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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)
In this paper we reflect on the meaning and evolution of the microworld idea. We point out a crucial distinction between user manipulation and modification at three distinct but mutually dependent levels — the interface, superstructural and platform levels. We exploit a case study of two 8-year-old girls playing and rebuilding a simple video game, to argue(More)
Preface There are many reasons to write a chapter of a research handbook; among these are a recognition of recent developments, the need to summarise a field of research, and the importance of providing a ready source of bibliographic references. It is also a chance for the authors to give their particular view of a given area, ride their particularly(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)
Not for the first time we are at a turning point in intellectual history. The appearances of new computational forms and literacies are pervading the social and economic lives of individuals and nations alike. Yet nowhere is this upheaval correspondingly represented in educational systems, in classrooms, or in school curricula. As far as mathematics is(More)
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)
Proportional Reasoning 2 Abstract We investigate how expert nurses undertake the calculation of drug dosages on the ward. This calculation is error-critical in nursing practice and maps onto the concepts of ratio and proportion. Using episodes of actual drug administration gleaned from ethnographic study, we provide evidence that experienced nurses use a(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)
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)
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)