Review of Post-16 Mathematics
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Super-Curricular Suggestions
Super- curricular suggestions Strong applicants to Cambridge and other competitive universities tend to have explored their chosen subject through wider reading outside the classroom, as well as doing very well in their GCSEs and A-levels. We call this sort of exploration ‘super-curricular’, as it builds on and enhances what you are studying in school. We do not expect you to pay for this sort of exploration and have endeavoured to provide resources that are mostly freely available. This selection of suggested reading lists and resources has been gathered from the Cambridge departmental and College websites, other universities and other sources on the internet. These lists are certainly NOT ‘required reading’ for Cambridge applicants. They simply provide some suggestions for places to start exploring your own interests in your chosen subject independently - you do not need to engage with any of the specific websites, books, podcasts etc mentioned and can easily find your own alternatives. The following lists are suggestions only. It is important to read critically by thinking carefully about the arguments, assumptions and evidence presented by the author. Reading is a great way to explore subjects that you find interesting – but there are many other ways to deepen your understanding: investigate your local museums, monuments, galleries and natural features, and think analytically about nature, machinery or the built environment. After the COVID-19 lockdown, perhaps you can visit some of these! The best thing about super-curricular activities is that there are no exams or deadlines to worry about – you are free to follow your own lines of enquiry into the areas that interest you the most. -
Music Learning and Mathematics Achievement: a Real-World Study in English Primary Schools
Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Supervisor: Dr Linda Hargreaves This final thesis is submitted for the degree of Doctor of Philosophy. Faculty of Education University of Cambridge October 2018 Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Abstract This study examines the potential for music education to enhance children’s mathematical achievement and understanding. Psychological and neuroscientific research on the relationship between music and mathematics has grown considerably in recent years. Much of this, however, has been laboratory-based, short-term or small-scale research. The present study contributes to the literature by focusing on specific musical and mathematical elements, working principally through the medium of singing and setting the study in five primary schools over a full school year. Nearly 200 children aged seven to eight years, in six school classes, experienced structured weekly music lessons, congruent with English National Curriculum objectives for music but with specific foci. The quasi-experimental design employed two independent variable categories: musical focus (form, pitch relationships or rhythm) and mathematical teaching emphasis (implicit or explicit). In all other respects, lesson content was kept as constant as possible. Pretests and posttests in standardised behavioural measures of musical, spatial and mathematical thinking were administered to all children. Statistical analyses (two-way mixed ANOVAs) of student scores in these tests reveal positive significant gains in most comparisons over normative progress in mathematics for all musical emphases and both pedagogical conditions with slightly greater effects in the mathematically explicit lessons. -
Higher Education Academy Subject Centres to Close
Media release 16 November 2010 For immediate release Higher Education Academy Subject Centres to Close The Council for the Mathematical Sciences (CMS) and the Heads of Departments of Mathematical Sciences (HoDoMS) note with regret the decision, recently announced by the Chief Executive of the Higher Education Academy (HEA) Craig Mahoney, to close the HEA's 24 Subject Centres, and in particular the Subject Centre for Mathematics, Statistics and Operational Research (MSOR). During its existence the MSOR Subject Centre has been and continues to be recognised by the university mathematics, statistics and operational research community as an extremely valuable contributor to improving teaching and the student experience. Widely appreciated initiatives have included the new lecturer course, postgraduate tutor training days and dissemination of good practice through the periodical MSOR Connections, and an annual conference. The CMS and HoDoMS support the HEA's commitment to maintaining its subject and discipline level work and would welcome the opportunity to work with the HEA to shape its subject level services in its new structure. The CMS and HoDoMS also hope that the HEA will use senior figures from within the mathematical sciences community to help it deliver its future agenda in MSOR. Dr Neil Challis, Chair of the MSOR Advisory Panel, commented, “We are sad to hear of the loss of the MSOR Subject Centre, and very anxious to understand what discipline focused support can be saved”. Professor Frank Kelly FRS, Chair of the Council for the Mathematical Sciences, added that, “The Council for the Mathematical Sciences, representing the main UK mathematical societies, regrets the loss of the Subject Centre for Mathematics, Statistics and Operational Research, which had been responsible for widely appreciated initiatives such as the new lecturer course. -
Engaging Mathematics for All Learners
Engaging mathematics for all learners PHOTO REDACTED DUE TO THIRD PARTY RIGHTS OR OTHER LEGAL ISSUES 2 Engaging mathematics for all learners Contents Foreword . .3 Introduction . .5 What are you trying to achieve? . .6 How will you organise learning? . .8 Planning a compelling learning experience 8 Getting started – what are rich mathematical activities? 8 Some strategies for devising and working with rich mathematical activities 9 Finding rich contexts for mathematics 13 How will you know that you are achieving your aims? . .20 Case studies . .22 1: Every Child Matters – using recreational activities to engage learners 22 2: Every Child Matters – working inclusively with all ability groups 23 3: Historical and cultural roots of mathematics – understanding numbers 24 4: Historical and cultural roots of mathematics – the golden ratio 26 5: Modelling with mathematics 27 6: Mathematics in society – ‘number sense’ 28 7: Mathematics in society – technology and the environment 29 8: Mathematics across the curriculum – performing arts 31 9: Mathematics across the curriculum – STEM 32 10: Mathematics across the curriculum – STEM and PE 33 11: Mathematics and curriculum dimensions – healthy lifestyles 34 12: Mathematics and curriculum dimensions – technology and the media 34 13: Mathematics and curriculum dimensions – creativity and critical thinking 35 14: Using timetable opportunities for engaging mathematical activities 1 36 15: Using timetable opportunities for engaging mathematical activities 2 37 16: Working together to trial engaging mathematical activities (Bowland maths)38 17: Working together to introduce rich tasks into the mathematics curriculum for all learners 39 Working together to engage learners . .40 Making it happen . .44 Resources . .46 Acknowledgements . -
Popularising Mathematics
Popularising Mathematics Philipp Legner August 2013 Abstract Mathematics has countless applications in science, engineering and technology, yet school mathematics is one of the most unpopular subjects, perceived as difficult, boring and not useful in life. ‘Popularisation’ projects can help bridge this gap, by showing how exciting, applicable and beautiful mathematics is. Some popularisation projects focus on telling the wider public about mathematics, including its history, philosophy and applications; other projects encourage you to actively do mathematics and discover surprising relationships and beautiful results using mathematical reasoning and thinking. In this report I will develop a framework to classify and evaluate popularisation, and analyse a wide range of existing projects – ranging from competitions to websites, movies, exhibitions, books and workshops. I also reflect upon my personal experiences in designing popularisation activities. I would like to thank Professor Dave Pratt for his advise while writing this report. Table of Contents Introduction 1 Part 1: A Framework for Mathematics Popularisation The Value of Mathematics ........................................................................... 2 Defining Mathematics Popularisation ...................................................... 4 Designing Mathematics Popularisation ................................................... 8 Evaluating Popularisation Projects ............................................................ 11 Part 2: Case Studies of Popularisation Projects -
Chapter 1: Teaching Mathematics
TEACHING MATHEMATICS IN THE SECONDARY SCHOOL 00_CHAMBERS_FM.indd 1 23/01/2019 5:17:30 PM DEVELOPING AS A REFLECTIVE SECONDARY TEACHER SERIES The core textbooks in this series provide practical guidance and support to student teachers through their training and beyond. These comprehensive guides help trainee teachers develop a more reflective and critical approach to their own practice. The series offers students: • An introduction to national subject frameworks • Support on all aspects of subject teaching, including planning creative lessons, how to improve classroom performance, classroom management, differentiation and teaching strategies • Examples of good practice and teacher commentaries • A research-based section demonstrating M-level work • Critical and analytical reflection on practice They are essential reading for student teachers following school-based or university- based routes into teaching. Reflective Teaching and Learning in the Secondary School, second edition Edited by Sue Dymoke Teaching English Carol Evans, Alyson Midgley, Phil Rigby, Lynne Warham and Peter Woolnough Teaching Computing, second edition Carl Simmons and Claire Hawkins Teaching History Ian Phillips Teaching Science Tony Liversidge, Matt Cochrane, Bernie Kerfoot and Judith Thomas 00_CHAMBERS_FM.indd 2 23/01/2019 5:17:31 PM THIRD EDITION TEACHING MATHEMATICS IN THE SECONDARY SCHOOL PAUL CHAMBERS AND ROBERT TIMLIN 00_CHAMBERS_FM.indd 3 23/01/2019 5:17:31 PM SAGE Publications Ltd © Paul Chambers and Robert Timlin 2019 1 Oliver’s Yard 55 City Road First edition -
What Is Specific About Research in Adult Numeracy and Mathematics Education?
