The University of York 13th 16th April 2004

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MATHS TAKES SHAPE - the Annual Easter Conference

The University of York 13th - 16th April 2004

Welcome From The President

The theme of this year’s Mathmatical Association Annual Conference is Maths Takes Shape, in other words it is a celebration of mathematics and all things geometrical. Geometry slipped out of the school syllabus for a while, but now it is beginning to enjoy a resurgence, particularly in response to the recent Royal Society Report on the Teaching of Geometry. At research level, geometry has never stopped flourishing. For example, during the last decade, the National Science Foundation, which is the main body for funding research in the USA, has given preference to all programmes that contain a strong component of geometry. And the Newton Institute in Cambridge, which has run six-month research programmes covering the whole of pure and applied mathematics ever since its foundation in 1992, has chosen to have 45% of those programmes wholly on, or with a major part in, geometry. The moral is that if our best students are to be prepared for the future we had better give them an early grounding in geometry right now. I am personally very pleased about this, and that is why I shall be talking about geometry in my Presidential Address, offering some three-dimensional theorems that might be suitable for teaching in schools.

Our opening speaker is Dr Cyril Isenberg of Kent University. He is most widely known for his popular lecture-demonstrations on applied mathematics and physics, and since 1984 has headed the team that annually sets the British Olympiad competition for A-level students. Our closing speaker is Dr David Acheson, Fellow in Mathematics at Jesus College, Oxford. His research is on fluid dynamics, on which he has written a university textbook, and in 1992 he discovered a strange gravity-defying ‘upside-down pendulum theorem’. Our after-dinner speaker is Professor Des MacHale, who has taught mathematics for over thirty years, and is currently at University College Cork. He has written several books, and is guaranteed to get his audience laughing through the humour of mathematics. The Primary Plenary Lecture will be given by Rob Eastaway, the leading mathematical writer and performer, who brings mathematics alive through magic and motivation, looking at the ordinary and making it extraordinary. Our Icebreaker session is to be given by Kjarten Poskitt, who will demonstrate and explain quirky maths, such as magic squares, knots, tricks, codes, amazing number predictions - the sort of things to be found in his Murderous Maths books.

I am looking forward to welcoming you all to the 2004 Mathematical Association Annual Conference. Please come and tell me of any ideas you have concerning primary schools, secondary schools, colleges, universities or research, and of how you think the MA can better support the teaching of mathematics at all levels.

I am particularly confident that you will enjoy the Conference.

Christopher Zeeman


We have another exciting programme of events

Made up of keynote lectures from leading figures in education and mathematics, practical sessions on aspects of mathematics education and how they may be supported and enhanced in the classroom, and many social opportunities to meet new colleagues and old friends.

Keynote Speakers for 2004

Cyril Isenberg, Opening Lecture The Geometry Of Soap Films And Soap Bubbles
Soap films and bubbles take up a shape that minimizes their surface area when they come to rest. These surfaces have important geometric properties that can be studied by teachers and their students. They are easily demonstrated and are both visually attractive and colourful. The lecturer will illustrate the address with numerous spectacular examples. In two dimensions these films solve the problem of linking centres by minimum paths, or roadways. These configurations have many practical applications and are a fruitful source of investigations by students.

Rob Eastaway, Primary Plenary Lecture Maths By Design
The mark of a well-designed product is not only that it does its job, but that it is beautiful. Good design applies to maths questions too. In this talk, author and broadcaster Rob Eastaway will share some of his favourite puzzles and maths problems, arguing that mathematical beauty and elegance can be found in well-crafted questions as well as in their solutions.

Dr David Acheson, Closing Lecture 1089 And All That
David will talk about the element of surprise in mathematics, starting with a strange ‘sum’ that always gives 1089 and moving on to examples from geometry, probability, chaos theory and fluid flow. He will even explore if mathematics can help explain the legendary ‘Indian Rope Trick’, though the emphasis will be on the various ways in which mathematics can have a certain magic of its own!

Kjarten Poskitt, Icebreakers Murderous Maths
Kjarten will demonstrate and explain quirky maths stuff such as magic squares, knots, tricks, codes, amazing number predictions and so on - the sort of stuff that's found in his Murderous Maths books. There’ll be plenty of audience participation and he'll be glad to answer any questions and (hopefully), there’ll be some good laughs along the way.

Traditionally, abstracts are not published for the following: -

Professor Sir Christopher Zeeman FRS Presidential Address
Known not only to mathematicians around the world, but to many researchers in other fields and to members of the general public as well. During his career, he has managed to combine his rare mathematics ability with his insight in other fields of knowledge, to mix his gift for writing with his oratorical talent, and to use his diplomatic skills in his leadership posts. He has been awarded the Senior Whitehead Prize and the Michael Faraday Medal, is bestowed with honorary degrees from many universities in England and abroad, and he received his knighthood in 1991.

Professor Des MacHale After-Dinner Speaker
Des has taught mathematics for over thirty years, currently in the Department of Mathematics at University College Cork. He is the author of several published books and is guaranteed to get his audience laughing through the humour of mathematics!

