Celia Hoyles

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Proof lies at the heart of mathematics yet we know from research in mathematics education that proof is an elusive concept for many mathematics students. The question that we are now asking is whether the introduction of dynamic geometry systems will improve the situation – or will it make the transition from informal to formal proof in mathematics even(More)
This paper presents categories of pedagogic strategies for helping students during mathematical explorations in microworlds, that take into account the constructivist theory of learning. We illustate the strategies using examples from empirical data supported by other research in the field. As precursor to designing intelligent support for exploratory(More)
This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as(More)
In this paper we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of(More)
Keywords: Exploratory learning Algebraic generalisation Intelligent support Teacher assistance Design a b s t r a c t This paper charts the design and application of a system to support 11–14 year old students' learning of algebraic generalisation, presenting students with the means to develop their understanding of the meaning of generality, see its power(More)
We describe an iteratively designed sequence of activities involving the modelling of 1-dimensional collisions between moving objects based on programming in ToonTalk. Students aged 13-14 in two settings (London and Cyprus) investigated a number of collision situations, classified into six classes based on the relative velocities and masses of the colliding(More)
  • Yishay Mor, Richard Noss, Celia Hoyles, Ken Kahn, Simpson, Gordon +4 others
  • 2016
Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. This paper reports on a design experiment in the domain of number sequences conducted in the course of the WebLabs(More)
Due to the ubiquity of IT in workplaces and increasing customer demands, employees need skills that often remain unrecognised in companies. We draw attention to what we call Techno-mathematical Literacies (TmL) – mathematical knowledge that is situated in the work context and mediated by the available technology. We describe a research project in which we(More)