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Mathematics Education in the Age of Artificial Intelligence pp 343–363Cite as

Exploring Dynamic Geometry Through Immersive Virtual Reality and Distance Teaching

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Part of the Mathematics Education in the Digital Era book series (MEDE,volume 17)

Abstract

Virtual reality provides an interesting environment to teach and learn 3D geometry. In this article, we discuss the use of Neotrie VR as a 3D whiteboard for distance teaching that we have carried out during the 2020–21 academic year, with students of the Mathematics degree at the University of Almería. We describe a concrete case on parametric equations of surfaces, for which a 3D graphing calculator has been implemented, as well as a stereoscopic view camera to show 3D videos, which the students can view with cheap stereoscopic glasses for mobile phones. From the side of the teacher, it is certainly much easier to explain 3D concepts on a 3D whiteboard like Neotrie than to use paper and pencil, blackboard, or any 2D digital tablet. Student feedback is also analyzed after using various supports for manipulating and observing learning, including GeoGebra, which can also serve to know how to use virtual reality for distance learning.

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Notes

  1. 1.

    https://www.GeoGebra.org.

  2. 2.

    https://grib3d.com.

  3. 3.

    https://shapes.learnteachexplore.com.

  4. 4.

    See for instance the project Holo-Math (https://holo-math.org/) to application in mathematics.

  5. 5.

    https://4dtoys.com.

  6. 6.

    http://www.scientix.eu/projects/project-detail?articleId=689498.

  7. 7.

    http://www2.ual.es/neotrie.

  8. 8.

    https://www.youtube.com/watch?v=SVYH6pgOr10.

  9. 9.

    https://topologia.wordpress.com.

  10. 10.

    https://youtu.be/aTFu6RqC2ZQ.

  11. 11.

    https://youtu.be/2irYPYOCkr4.

  12. 12.

    https://youtu.be/oq4Xk99Sa64.

  13. 13.

    https://youtu.be/rlbr-s0wg4M.

  14. 14.

    https://youtu.be/ALr5DdcAvYY.

  15. 15.

    http://www2.ual.es/neotrie/project/introduccion-a-la-topologia-algebraica.

  16. 16.

    https://engagevr.io.

  17. 17.

    https://www.youtube.com/watch?v=_T2-9MwA5JI.

  18. 18.

    Geometric artwork in augmented and virtual realityhttps://www.antonbakker.com/momath.

References

  • Cangas, D., Crespo, D., Rodríguez, J. L., & Zarauz, A. (2019a). Neotrie VR: Nueva geometría en realidad virtual. Pi-InnovaMath, 2, 1–8.

    Google Scholar 

  • Cangas, D., Morga, G., & Rodríguez, J. L. (2019b). Geometric teaching experience with Neotrie VR. Psychology, Society, & Education, 11(3), 355–366.

    Google Scholar 

  • Chavil, D. Y., Rodríguez, J. L., & Romero, M. I. (2020). Introducción al concepto de fractal en enseñanza secundaria usando realidad virtual inmersiva. Desde Sur Rev Cienc Hum Soc, 12, 615–629.

    Google Scholar 

  • Bambury, S. (2021). Immersive Tech For Distance. Learning pt. 1. https://www.virtualiteach.com/post/immersive-tech-for-distance-learning-pt-1. Cited February 17, 2021.

  • Codina, A., & Morales C. (2020). Cognición y metacognición en geometría con realidad virtual utilizando Neotrie VR. Investigación en didáctica de la matemática, homenaje a Encarnación Castro, Editorial Octaedro 2020 (pp. 155–178).

    Google Scholar 

  • Dalgarno, B., & Lee, M. (2010). What are the learning affordances of 3-D virtual environments? British Journal of Educational Technologies, 41(1, Special Issue: Crossing Boundaries: Learning and Teaching in Virtual Worlds), 10–32.

    Google Scholar 

  • Derks, L. (2020). How to explain virtual reality. https://ictlaurens.medium.com/how-to-explain-virtual-reality-415c2dc89277. Cited November 4th, 2020.

  • Dimmel, J., & Bock, C. (2019). Dynamic mathematical figures with immersive spatial displays: The case of handwaver. In G. Aldon & J. Trgalová (Eds.), Technology in mathematics teaching. Mathematics Education in the Digital Era (Vol. 13). Cham: Springer.

    Google Scholar 

  • Duval, R. (2021). Registres de représentations sémiotique et fonctionnement cognitif de la pensée. In Annales de Didactique et de Sciences Cognitives (Vol. 5, pp. 37–65). IREM de Strasbourg, France.

    Google Scholar 

  • Extremera, J., Vergara, D., Dávila, L. P., & Rubio, M. P. (2021). Virtual and augmented reality environments to learn the fundamentals of crystallography. Crystals, 10(6), 456, 1–18.

    Google Scholar 

  • Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415.

