Transforming the mathematical practices of learners and teachers through digital technology^*

*  This article derives from the keynote presentation of the author to the International Congress of Mathematics Education (ICME), delivered in Mexico in 2008. The text is inevitably in part retrospective. It has been updated in relevant parts without the pretence of producing an exhaustive review of the research in the intervening years. Some parts of this article were elaborated in Hoyles and Noss (2009). Earlier versions of the first part of the article appeared in Hoyles (2012) and in Spanish in Hoyles (2015a).

ABSTRACT

This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital tool-use that distinguish their differing potential are presented: (1) dynamic and graphical tools; (2) tools that outsource processing power; (3) tools that offer new representational infrastructures for mathematics; (4) tools that help to bridge the gap between school mathematics and the students’ world; (5) tools that exploit high-bandwidth connectivity to support mathematics learning; and (6) tools that offer intelligent support for the teacher when their students engage in exploratory learning with digital technologies. Following exemplification of each category, the article ends with some reflections on the progress of research in this area and identifies some remaining challenges.

KEYWORDS:

• Digital technology
• transforming mathematical practices

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

*  This article derives from the keynote presentation of the author to the International Congress of Mathematics Education (ICME), delivered in Mexico in 2008. The text is inevitably in part retrospective. It has been updated in relevant parts without the pretence of producing an exhaustive review of the research in the intervening years. Some parts of this article were elaborated in Hoyles and Noss (2009). Earlier versions of the first part of the article appeared in Hoyles (2012) and in Spanish in Hoyles (2015a).

1 A framework for design research was proposed in the seminal paper by Cobb, Confrey, diSessa, Lehrer, and Schauble (2003), and was the subject of a special issue of ZDM: Mathematics Education. Hoyles and Noss (2015).

2 “Justifying and Proving in School Mathematics”, Hoyles and Healy, funded by the Economic and Social Research Council, 1999–2003.

3 ScratchMaths: supporting computational and mathematical thinking through programming, Noss and Hoyles, funded by the Education Endowment Fund, 2014–18.

4 Techno-mathematical Literacies in the Workplace Noss & Hoyles 2003–7 funded by the Teaching and Learning Research Programme, TLRP, ESRC.

5 Longitudinal Study of Mathematics Reasoning, Hoyles & Küchemann funded by the Economic and Social Research Council, 1999–2003.

6 The MiGen project funded by EPSRC/ESRC, TLRP-TEL, (Technology Enhanced Learning programme) 2007–2011, Grant number RES-139-25-0381

7 See http://mc2-project.eu/