Skip to main content
SpringerLink
Log in

Next steps in implementing Kaput’s research programme

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These ‘design principles’ focus on the evolution of digital representations since the early 1990s, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput’s notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is Kaput’s notion of communication and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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 

  • Bakker, A., Hoyles, C., Kent, P., & Noss, R. (2006). Improving work processes by making the invisible visible. Journal of Education and Work, 19(4), 343–361.

    Article  Google Scholar 

  • Bednarz, N., Kieran, C., & Lee, L. (Eds.) (1996) Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer.

  • diSessa, A. (2000). Changing minds, computers, learning and literacy. Cambridge, MA: MIT.

    Google Scholar 

  • Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (pp. 55–69), Vol. 1. Hiroshima University.

  • Goldenberg, P. (2000). Thinking (and talking) about technology in Math Classrooms. Education Development Center. http://www2.edc.org/mcc/PDF/iss_tech.pdf.

  • Hallett, D., & Tzanakis, C. (Eds.) (2002) Proceedings of the International Conference on the Teaching of Mathematics (at the Undergraduate Level) 2nd, Hersonissos, Crete, Greece, July 1–6, 2002.

  • Hoyles, C., Bakker, A., Kent, P., & Noss, R. (2007). Attributing meanings to representations of data: The case of statistical process control. Mathematical Thinking and Learning (in press).

  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.

    Article  Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.) Second international handbook of mathematics education (pp. 323–350). Dordrecht: Kluwer.

    Google Scholar 

  • Hoyles, C., & Noss, R. (2007). The meanings of statistical variation in the context of work. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics educations. Hillsdale, NJ: Lawrence Erlbaum Associates.

  • Hoyles, C., Noss, R., & Kent, P. (2004). On the integration of digital technologies into mathematics classrooms. International Journal for Computers in Mathematical Learning, 9(3), 309–326.

    Article  Google Scholar 

  • Kahn, K. (1996). ToonTalk – An animated programming environment for children. Journal of Visual Languages and Computing, 7(2), 197–217.

    Article  Google Scholar 

  • Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). New York: Macmillan.

    Google Scholar 

  • Kaput, J., Carraher D., & Blanton, M. (2002). Algebra in the early grades. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Kaput, J., Hoyles, C., & Noss, R. (2002). Developing new notations for a learnable mathematics in the computational era. In L. English (Ed.), Handbook of international research in mathematics education (pp. 51–75). London: Erlbaum.

    Google Scholar 

  • Kent, P., & Noss, R. (2000). The visibility of models: Using technology as a bridge between mathematics and engineering. International Journal of Mathematics Education in Science and Technology, 31(1), 61–69.

    Article  Google Scholar 

  • Kent, P., Noss, R., Guile, D., Hoyles, C., & Bakker, A. (2007). Characterising the use of mathematical knowledge in boundary crossing situations at work. Mind, Culture, and Activity, 14(1–2), 64–82.

    Google Scholar 

  • Küchemann, D., & Hoyles, C. (2007). From empirical to structural reasoning in mathematics: tracking changes over time. In M. Blanton, D. Stylianou, & E. Knuth (Eds.), The learning and teaching of proof across the grades. Mahwah, NJ: Erlbaum (in press).

  • Lobato, J. (2005). The actor-oriented abstraction approach: Coordinating individual and social levels of abstraction. In J. Lobato (Ed.) Abstraction in mathematics learning: Comparing alternative emerging conceptions. Symposium conducted at the annual meeting of the American Educational Research Association, Montréal, Canada.

  • Mason, J. (2005). Frameworks for learning, teaching and research: Theory and practice. In G. M. Lloyd, M. R. Wilson, J. L. M. Wilkins, & S. L. Behm (Eds.), Proceedings of the 27th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education [CD-ROM]. Roanoke, VA: Virginia Tech.

    Google Scholar 

  • Mor, Y., Noss, R., Hoyles C., & Simpson, G. (2006). Designing to see and share structure in number sequences. International Journal for Technology in Mathematics Education, 13(2), 65–78.

