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Celia Hoyles Unit

Hans Freudenthal Award 2003

Credits: All modules, except module 0, are presented and have been filmed by Celia Hoyles herself. Module 0 has been prepared in collaboration with Núria Planas, who presents it and has been filmed at Universitat Autònoma de Barcelona (Spain).

Module 0

See also:

Official citation for the 2003 Hans Freudenthal ICMI Award

Interviews with Celia Hoyles:

Karp, A. (Ed.) (2014). Leaders in mathematics education: Experience and vision (Chap.5 Interview with Celia Hoyles, pp. 87-99). Rotterdam: Sense Publishers.


Introduction to the first three modules: 
Mathematics education in the digital age: Promise and reality

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.

Module 1

Setting the scene

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.   


Module 2

Putting into practice: A curriculum innovation approach

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

Module 3

Putting into practice: Programming and computational thinking

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.


Epilogue. 'Mathematics used at work, techno-mathematical literacies and future policy directions'

Following the modules in the Unit, I present a concluding epilogue in the form of an interview. The goal of this epilogue is to mention some of my studies in mathematics education that were not directly focused on in the modules: including the mathematics used at work, techno-mathematical literacies, and mathematics anxiety. I conjecture about future policy directions in mathematics education drawn from my knowledge gained over several decades of research on mathematics teaching and learning, particularly in relation to mathematics teacher education and the challenges and tensions of mathematics education research and practice in our post-covid digital age. I use examples from my country, but I am confident they will resonate with the international community. I end by saying very sincerely that I hope that the contents of this epilogue and indeed of all my Unit illustrate the richness and variety of research in our field, a variety that brings enormous challenge but also enormous motivation for future work and collaboration across the community.

Hoyles, C. Noss, R., Kent, P. & Bakker, A. (2010). Improving mathematics at work: The need for techno-mathematical literacies. Routledge. 
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
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, 9(4), 331-360
Kent, P., Noss, R., Guile, D., Hoyles, C., & Bakker, A. (2007). Characterizing the use of mathematical knowledge in boundary-crossing situations at work. Mind, Culture, and Activity 14(1-2), 64-82.  
Bakker, A, Kent, P., Hoyles, C., & Noss, R. (2011). Designing for communication at work: A case for technology-enhanced boundary objects. In S. Akkerman, & A. Bakker (Eds.), Learning at the boundary. An International Journal of Educational Research special issue 
Techno-mathematical literacies in the workplace. Research briefing. Octobre 2007.