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  • Articles  (87)
  • 2010-2014  (87)
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  • Articles  (87)
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  • 1
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    The two envelope problem: there is no conundrum (2014)
    Oxford University Press
    Details
    Publication Date: 2014-11-22
    Description: We consider the famous two envelope conundrum and show, in a very simple way, that there is no conundrum. Our discussion is supported by numerical simulations. We use the problem to raise the issue of disputes in mathematics, rarely touched upon in mathematics education. We suggest that it is worthwhile to expose students of mathematics to such controversies and that this problem can be introduced in the classroom via an experimental demonstration.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    Why is statistics perceived as difficult and can practice during training change perceptions? Insights from a prospective mathematics teacher (2014)
    Oxford University Press
    Details
    Publication Date: 2014-11-22
    Description: An investigation into prospective mathematics/statistics teachers’ (n = 134) conceptual understanding of statistics and attitudes to statistics carried out at the University of Limerick revealed an overall positive attitude to statistics but a perception that it can be a difficult subject, in particular that it requires a great deal of discipline and time to learn. This latter result motivated a follow-up qualitative study (n = 9) to uncover the factors contributing to positive attitude and the concomitant perceptions of difficulty. What emerged was evidence of the lasting impact secondary teachers and their perceptions of statistics had on these students. The study also reveals the potential of teaching practice to act as a vehicle to challenge the perceived difficulty of learning statistics and provide prospective teachers with the opportunity to develop confidence in statistics as both learners and teachers.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 3
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    Contrasts in mathematical challenges in A-level Mathematics and Further Mathematics, and undergraduate mathematics examinations (2014)
    Oxford University Press
    Details
    Publication Date: 2014-11-22
    Description: This article describes part of a study which investigated the role of questions in students’ approaches to learning mathematics at the secondary–tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics questions in England and Wales to focus on requiring students to demonstrate a routine use of procedures, whereas those in first-year undergraduate mathematics primarily required students to be able to draw implications, conclusions and to justify their answers and make conjectures. While these findings confirm the need for reforms of examinations at this level, questions must also be raised over the nature of undergraduate mathematics assessment, since it is sometimes possible for students to be awarded a first-class examination mark solely through stating known facts or reproducing something verbatim from lecture notes.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 4
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    Generations of research on new technologies in mathematics education (2014)
    Oxford University Press
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    Publication Date: 2014-08-24
    Description: This article traces some of the influential ideas and motivations that have shaped a large part of the research on the use of new technologies in mathematics education over the past 40 years. Particular attention is focused on Papert's legacy, Celia's Hoyles' transformation of it, and how both relate to the current research landscape that features not only dramatic changes in hardware and software, but also new philosophical perspectives on the embodied nature of the learner and of mathematics.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 5
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    Evidence-based, theoretically informed design as a means to investigate and transform proof practices in school mathematics (2014)
    Oxford University Press
    Details
    Publication Date: 2014-08-24
    Description: This article focusses on a programme of research into the teaching and learning of proof inspired by Celia Hoyles. By revisiting the first of a series of projects into justifying and proving in school mathematics developed by Celia in the 1990s and by considering how the innovative research methods adopted as well as the results obtained impacted upon our own subsequent research in Brazil, we explore how her work in this area exemplifies various aspects of her contribution to the field of mathematics education as a whole. We highlight, in particular, how we have been influenced by her commitment to understand the social shaping of mathematical practices and to create mathematical cultures, tools, activities and teaching approaches that make mathematics an attractive and accessible option to the many rather than the few.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 6
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    Characteristics and impact of the Further Mathematics Knowledge Networks: analysis of an English professional development initiative on the teaching of advanced mathematics (2014)
    Oxford University Press
    Details
    Publication Date: 2014-08-24
    Description: Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims and mathematical/pedagogical foci; Professional development activity at network meetings; Perceived impacts of the networks on professional learning and collective organization, and on classroom practice and student response. This provides some support for the claim that involving teachers in collaborative reflection and enquiry pays dividends in producing real results in the classroom. However, these findings rest predominantly on the professional judgement of participants.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 7
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    New representational infrastructures: broadening the focus on functions (2014)
    Oxford University Press
    Details
    Publication Date: 2014-08-24
    Description: For more than 10 years, I had the honour and pleasure to work with Celia Hoyles and Richard Noss. We share a common concern for more learnable mathematics, especially in algebra, and for the need to build new representational infrastructures taking advantage of technology. Beyond this common concern, my choice to work in the French institutional context and paradigms for the Casyopee project led to a different approach. Roughly speaking, in these context and paradigms the stake is to help students access existing representations while Hoyles and Noss privilege building new more learnable representations. The aim of the article is to investigate empirically how, in spite of this gap, Hoyles and Noss’ approach can be an inspiration for enlarging the focus on a given topic, freeing oneself of a too strict dependency to one’s own context.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 8
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    Reflections on the Complexities of Teaching and Learning Mathematics (2014)
    Oxford University Press
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    Publication Date: 2014-08-24
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 9
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    Webbing and orchestration. Two interrelated views on digital tools in mathematics education (2014)
    Oxford University Press
    Details
    Publication Date: 2014-08-24
    Description: The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of webbing and instrumental orchestration are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate the distinct and joint journeys of these two theoretical perspectives. Taking some key moments in recent history as points of departure, we conclude that the two perspectives share an importance attributed to digital tools, and that initial differences, such as different views on the role of digital tools and the role of the teacher, have become more nuances. The two approaches share future challenges to the organization of teachers’ collaborative work and their use of digital resources.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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  • 10
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    Establishing the use of 'metre' as a measure unit: an interdisciplinary approach for teaching mathematics (2014)
    Oxford University Press
    Details
    Publication Date: 2014-06-04
    Description: The present article focuses on exploring the dynamics of an interdisciplinary approach in teaching mathematics as a process that cultivates creativity in the school curriculum. We specifically describe here a research project that aims: first, to encourage students to develop and express their creativity; second, to support them towards envisioning mathematics in relation to other school subjects; and third, to assist them in realizing the social role of mathematics itself as a subject closely related to citizenship. The project entitled ‘ Sensitive pendulum or heavy earth ’ was focused on actively engaging students with the main historical arguments concerning the idea of appropriating a common measure unit for length by the French National Assembly during the French Revolution. In order to motivate students and productively organize their efforts in this pedagogic setting we exploited certain drama techniques such as role-playing and role-playing debate. As a result, a short period (i.e. 6 weeks) interdisciplinary project was organized with two classes of 22 and 23 students who attend the 11th grade of an inner city Lyceum school in Athens, Greece. The students involved in this project got responses regarding the very-often-emerging question: why mathematics is useful. At the same time, students seem to change their perception of mathematics and to move towards appreciating its multi-disciplinary and creative nature as well as the broader significance of mathematics in society.
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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