What is specific about research in adult numeracy and mathematics education? Diana Coben King’s College London, UK <[email protected]> Abstract After decades of neglect, adult numeracy and mathematics education are coming to be recognised as worthy of serious research but the area is beset by conceptual difficulties. Adult numeracy and mathematics may at last be ‘on the educational research map’, but where exactly are they on the map? This article explores the question of what is specific about research in adult numeracy and mathematics education. It reviews ways of conceptualising adult numeracy and mathematics education for research purposes and considers the implications of these conceptualisations for research and for the development of the field. Key words: conceptualisations, adult numeracy, mathematics education, policy, research, development frameworks Introduction In the latest International Handbook of Research on Mathematics Education, it is suggested that: • ….adult mathematics teaching and learning deserve attention in their own right; • practice and research in adult mathematics education demand a broad conception of mathematics that is not limited to specialized mathematics…; • there is a coalition of interests in the field across a wide spectrum of related or contributing disciplines; • there is a recognition that research must be closely linked with practice in a field where development and improvement in practice have priority status; and • the community of researchers is truly international... (FitzSimons, Coben, & O'Donoghue, 2003, p.117) The inclusion of an adult-focussed chapter in the International Handbook attests to the growing international recognition of the importance of research and development in this area. While most research about mathematics education focuses on children (Dossey, 1992), adult mathematics teaching and learning both deserve, and are beginning to receive attention in their own right. -
Individual Differences in Arithmetic: Implications for Psychology, Neuroscience, and Education/Ann Dowker
Individual Differences in Arithmetic Standards in numeracy are a constant concern to educational policy makers. However, why are differences in arithmetical performance so marked? In Individual Differences in Arithmetic, Ann Dowker seeks to provide a better understanding of why these differences in ability exist, encouraging a more informed approach to tackling numeracy difficulties. This book reviews existing research by the author and by others on the subject of arithmetical ability and presents strong evidence to support a componential view of arithmetic. Focusing primarily on children, but including discussion of arithmetical cognition in healthy adult and neuro-psychological patients, each of the central components of arithmetic is covered. Within this volume, findings from developmental, educational, cognitive and neuropsychological studies are integrated in a unique approach. This book covers subjects such as: • Counting and the importance of individual differences. • Arithmetic facts, procedures and different forms of memory. • Causes of, and interventions with, mathematical difficulties. • The effects of culture, language and experience. The educational implications of these findings are discussed in detail, revealing original insights that will be of great interest to those studying or researching in the areas of education, neuroscience and developmental and cognitive psychology. Ann Dowker is a University Research Lecturer in the Department of Experimental Psychology, University of Oxford. Individual Differences in Arithmetic -
Teaching and Learning Geometry 11-19 Report of a Royal Society / Joint Mathematical Council Working Group Teaching and Learning Geometry 11-19
JMC Teaching and learning geometry 11-19 Report of a Royal Society / Joint Mathematical Council working group Teaching and learning geometry 11-19 Contents page Preparation of this report v Chairman’s preface vii Summary xi 1 Introduction 1 2 Geometry and its teaching and learning 3 3 The place of geometry in the curriculum 5 4 The 11-16 curriculum 7 5 The development of the curriculum 9 6 Status and allocation of time for geometry 13 7 Geometry 16-19 15 8 The role of assessment 17 9 Teaching of geometry 19 10 Improving the take up of mathematics 21 11 Conclusion 23 12 References and glossary 25 Contents (continued) Appendix 1 The working group 27 Appendix 2 National and international contexts for mathematics 31 Appendix 3 Some recent government initiatives in education 35 Appendix 4 Expectations of geometry in education 37 Appendix 5 Geometry in history and society 41 Appendix 6 Geometry in the current 11-16 curriculum 45 Appendix 7 Geometry in the Key Stage 3 mathematics strategy 49 Appendix 8 Spatial thinking and visualisation 55 Appendix 9 Proof – ‘why and what?’ 57 Appendix 10 Examples of applications of geometry 65 Appendix 11 3-dimensional geometry 69 Appendix 12 Frameworks for developing schemes of work for the curriculum 75 Appendix 13 Integrated approaches to geometry teaching 81 Appendix 14 Bibliography and guide to resources 87 © The Royal Society 2001 Requests to reproduce all or part of this document should be submitted to: Education Manager The Royal Society 6 Carlton House Terrace London SW1Y 5AG Preparation of this report This report has been endorsed by the Council of the Royal Society and the JMC. -
