Skip to main content

Towards a Socio-material Reframing of Mathematically Challenging Tasks

  • Chapter
  • First Online:
Mathematical Challenges For All

Part of the book series: Research in Mathematics Education ((RME))

  • 600 Accesses

Abstract

In this chapter, we investigate Leikin’s (2014) (Challenging mathematics with multiple solution tasks and mathematical investigations in geometry. In: Li Y et al. (Eds.), Transforming mathematics instruction: multiple approaches and practices, advances in mathematics education (pp 59–80). Springer International Publishing, Cham, 2014) concept of mathematical challenge in the context of a digital technology environment called TouchCounts. Based on an analysis of a grade 1 classroom, we propose a reframing of mathematical challenge that better suits this environment, and that also takes into account the socio-material dimensions of mathematical activity, in line with the inclusive materialist approach of de Freitas and Sinclair (Mathematics and the body: Material entanglements in the classroom. Cambridge University Press, New York, 2014). Our reframing leans on the distributed and material aspects of mathematical activity, shifting the focus from individual, mental cognitive states to more collective, embodied affect.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Please see the video on this webpage to consider how TouchCounts works: http://touchcounts.ca/about.html.

  2. 2.

    Placing more than 10 fingers simultaneously would require the help of another classmate, of course.

  3. 3.

    The children had previously worked on a task that involved 6 children, which the researcher reminded them of.

References

  • Artigue, M. (2002). Learning mathematics in a 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(3), 245–274.

    Article  Google Scholar 

  • de Freitas, E., & Ferrara, F. (2015). Movement, memory and mathematics: Henri Bergson and the ontology of learning. Studies in Philosophy and Education, 34(6), 565–585.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • de Freitas, E., Ferrara, F., & Ferrari, G. (2019). The coordinated movements of collaborative mathematical tasks: The role of affect in transindividual sympathy. ZDM Mathematics Education, 51(2), 305–318.

    Article  Google Scholar 

  • Ferrara, F., & Ferrari, G. (2020). Reanimating tools in mathematical activity. International Journal of Mathematical Education in Science and Technology, 51(2), 307–323.

    Article  Google Scholar 

  • Herbel-Eisenmann, B., & Wagner, D. (2010). Appraising lexical bundles in mathematics classroom discourse: Obligation and choice. Educational Studies in Mathematics, 75(1), 43–63.

    Article  Google Scholar 

  • Jackiw, N. (2006). Mechanism and magic in the psychology of dynamic geometry. In N. Sinclair, W. Higginson, & D. Pimm (Eds.), Mathematics and the aesthetic: New approaches to an ancient affinity (pp. 145–159). Springer.

    Google Scholar 

  • Jackiw, N., & Sinclair, N. (2010). Learning through teaching, when teaching machines. In R. Leikin & R. Zazkis (Eds.), Learning through teaching mathematics (pp. 153–168). Springer.

    Google Scholar 

  • Jackiw, N., & Sinclair, N. (2014). TouchCounts [software application for the iPad]. Simon Fraser University.

    Google Scholar 

  • Leikin, R. (2014). Challenging mathematics with multiple solution tasks and mathematical investigations in geometry. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices, advances in mathematics education (pp. 59–80). Springer.

    Google Scholar 

  • Leung, A. (2017). Exploring techno-pedagogic task design in the mathematics classroom. In A. Leung, & A. Baccaglini-Frank (Eds.), Digital technologies in desgining mathematics education tasks: Potential and pitfals (pp. 3–16). Springer.

    Google Scholar 

  • Leung, A., & Baccaglini-Frank, A. (2017). Digital technologies in desgining mathematics education tasks: Potential and pitfals. Springer.

    Google Scholar 

  • Mackrell, K., Maschietto, M., & Soury-Lavergne, S. (2013). The interaction between task design and technology design in creating tasks with Cabri Elem. In A. Watson, M. Ohtani, J. Ainley, J. Bolite Frant, M. Doorman, C. Kieran, A. Leung, C. Margolinas, P. Sullivan, D. R. Thompson, & Y. Yang (Eds.), Task design in mathematics education. Proceedings of ICMI study 22 (pp. 81–89). ICMI.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. ICMI 11 survey team 7: The notion and role of theory in mathematics education research. Working paper. Available: http://www.laurentian.ca/educ/lradford/.

  • Sinclair, N., & de Freitas, E. (2019). Body studies in mathematics education: Diverse scales of mattering. ZDM Mathematics Education, 51(2), 227–237.

    Article  Google Scholar 

  • Sinclair, N., & Ferrara, F. (2021). Experiencing number in a digital, multitouch environment. For the Learning of Mathematics, 41(1), 22–29.

    Google Scholar 

  • Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with TouchCounts: The role of emotions and the body in mathematical communication. Technology, Knowledge and Learning, 19(1–2), 81–99.

    Article  Google Scholar 

  • Sinclair, N., & Zazkis, R. (2017). Everybody counts: Designing tasks for TouchCounts. In A. Leung, & A. Baccaglini-Frank (Eds.), Digital Technologies in Designing Mathematics Education Tasks (pp. 175–192). Springer.

    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.

    Google Scholar 

  • Turkle, S. (2011). Evocative objects: Things we think with. MIT Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nathalie Sinclair .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sinclair, N., Ferrara, F. (2023). Towards a Socio-material Reframing of Mathematically Challenging Tasks. In: Leikin, R. (eds) Mathematical Challenges For All . Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-18868-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-18868-8_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-18867-1

  • Online ISBN: 978-3-031-18868-8

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics