Valero-Franco, C., & Berns, A. (2023). A virtual reality app created with CoSpaces: Student perceptions and attitudes. In M. Bowdon, K. Yee, & W. Dorner (Eds.), Ethical considerations of virtual reality in the college classroom: Cross-disciplinary case studies of immersive technology implementation (pp. 164–179). Routledge.

    Chapter  Google Scholar 

  • Vidergor, H. E., & Ben-Amram, P. (2020). Khan academy effectiveness: The case of math secondary students’ perceptions. Computers & Education, 157, 103985.

    Article  Google Scholar 

  • Weinhandl, R., Lavicza, Z., Hohenwarter, M., & Schallert, S. (2020). Enhancing flipped mathematics education by utilising GeoGebra. International Journal of Education in Mathematics, Science and Technology, 8(1), 1–15.

    Article  Google Scholar 

  • Wollny, S., Schneider, J., Di Mitri, D., Weidlich, J., Rittberger, M., & Drachsler, H. (2021). Are we there yet? A systematic literature review on chatbots in education. Frontiers in Artificial Intelligence, 4, 654924.

    Article  Google Scholar 

  • Yohannes, A., & Chen, H. L. (2023). GeoGebra in mathematics education: A systematic review of journal articles published from 2010 to 2020. Interactive Learning Environments, 31(9), 5682–5697.

    Article  Google Scholar 

  • Zhai, X. (2021). Advancing automatic guidance in virtual science inquiry: From ease of use to personalization. Educational Technology Research and Development, 69(1), 255–258.

    Article  Google Scholar 

  • Zourmpakis, A. I., Papadakis, S., & Kalogiannakis, M. (2022). Education of preschool and elementary teachers on the use of adaptive gamification in science education. International Journal of Technology Enhanced Learning, 14(1), 1–16.

    Article  Google Scholar 

  • Zourmpakis, A. I., Kalogiannakis, M., & Papadakis, S. (2023). A review of the literature for designing and develo** a framework for adaptive gamification in physics education. In M. F. Taşar, & P. R. L. Heron (Eds.), The international handbook of physics education research: Teaching physics (pp. 5–1–5–26). Melville, NY: AIP Publishing. https://doi.org/10.1063/9780735425712_005

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Acknowledgements

We would like to express our gratitude to Hiu Laam Naomi Lee and her team for creating the CoSpaces Edu resources.

Funding

The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. EdUHK 28604623) and by Department of Mathematics and Information Technology (Departmental Research Grant; MIT/DRG01/23–24), The Education University of Hong Kong.

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, The Education University of Hong Kong, Hong Kong, China

    Chung Kwan Lo & Fletcher Ng

  2. Faculty of Education, The University of Hong Kong, Hong Kong, China

    Davy Tsz Kit Ng

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  1. Chung Kwan Lo
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  2. Davy Tsz Kit Ng
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Contributions

All authors contributed to the study conception and design, material preparation, data collection and analysis. The first draft of the manuscript was written by Chung Kwan Lo and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Chung Kwan Lo.

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Ethical Approval and Consent to Participate.

The participants have been well informed about the research purpose and methods. The study has obtained approval of the university’s ethics application committee. The approval has been obtained from school and students via consent form.

Conflict of Interest

The authors declared there is no conflict of interest.

Appendix

Appendix

Table

Table 6 Comparison of the learning activities in CoSpaces Edu and GeoGebra
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6

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Lo, C.K., Ng, D.T.K. & Ng, F. Observing Mathematical Properties in the Virtual World: An Exploratory Study of Online Independent Learning of Locus Concepts. Int J of Sci and Math Educ (2024). https://doi.org/10.1007/s10763-024-10466-2

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