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Towards a Materialist Vision of ‘Learning as Making’: the Case of 3D Printing Pens in School Mathematics

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Abstract

In this paper, we build on a previously developed notion of ‘learning as Making’ to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one’s moving hand. In particular, we present two examples of Maker-centred lessons for teaching and learning of primary mathematics. In these lessons, the students actively constructed artefacts with 3D Printing Pens while engaging in inquiry-based learning activities, where the target concepts were properties of prisms and cross-sections at the primary 5 (age 10–11) and primary 6 (age 11–12) levels respectively. We use diffractive analysis to capture the fine details in students’ body-material interactions while engaging in the tasks with or without the 3D Printing Pens during the lessons. Through the lens of Making as a material act of creation and seeking to update Papert’s constructionist view of learning, we propose to rethink Making in school mathematics according to a four-fold characterisation: Making is co-constructing meanings, Making is mathematising, Making is assembling with technology and Making is inventing. We discuss our contribution towards advancing a materialist perspective of learning mathematics and implications for a ‘learning as Making’ pedagogy and curriculum.

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References

  • Bannan, B., Cook, J., & Pachler, N. (2016). Reconceptualizing design research in the age of mobile learning. Interactive Learning Environments, 24(5), 938–953.

    Article  Google Scholar 

  • Barad, K. (2008). Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning. Durham, NC: Duke University Press.

  • Bennett, J. (2010). Vibrant matter: A political ecology of things. Durham, NC: Duke University Press.

  • Châtelet, G. (2000). Figuring space: Philosophy, mathematics, and physics (p. 2000). Dordrecht, Netherlands: Kluwer.

  • Chu, S. L., Quek, F., Saenz, M., Bhangaonkar, S., & Okundaye, O. (2015). Enabling instrumental interaction through electronics making: Effects on children’s storytelling. In H. Schoenau-Fog, L. Bruni, S. Louchart, & S. Baceviciute (Eds.), Interactive storytelling (pp. 329–337). Cham, Switzerland: Springer.

  • Coles, A., & Sinclair, N. (2018). Re-thinking ‘concrete to abstract’: Towards the use of symbolically structured environments. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 275–282). Umeå, Sweden: PME.

  • de Freitas, E. (2012). The diagram as story: Unfolding the event-structure of the mathematical diagram. For the Learning of Mathematics, 32(2), 27–33.

  • de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics. Educational Studies in Mathematics, 83(3), 453–470.

  • de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the classroom. New York, NY: Cambridge University Press.

  • de Freitas, E., Ferrara, F., & Ferrari, G. (2017). The coordinated movements of a learning assemblage: Secondary school students exploring Wii graphing technology. In E. Faggiano, F. Ferrara, & A. Montone (Eds.), Innovation and technology enhancing mathematics education. Mathematics education in the digital era (Vol. 9, pp. 59–75). Cham, Switzerland: Springer.

  • Deleuze, G., & Parnet, C. (2007). Dialogues II. New York, NY: Columbia University Press.

  • English, L. (2016). STEM education K-12: Perspectives on integration. International Journal of STEM Education, 3(3). https://doi.org/10.1186/s40594-016-0036-1.

  • Fleming, L. (2015). Worlds of Making. Best practices of establishing a Maker Space for your school. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Gerofsky, S. (2018). Introduction: Geometries of liberations. In S. Gerofsky (Ed.), Contemporary environmental and mathematics education modelling using new geometrical approaches: Geometries of liberations (pp. 1–8). Cham, Switzerland: Palgrave Macmillan.

  • Hall, R. & Stevens, R. (2015). Interaction analysis approaches to knowledge in use. In A. A. diSessa, M. Levin, & J. S. Brown (Eds.), Knowledge and interaction: A synthetic agenda for the learning sciences (pp. 72-108). New York, NY: Routledge.

  • Hegedus, S., & Tall, D. (2016). Foundations for the future: The potential of multimodal technologies for learning mathematics. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 543–562). New York, NY: Routledge.

  • Hong Kong Curriculum Development Council (HKCDC). (2015). Ongoing renewal of the school curriculum – focusing, deepening and sustaining updating the mathematics education key learning area curriculum (primary 1 to secondary 6). Hong Kong: The Printing Department.

    Google Scholar 

  • Kelton, M. L., & Ma, J. Y. (2018). Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration. Educational Studies in Mathematics, 98(2), 177–196.

    Article  Google Scholar 

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.

  • Rotman, B. (2008). Becoming beside ourselves: The alphabet, ghosts and distributed human being. Durham, NC: Duke University Press.

  • Maheux, J. F., & Proulx, J. (2015). Doing|mathematics: Analysing data with/in an enactivist-inspired approach. ZDM Mathematics Education, 47(2), 211–221.

  • Mazzei, L. (2014). Beyond an easy sense: A diffractive analysis. Qualitative Inquiry, 20(6), 742–746.

  • Merleau-Ponty, M. (1945). Phenomenologie de la Perception [Phenomenology of Perception]. Paris, France: Gallimard.

  • Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2013). Playing mathematical instruments: Emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372–415.

  • Ng, O. (2017). Exploring the use of 3D computer-aided design and 3D printing for STEAM learning in mathematics. Digital Experiences in Mathematics Education, 3(3), 257–263.

  • 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, Switzerland: Springer.

  • Ng, O., Sinclair, N., & Davis, B. (2018). Drawing off the page: How new 3D technologies provide insight into cognitive and pedagogical assumptions about mathematics. The Mathematics Enthusiast, 15(3), 563–578.

  • Ng, O., & Chan, T. (2019). Learning as Making: Using 3D computer-aided design to enhance the learning of shapes and space in STEM-integrated ways. British Journal of Educational Technology, 50(1), 294–308.

    Article  Google Scholar 

  • Papert, S., & Harel, I. (1991). Situating constructionism. In S. Papert & I. Harel (Eds.), Constructionism (pp. 1–11). New York, NY: Ablex Publishing.

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York, NY: Basic Books.

  • Radford, L., Edwards, L., & Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(3), 91–95.

    Article  Google Scholar 

  • Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: The murky and furtive world of mathematical inventiveness. ZDM Mathematics Education, 45(2), 239–252.

  • Sinclair, N. (2017). Mathematics learning as an entanglement of child, concept and technology. In S. Smythe, C. Hill, M. MacDonald, D. Dagenais, N. Sinclair, & K. Toohey (Eds), Disrupting boundaries in education and research (pp. 116–143). Cambridge, England: Cambridge University Press.

  • Varela, F. J., Thompson, E. T., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.

  • Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over fifty years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835.

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Acknowledgments

The authors would like to thank the annoynomous teachers and students who participated in this research.

Funding

This study is funded by The Chinese University of Hong Kong Direct Grant (Reference no. 4058058).

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Authors and Affiliations

  1. Department of Curriculum and Instruction, Faculty of Education, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Oi-Lam Ng

  2. Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, Turin, Italy

    Francesca Ferrara

Authors
  1. Oi-Lam Ng
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  2. Francesca Ferrara
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The authors contributed equally in this paper, of which the data was drawn from the first author’s research.

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Correspondence to Oi-Lam Ng.

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Ng, OL., Ferrara, F. Towards a Materialist Vision of ‘Learning as Making’: the Case of 3D Printing Pens in School Mathematics. Int J of Sci and Math Educ 18, 925–944 (2020). https://doi.org/10.1007/s10763-019-10000-9

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  • DOI: https://doi.org/10.1007/s10763-019-10000-9

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