    CrossRef  Google Scholar 

  • Gálvez, J. F., & y Rodríguez, J. L. (2019). Manipulación y clasificación de superficies compactas. Bubok Publishing SL.

    Google Scholar 

  • Hart, V., Hawksley, A., Matsumoto, E., & Segerman, H. (2017). Non-euclidean virtual reality I: Explorations of \(H^3\). In Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Culture (pp. 33–40) Waterloo, Canada.

    Google Scholar 

  • Hawkins, A., & Sinclair, N. (2008). Explorations with sketchpad in topogeometry. The International Journal of Computer Mathematics, 13, 71–82.

    Google Scholar 

  • Jang, S., Vitale, J. M., Jyung, R. W., & Black, J. B. (2017). March). Direct manipulation is better than passive viewing for learning anatomy in a three-dimensional virtual reality environment. Computers & Education, 106, 150–165.

    CrossRef  Google Scholar 

  • Kaufmann, H., Schmalstieg, D., & Wagner, M. (2000). Construct3D: A virtual reality application for mathematics and geometry education. Education and Information Technologies, 5, 263–276.

    CrossRef  Google Scholar 

  • Kaufmann, H. (2009). Virtual environments for mathematics and geometry education. Themes in Science and Technology Education, 2(1), 131–152.

    Google Scholar 

  • Kosniowski, C. (1980). A first course in algebraic topology. Cambridge University Press, (first printed version, 1980; online publication 2010). https://doi.org/10.1017/CBO9780511569296.

  • Ng, O., & Sinclair, N. (2018). Drawing in space: Doing mathematics with 3D pens. In L. Ball, P. Drijvers, S. Ladel, H.-S. Siller, M. Tabach, & C. Vale (Eds.), Uses of technology in primary and secondary mathematics education (pp. 301–313). Cham: Springer.

    CrossRef  Google Scholar 

  • Prodromou, T. (Ed.). (2020). Augmented reality in educational settings. Leiden Boston: Brill Sense.

    Google Scholar 

  • Radiantia, J., Majchrzaka, T.A., Frommb, J., & Wohlgenannt, I. (2020). A systematic review of immersive virtual reality applications for higher education: Design elements, lessons learned, and research agenda. Computer & Education, 147.

    Google Scholar 

  • Rodríguez J. A., & Romero, M. I. (2019). Optimización de superficies a partir de un volumen dado mediante realidad: una experiencia en \(6^\circ \) de Primaria. Actas del Congreso Innovación y tecnología en contextos educativos, UmaEditorial (pp. 583–593).

    Google Scholar 

  • Rodríguez, J. L., Romero, I., & Codina, A. (2021). The Influence of NeoTrie VR’s immersive virtual reality on the teaching and learning of geometry. Mathematics, 9, 2411. https://doi.org/10.3390/math9192411.

  • Sánchez, C. (2020). Visualización y tratamiento de gráficas 3D en Neotrie VR, final degree project, Universidad de Almería.

    Google Scholar 

  • Sinclair, N., Bartolini, B., Maria, G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM Mathematics Education, 48, 691–719.

    CrossRef  Google Scholar 

  • Song, K. S., & Lee, W. Y. (2002). A virtual reality application for geometry classes. Journal of Computer Assisted Learning, 18, 149–156.

    CrossRef  Google Scholar 

  • Weeks. J. (2001). Exploring the shape of space (2001) and the Jeffrey Weeks’ geometry and topology website. http://www.geometrygames.org/.

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Acknowledgements

To Diego Cangas for the daily technical support, and to the members of the Neotrie project, who with their contributions are enriching the software to make it more useful and interesting to teach geometry. Special thanks to Isabel Romero for the accurate improvements made in all the revisions of this work, as well as the effort and substantial changes proposed by  the referees. The author was partially funded by the Ministry of Science and Innovation grant PID2020-117971GB-C22 and FEDER-Junta de Andalucía grant UAL2020-SEJ-B2086.

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Authors and Affiliations

  1. Universidad de Almería, ES -04120 La Cañada de San Urbano, Almería, Spain

    José L. Rodríguez

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  1. José L. Rodríguez
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Correspondence to José L. Rodríguez .

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Editors and Affiliations

  1. Département de didactique, Université de Montréal, Montréal, QC, Canada

    Philippe R. Richard

  2. Departamento de Ingeniería Industrial, Universidad Antonio de Nebrija, Madrid, Spain

    M. Pilar Vélez

  3. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

    Prof. Steven Van Vaerenbergh

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Rodríguez, J.L. (2022). Exploring Dynamic Geometry Through Immersive Virtual Reality and Distance Teaching. In: Richard, P.R., Vélez, M.P., Van Vaerenbergh, S. (eds) Mathematics Education in the Age of Artificial Intelligence. Mathematics Education in the Digital Era, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-86909-0_15

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