    Google Scholar 

  • Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge. Educational Studies in Mathematics, 65(3), 367–384.

    Article  Google Scholar 

  • Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics, 33(2), 203–233.

    Article  Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer.

    Google Scholar 

  • Noss, R., & Hoyles, C. (2006). Exploring mathematics through construction and collaboration. In K. R. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 389–405). Cambridge: CUP.

    Google Scholar 

  • Noss, R., Hoyles, C, Gurtner, J.-L., Adamson, R., & Lowe, S. (2002). Face-to-face and online collaboration: Appreciating rules and adding complexity. International Journal of Continuing Engineering Education and Lifelong Learning, 12(5/6), 521–539.

    Article  Google Scholar 

  • Papert, S. (2006) Afterward: After how comes what. In K. R. Sawyer (Ed.), Cambridge handbook of the Learning Sciences (pp. 581–586). Cambridge: CUP.

    Google Scholar 

  • Sacristan, A., & Noss, R. (2007). Computational construction as a means to coordinate representations of infinity (in press).

  • Schreiber, C. (2004) The interactive development of mathematical inscriptions – a semiotic perspective on pupils’ externalisation in an internet chat about mathematical problems. Zentrablatt für Didaktik der Mathematik, 36(6), 185–194.

    Article  Google Scholar 

  • Shaffer, D. W. (2005). Studio mathematics: The epistemology and practice of design pedagogy as a model for mathematics learning WCER Working Paper No. 2005-3. Madison: University of Wisconsin-Madison, Wisconsin Center for Education Research. Available at: http://www.wcer.wisc.edu/publications/workingPapers/.

  • Shaffer, D. W., & Kaput, J. (1999). Mathematics and virtual culture: A cognitive evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37(2), 97–119.

    Article  Google Scholar 

  • Sherin, B. (2001). A comparison of programming languages and algebraic notation as expressive languages for physics. International Journal of Computers for Mathematics Learning, 6, 1–61.

    Article  Google Scholar 

  • Simpson, G., Hoyles, C., & Noss, R. (2005). Designing a programming-based approach for modelling scientific phenomena. Journal of Computer Assisted Learning, 21, 143–158.

    Article  Google Scholar 

  • Simpson, G. Hoyles, C., & Noss, R. (2006). Exploring the mathematics of motion through construction and collaboration. Journal of Computer Assisted Learning, 22, 1–23.

    Article  Google Scholar 

  • Stacey, K., Chick, H., & Kendal, M. (2004). The future of the teaching and learning of algebra. Dordrecht: Kluwer.

    Google Scholar 

  • Wilensky, U. (1999). NetLogo [Computer software]. Center for Connected Learning and Computer-Based Modeling: Evanston, IL.

  • Wolfram, S. (2002). A new kind of science. Champaign: Wolfram Media.

    Google Scholar 

Download references

Acknowledgements

The Techno-mathematical Literacies in the workplace project [http://www.ioe.ac.uk/tlrp/technomaths] is funded by the Teaching and Learning Research Programme [http://www.tlrp.org], a programme of the U.K. Economic and Social Research Council (Award no. L139-25-0119). The WebLabs project was funded under grant IST 2001-3220 of the Information Society Technologies Programme of the European Commission. We acknowledge the contribution of all the WebLabs team, and notably the UK researchers, Y. Mor and G. Simpson. See http://www.weblabs.eu.com.

Author information

Authors and Affiliations

  1. Institute of Education, University of London, 20 Bedford Way, London, WC1H 0AL, UK

    Celia Hoyles & Richard Noss

Authors
  1. Celia Hoyles
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard Noss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Celia Hoyles.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoyles, C., Noss, R. Next steps in implementing Kaput’s research programme. Educ Stud Math 68, 85–97 (2008). https://doi.org/10.1007/s10649-007-9102-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-007-9102-4

Keywords

Search

Navigation