Fingers-on Geometry: The Emergence of Symmetry in a Primary School Classroom with Multi-touch Dynamic Geometry

  • Sean ChorneyEmail author
  • Nathalie Sinclair
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 12)


In this chapter, we describe a research project with first grade children using a multi-touch dynamic geometry sketch. We approach our analysis through the lens of inclusive materialism (de Freitas & Sinclair, 2014), which considers the intra-actions involved in the child-device-geometry assemblages and thus to the way in which new mathematical ideas emerge in this assemblage. Drawing on the design experimentation methodology (de Freitas, 2016), we analyse the assemblage in order to study how concepts such as symmetry arise. We therefore seek to investigate the way digital technology can become a device for producing new concepts. We focus particularly on how the multi-touch environment, in which geometry objects can be continuously dragged with fingers, occasions new gestures and body motions that provide the basis for emerging geometrical ideas.


  1. Artigue, M. (2002). Learning mathematics in CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245–274.CrossRefGoogle Scholar
  2. Barad, K. (2007). Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning. Durham, NC: Duke University Press.CrossRefGoogle Scholar
  3. Barad, K. (2010). Quantum entanglements and hauntological relations of inheritance: dis/continuities, spacetime enfoldings, and justice-to-come. Derrida Today, 3(2), 240–268.CrossRefGoogle Scholar
  4. Barad, K. (2012). On touching: The inhuman that therefore I am. Differences: A Journal of Feminist Cultural Studies, 23(3), 206–223.CrossRefGoogle Scholar
  5. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (2nd revised ed., pp. 746–805). New York: Routledge.Google Scholar
  6. Bornstein, M. H., & Stiles-Davis, J. (1984). Discrimination and memory for symmetry in young children. Developmental Psychology, 20(4), 637–649.CrossRefGoogle Scholar
  7. Braidotti, R. (2013). The posthuman. Cambridge, UK; Malden, MA: Polity Press.Google Scholar
  8. Bryant, P. (2008). Paper 5: Understanding spaces and its representation in mathematics. In T. Nunez, P. Bryant, & A. Watson (Eds.), Key understanding in mathematics learning: A report to the Nuffield Foundation. Retrieved April 28, 2013, from
  9. Clements, D., & Sarama, J. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Erlbaum.Google Scholar
  10. de Freitas, E. (2016). Diffractive apparatus: Rethinking the design experiment in light of quantum ontology. Washington, DC: Paper presented at the American Educational Research Association.Google Scholar
  11. de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the classroom. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
  12. Duval, R. (2005). Les conditions cognitives de l’apparentissage de la géométrie: Développement de la visualisation, differenciation des raisonnement et coordination de leurs fonctionnements. Annales de didactique et sciences cognitives, 10, 5–53.Google Scholar
  13. Haraway, D. (1992). The promises of monsters. A regenerative politics for inappropriate/d others. In L. Grossberg, C. Nelson, & P. Treichler (Eds.), Cultural Studies. London and New York: Routledge.Google Scholar
  14. Haraway, D. (2008). When species meet. Minneapolis, MN: University of Minnesota Press.Google Scholar
  15. Jackiw, N. (1991, 2001). The Geometer’s Sketchpad [Computer Program]. Emeryville, CA: Key Curriculum Press.Google Scholar
  16. Lenz Taguchi, H. (2012). A diffractive and Deleuzian approach to analyzing interview data. Feminist Theory, 13(3), 265–281.CrossRefGoogle Scholar
  17. Ng, O., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM—The International Journal on Mathematics Education, 51(3), 421–434.Google Scholar
  18. Pickering, A. (1995). The mangle of practice: Time, agency, and science. Chicago: The university of Chicago Press.CrossRefGoogle Scholar
  19. Seo, K.-H., & Ginsburg, H. (2004) What is developmentally appropriate in early childhood mathematics education? In D. H. Clements, J. Sarama, & A.-M. Dibias (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education. (pp. 91–104). Mahwah, NJ: Erlbaum.Google Scholar
  20. Serres, M. (2011). Variations on the body. [Translation: Randolph Burks]. Minneapolis, MN: University of Minnesota Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada

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