Karp, A. (Ed.) (2014). Leaders in mathematics education: Experience and vision (Chap.5 Interview with Celia Hoyles, pp. 87-99). Rotterdam: Sense Publishers.
The three modules, Setting the scene; Putting into practice: A curriculum innovation approach; and Putting into practice: Programming and computational thinking, together are intended to convey the research and practice at the core of my work in mathematics education over many years. My enduring goal has been to design and implement innovations in curriculum and in teaching that foster a mathematical way of thinking among all students, predominantly by supporting them to become aware of and appreciate mathematical structure, and be better able to interact with abstraction. While digital technologies have in my view enormous potential for the realisation of this goal, there are obstacles that need to be addressed at every stage of the design of the innovation and its implementation in different contexts. This means any innovation must be robustly designed in terms of activities and embedded digital tools and rigorously evaluated in terms of impact on different student groups. Most of the research presented has been conducted by me in collaboration with a range of colleagues, in particular with Richard Noss.
This module is devoted to the presentation of the underpinnings of my research namely:
1) the centrality of representations;
2) the situatedness of abstraction; and
3) the importance of developing mathematical habits of mind among all students.
This module is devoted to discussion of how the underpinnings presented in Module 1 can be made to work in classrooms and in different country contexts. In my case, the process adopted is through the robust design of curriculum innovations, namely microworlds, aiming to promote learning of particular mathematical concepts through embedding appropriate digital technologies by which the learner can explore these concepts. These microworlds are rigorously and iteratively evaluated. I present an example of such an approach using specially- designed digital tools followed by a short review of research on programming and mathematics that forms the background for Module 3
Like Module 2 this module is devoted to presenting some of my collaborative research work that involved the iterative design of microworlds but this time the digital tools comprise a programming language. This brings to into focus the processes of programming (in my case in Logo and in Scratch) and the challenges to be faced; and more generally issues around the development of computational thinking. A key question remains is how programming and the promotion of computational thinking can be made to ‘fit’ with the mathematics curriculum to enhance the learning experience of students. I address this question through discussing the design and evaluation of our research project ScratchMaths.
Bibliography for Modules 1, 2 and 3
Clark-Wilson, A. & Hoyles, C. (2019). From curriculum design to enactment in technology enhanced mathematics instruction—Mind the gap! International Journal of Educational Research, 94, 66-76.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428
Hoyles, C. (1991). Developing mathematical knowledge through microworlds. In A. J. Bishop, S. Mellin-Olsen & J. Van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 147-172). Kluwer.
Hoyles, C. (1993). Microworlds/Schoolworlds: The transformation of an innovation. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology. NATO ASI, Series F, 121, 1-17.
Hoyles, C., Küchemann, D., Healy, L. & Yang, M. (2005). Students’ developing knowledge in a subject discipline: Insights from combining quantitative and qualitative methods. International Journal of Social Research Methodology, 8(3), 225-238
Hoyles. C. & Lagrange J-B. (Eds.) (2010). Mathematics education and technology: Rethinking the terrain. Springer.
Hoyles, C. & Noss, R. (1992), Learning mathematics and Logo. MIT press.
Hoyles C. & Noss, R (2009). The technological mediation of mathematics and its learning. In T. Nunes (Ed.), Special Issue, ‘Giving meaning to mathematical signs: Psychological, pedagogical and cultural processes’ Human Development, 52(2), 129-147
Hoyles, C., Noss, R. & Adamson, R. (2002). Rethinking the microworld idea. Journal of Educational Computing Research, 27(1&2), 29-53.
Noss, R. & Hoyles, C. (1996), Windows on mathematical meanings: Learning cultures and computers. Kluwer.