Curriculum Vitae
Curriculum Vitae Prof. Carola{Bibiane Schonlieb¨ Address Department of Applied Mathematics and Theoretical Physics (DAMTP) University of Cambridge Wilberforce Road Cambridge CB3 0WA, UK & Jesus College Cambridge CB5 8BL, UK Tel.: business +44/1223/764251 Email: [email protected] Homepage: http://www.damtp.cam.ac.uk/research/cia/, http://www.damtp.cam.ac.uk/user/cbs31/ Personal Details Date of birth: 21th of December, 1979 Place of birth: Vienna, Austria Present Citizenship: Austrian Career 09/2018{ Professor of Applied Mathematics, Department of Applied Mathematics and Theo- retical Physics, University of Cambridge, UK. 09/2016{ Alan Turing Institute Fellow, Alan Turing Institute, British Library, London, UK. 03/2016{ Co-Director then Director of the EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, Faculty of Mathematics, University of Cam- bridge, UK. 11/2015{ Director of the Cantab Capital Institute for Mathematics of Information, Faculty of Mathematics, University of Cambridge, UK. 10/2015{08/2018 Reader in Applied and Computational Analysis, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. 10/2011{ Head of Cambridge Image Analysis, Department of Applied Mathematics and Theo- retical Physics, University of Cambridge, UK. 10/2011{ Fellow of Jesus College, Cambridge, UK. 09/2010{09/2015 Lecturer in Applied and Computational Analysis, Department of Applied Mathemat- ics and Theoretical Physics, University of Cambridge, UK. 09/2009{09/2010 Postdoctoral Research Fellow, Institute of Numerical and Applied Mathematics, Georg- August Universit¨at G¨ottingen, Germany. 10/2008{09/2009 Research Associate, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. -
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 309 November 2002 FORTHCOMING SOCIETY MEETINGS Friday 22 November 2002 - London Annual General Meeting J.T. Stuart (Presidential Address), J.D. Gibbon Monday 25 November 2002 South West and South Wales Regional Meeting Contemporary Aspects of Mathematical Physics Friday 28 February 2003 - Edinburgh Mary Cartwright Lecture Tuesday 11 March 2003 - Manchester Northern Regional Meeting Geometric Representation Theory Wednesday 14 May 2003 - Coventry Midlands Regional Meeting Uncertainty Modelling NEW LOOK FOR NEWSLETTER After nearly 30 years the Newsletter will to keep a clear line between an essentially soon be taking on a new look. Nothing too ephemeral publication like the Newsletter radical or shocking, we hope, for the many and an archived technical journal (notwith- loyal readers whose heart regularly warms standing the valuable series of photographs to the sight of the reassuring AS brown of past Presidents and Honorary Members envelope in the mail at the beginning of each that we have published since January 1988). month - but something a little more 21st Correspondence columns have been tried in century and (dare we say it?) professional in the past and failed, perhaps because the its design, layout and graphics. We hope too turnaround time is too long. We expect to that the mention of colour in this context have more reviews of mathematics-related will not cause apoplexy in mathematics cultural events as well as books of wide common rooms. We are clear, however, interest. Any other ideas? As editors of that we want to retain a handy pocket-sized newsletters of all organisations have format, and we do not aim to copy the fash- intoned, doubtless since the first subscrip- ion styles of any of our sister publications. -
Volume 3 Research Reports Ead - Kou
Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education Prague, Czech Republic July 16-21, 2006 Volume 3 Research Reports Ead - Kou Editors: Jarmila Novotná Hana Moraová, Magdalena Krátká, Naďa Stehlíková Charles University in Prague Faculty of Education Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education Volume 3 Editors Jarmila Novotná Hana Moraová Magdalena Krátká Naďa Stehlíková Charles University in Prague Faculty of Education Czech Republic The Proceedings are also available on CD-ROM Copyright © 2006 left to the authors All rights reserved ISSN 0771-100X Logo: Ivan Špirk Cover Design: Jarmila Novotná & Ivan Špirk Printing: Atelier Guimaec, s.r.o 3-ii PME30 — 2006 TABLE OF CONTENTS VOLUME 3 Research Reports Eade, Frank & Dickinson, Paul 3-1 Exploring realistic mathematics education in English schools Ebersbach, Mirjam & Resing, Wilma C. M. 3-9 Reasoning about non-linearity in 6- to 9-year-olds: the role of task presentation Eichler, Andreas 3-17 Teachers, classroom, students – A holistic view on beliefs concerning the educational practice Elia, Iliada & Gagatsis, Athanasios 3-25 The effects of different modes of representation on problem solving: Two experimental programs Ell, Fiona 3-33 Can moderate hermeneutics help us to understand learning and teaching in the mathematics classroom? Evans, Jeff & Zan, Rosetta 3-41 Sociocultural approaches to emotions in mathematics education: Initial comparisons Falkenberg, Thomas 3-49 Moral