The second day of ICME 11 includes several activities, and one plenary lecture. Celia Hoyles (UK) is going to make a presentation about technology and mathematics education. Her talk is entitled “Transforming the mathematical practices of learners and teachers through digital technology”, and here is the online description of it:
My presentation takes inspiration from the work of Seymour Papert, Jim Kaput, Richard Noss and all the colleagues with whom I have been fortunate enough to collaborate in the area of mathematics education and technology over many years, in the U.K and beyond.
Drawing on the mass of evidence from research and practice, I will first set out what I see as the vision of the potential of Information and Communication Technologies (ICT) to transform the teaching and learning of mathematics. I suggest it can offer:
- dynamic & visual tools that allow mathematics to be explored in a shared space – changing how mathematics is learned and taught;
- tools that outsource processing power that previously could only be undertaken by humans – changing the collective focus of attention during mathematics learning;
- new representational infrastructures for mathematics – changing what can be learned and for whom;
- connectivity – opening new opportunities for shared knowledge construction and for student autonomy over their mathematical work;
- connections between school mathematics and learners’ agendas and culture – bridging the gap between school mathematics and problem solving ‘in the real world’;
- some intelligent support to the teacher while learners are engaged in an exploratory environment;
Under each of the six headings, I will present research evidence and examples that illustrate their transformative potential. I will also identify: first, the costs and challenges at least partly to explain why in so many cases, impact has not reached expectations; and, second, actions that can be undertaken as contingencies against these risks. In this part of the talk, I will draw on some the outcomes of the recent ICMI Study 17, Technology Revisited that considered these questions from the important and under-represented vantage point of the situation of developing countries: how technology could be used for the benefit of these countries rather than serve as yet another source of disadvantage.
Taken together, the overriding evidence suggests that in order for ICT to move from the periphery to centre stage in mathematics teaching and learning and for its potential for transforming mathematical practice for the benefit of all learners to be realised, teachers must be part of the transformative process:
i) to do mathematics for themselves with the digital tools (before and alongside thinking about pedagogy and embedding in practice) thus allowing teachers, regardless of experience, the time and space to take on the role of learner,
ii) to co-design activity sequences that embed the ICT tools and make explicit appropriate didactic strategies,
iii) to try out iteratively in classrooms as a collective effort and debug together.
This design process is challenging, not least because at every phase the dialectical influence of tools on mathematical expression and communication must be taken into account.
A further challenge facing innovations using ICT is scaling up, since, all too often, design experiments while reporting positive results wither away soon after any funding ends. One way we are working in England to break this cycle is through the National Centre for Excellence in the Teaching of Mathematics. The National Centre was set up in England in 2006 (see http://www.ncetm.org.uk, and I have been its director since June 2007. Its major aim is to develop a sustainable national infrastructure for subject-specific professional development of teachers of mathematics that will enable the mathematical potential of learners to be fully realised. The NCETM offers a blend of approaches to effective Continuing Professional development (CPD): national and regional face-to-face meetings, and tools and resources on its portal designed to promote and sustain collaborative CPD among teachers of mathematics (for example through on-line communities). These networks and communities include the use of ICT in classrooms.
A major challenge faced by the NCETM is to reach out to all teachers of mathematics across all the phases of education in ways that develop ownership of NCETM’s CPD offer and, in particular, ownership of and fluency with the tools available on the portal. If this ownership is achieved, the tools will grow with use, as teachers contribute to the content and to the on-line communities and in so doing support each other in transforming their practice. It is my contention that it is only through this process of mutual support that the potential of ICT will be realised – not only the potential already on offer, but also through new technological innovations such as personal and mobile technology, and all that will become available in the future.