Abstract
Mathematical experiences are intrinsic to our everyday lives, yet mathematics education is mostly confined to textbooks. Seymour Papert used the term ‘Mathland’ to propose a world where one would learn mathematics as naturally as one learns French while growing up in France. We built a Mixed Reality application that augments the physical world with interactive mathematical concepts to enable constructionist mathematical learning in the real world. Using Mathland, people can collaboratively explore, experience and experiment with mathematical phenomena in playful, applied and exploratory ways. We implemented Mathland using the Microsoft Hololens and two custom controllers to afford complete immersion through tangible interactions, embodiment and situated learning. Our preliminary study with 30 participants shows that a considerable percentage of participants found Mathland to not only be engaging (83%), but also efficacious in the areas of collaborative learning (92.8%), problem solving (96.6%) and mathematics education (90%).
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References
Lyons, I.M., Beilock, S.L.: Mathematics anxiety: separating the math from the anxiety. Cereb. Cortex. 22, 2102–2110 (2012)
Chang, H., Beilock, S.L.: The math anxiety-math performance link and its relation to individual and environmental factors: a review of current behavioral and psychophysiological research. Curr. Opin. Behav. Sci. 10, 33–38 (2016)
Ellis, J., Fosdick, B.K., Rasmussen, C.: Women 1.5 times more likely to leave STEM pipeline after calculus compared to men: lack of mathematical confidence a potential culprit. PLoS One 11, e0157447 (2016)
Weeden, K.A., Thébaud, S., Gelbgiser, D.: Degrees of difference: gender segregation of US doctorates by field and program prestige. Sociol. Sci. 4, 123–150 (2017)
Maloney, E.A., Beilock, S.L.: Math anxiety: who has it, why it develops, and how to guard against it. Trends Cogn. Sci. 16, 404–406 (2012)
Beilock, S.L., Willingham, D.T.: Math anxiety: can teachers help students reduce it? Ask the cognitive scientist. Am. Educ. 38, 28 (2014)
Dowker, A., Sarkar, A., Looi, C.Y.: Mathematics anxiety: what have we learned in 60 years? Front. Psychol. 7, 508 (2016)
Perkins, D.: The many faces of constructivism. Educ. Leadersh. 57, 6–11 (1999)
Papert, S.: Mindstorms: Children, Computers, and Powerful Ideas. Basic Books Inc., New York (1980)
National Research Council: Everybody Counts: A Report to the Nation on the Future of Mathematics Education (1989)
Draper, R.J.: School mathematics reform, constructivism, and literacy: a case for literacy instruction in the reform-oriented math classroom. J. Adolesc. Adult Lit. 45, 520–529 (2002)
Papert, S., et al.: Logo Philosophy and Implementation. Logo Computer Systems Inc., Boston (1999)
Chi, M.T.H., Feltovich, P.J., Glaser, R.: Categorization and representation of physics problems by experts and novices. Cogn. Sci. 5, 121–152 (1981)
Belcher, J.: From the mind’s eye to 3D animation: teaching electromagnetism with learning technology. Last Retrieved August 1, 2003 (2003)
Victor, B.: Kill Math. http://worrydream.com/KillMath/
Cordova, D.I., Lepper, M.R.: Intrinsic motivation and the process of learning: beneficial effects of contextualization, personalization, and choice. J. Educ. Psychol. 88, 715 (1996)
Stock, P.: Armadillo Run. https://www.armadillorun.com/
Lee, K.: Augmented reality in education and training. TechTrends 56, 13–21 (2012)
Salzman, M.C., Loftin, R.B., Dede, C., McGlynn, D.: ScienceSpace: lessons for designing immersive virtual realities. In: Conference Companion on Human Factors in Computing Systems, pp. 89–90. ACM (1996)
Fantastic Contraption. http://fantasticcontraption.com/
Kaufmann, H.: Construct3D: an augmented reality application for mathematics and geometry education. In: Proceedings of the Tenth ACM International Conference on Multimedia, pp. 656–657. ACM (2002)
Shapiro, L.: Embodied Cognition. Routledge, Abingdon (2010)
Anderson, J.R., Reder, L.M., Simon, H.A.: Situated learning and education. Educ. Res. 25, 5–11 (1996)
Lakoff, G., Núñz, R.: Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being. Basic Books, New York (2000)
Goldin-Meadow, S., Cook, S.W., Mitchell, Z.A.: Gesturing gives children new ideas about math. Psychol. Sci. 20, 267–272 (2009)
Abrahamson, D., Gutiérrez, J., Charoenying, T., Negrete, A., Bumbacher, E.: Fostering hooks and shifts: tutorial tactics for guided mathematical discovery. Technol. Knowl. Learn. 17, 61–86 (2012)
Zuckerman, O., Arida, S., Resnick, M.: Extending tangible interfaces for education: digital montessori-inspired manipulatives. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 859–868. ACM, New York (2005)
Bujak, K.R., Radu, I., Catrambone, R., MacIntyre, B., Zheng, R., Golubski, G.: A psychological perspective on augmented reality in the mathematics classroom. Comput. Educ. 68, 536–544 (2013)
Schmalstieg, D., Fuhrmann, A., Hesina, G., Szalavári, Z., Encarnaçao, L.M., Gervautz, M., Purgathofer, W.: The studierstube augmented reality project. Presence: Teleoper. Virtual Environ. 11, 33–54 (2002)
Slater, M., Wilbur, S.: A framework for immersive virtual environments five: speculations on the role of presence in virtual environments. Presence: Teleoper. Virtual Environ. 6, 603–616 (1997)
Kim, Y., Park, N.: Elementary education of creativity improvement using Rube Goldberg’s invention. In: Park, J., Kim, J., Zou, D., Lee, Y. (eds.) Information Technology Convergence, Secure and Trust Computing, and Data Management. LNEE, vol. 180, pp. 257–263. Springer, Heidelberg (2012). https://doi.org/10.1007/978-94-007-5083-8_32
Wolfe, M.F., Goldberg, R.: Rube Goldberg: Inventions! Simon and Schuster, New York (2000)
Miller, A., Rosenbaum, C., Blikstein, P.: MagneTracks: a tangible constructionist toolkit for Newtonian physics. In: Proceedings of the Sixth International Conference on Tangible, Embedded and Embodied Interaction, pp. 253–256. ACM, New York (2012)
Hestenes, D., Wells, M., Swackhamer, G.: Force concept inventory. Phys. Teach. 30, 141–158 (1992)
Media Lab Learning. http://learn.media.mit.edu/creative-learning
Resnick, M., Maloney, J., Monroy-Hernández, A., Rusk, N., Eastmond, E., Brennan, K., Millner, A., Rosenbaum, E., Silver, J., Silverman, B., Kafai, Y.: Scratch: programming for all. Commun. ACM 52, 60–67 (2009)
Johnson-Glenberg, M.C., Birchfield, D.A., Tolentino, L., Koziupa, T.: Collaborative embodied learning in mixed reality motion-capture environments: two science studies. J. Educ. Psychol. 106, 86 (2014)
Figure 8. https://www.figur8.me/
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Khan, M., Trujano, F., Maes, P. (2018). Mathland: Constructionist Mathematical Learning in the Real World Using Immersive Mixed Reality. In: Beck, D., et al. Immersive Learning Research Network. iLRN 2018. Communications in Computer and Information Science, vol 840. Springer, Cham. https://doi.org/10.1007/978-3-319-93596-6_9
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DOI: https://doi.org/10.1007/978-3-319-93596-6_9
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