The following sessions need to be booked on the enclosed form.

[P = Primary, S = Secondary, 16+ = Post 16, G = General]

1.1 Cullingworth, Barbara Extending The More Able Pupils In Years 5 And 6 [P]
For over a year now I have been trying to help some of the more able pupils in the top classes of the local Primary School, in a small room mainly with paper and pencils. I am willing to share some of the ideas that have been successful and would be delighted if you wished to bring some of your ideas to share as well!

1.2 Abbott, Steve Using And Applying Mathematics At The Football Stadium [S]
Schools are increasingly concerned that ‘using and applying mathematics’ should permeate their teaching. In this session we use the theme of the football stadium to address many aspects of secondary mathematics, including problem solving. With many clubs offering stadium tours, why not organise some field work?

1.3 Ransom, Peter The Damn Maths Busters [S/G]
What ho! Join 617 squadron for a geometrical raid on the dams of Nazi Germany. Navigator Flt Sgt ‘Kidnap’ Ransom will brief you on destroying the MÖhne and Eder dams. Participants will be put into crews of 3 and after doing their work will fly a simulation mission. No flak please. WAAFs welcome. Tally ho!

1.4 Butler, Douglas Making The Most Of ICT In The Classroom [S/16+]
Douglas will show a number of lesson plans that incorporate Java and Flash animations off the web, and will show some creative ideas for using Autograph in 1D (statistics), 2D and 3D. Finally he will put this all together as an electronic worksheet using Word and hyperlinks.

1.5 French, Doug Geometry At Key Stage 3: Reasoning With Angles [S]
Simple angle properties associated with parallel lines, triangles and other polygons offer a rich field for developing students’ ability to reason mathematically. This session will look at classroom approaches using these ideas to solve numerical problems and to prove general properties with simple algebra.

1.6 Stripp, Charlie The new GCE AS/A level specifications for Mathematics [16+]
Following the devastating fall in the number of students completing Mathematics A level, resulting from the Curriculum 2000 changes, QCA have reviewed A/AS Mathematics and ordered significant changes to the specifications, which take effect from September 2004. This session discusses the 2004 changes in detail, along with their implications for the teaching and learning of AS/A level Mathematics.

1.7 Woodrow, Derek ICME And ICMI – The International Picture [G]
The ICME (International Congress on Mathematical Education) conferences now attract up to 4000 delegates and are probably the largest conferences on mathematical education which are accessible for U.K. teachers. Being so huge has advantages and disadvantages and I will describe the evolving structure of the Congress and how to make best use of it. The Congress has developed a number of on going study groups, of which PME (to which BSRLM is affiliated) is particularly well known, and also organises smaller ICMI study conferences on specific issues. The next Congress (ICME 10) is in July 2004 in Copenhagen and has developed a radically different structure involving much more discussion and hands-on activities together with expert discourse.

2.1 Wyllie, Pam QCA Primary Update [P]
The QCA speaker will provide an update on mathematics at QCA. We will outline QCA’s role in monitoring the curriculum and we will inform participants of current work in curriculum development, support and guidance. We will consider all mathematics qualifications and seek feedback from those who attend.

2.2 Glatter, Annette Making Maths Fun [S]
How can we make maths fun in the classroom? How can we motivate the unmotivated and motivate the motivated even more? Come and see this ingenious idea to see how!

2.3 Laborde, Jean-Marie Descartes Returns With Cabri [S]
The idea is to show, based on historical examples in maths and physics, how geometry used to be central in supporting major scientific development (Descartes in his Optics, Newton and the universal gravitation, Durer and perspective drawing, etc.). We will show why later geometry declined and finally, how, today, with dynamic geometry systems like Cabri Geometry, we are back at a renaissance of the power of geometry as a ‘thinking’ tool for students and teachers, and as a modelling tool for engineers and others.

2.4 Findlow, Paul QCA Secondary Update [S]
The QCA speaker will provide an update on mathematics at QCA. We will outline QCA’s role in monitoring the curriculum and we will inform participants of current work in curriculum development, support and guidance. We will consider all mathematics qualifications and seek feedback from those who attend.

2.5 Tynan, Bernadette Bending It Like Beckham: Challenging The More Able And Inspiring All
Children At KS3 [S]
Challenge and enrichment, more able, different learning styles, developing creativity and inclusive are all key phrases and words in education right now – but what about practical help to do all this in the classroom? The presentation focuses upon a working framework to provide practical help for the education professional. Enjoy!

2.6 Thomas, Peter Post-16 Forum [16+]
Find out what is going on in Post-16 mathematics; put forward your views and find out what other people are thinking.

2.7 Webster, Roger The Summer Of 65 And The Gentle Art Of Geometry [G]
This will be a look back at how I fell in love with geometry as a young man when I taught a Summer School for the recently deceased H. S. M. Coxeter at the University of Toronto in 1965. It will be light-hearted, not too technical, and suitable for a general audience.

3.1 Harper, Bill Making Fun Of Geometry [P/S]
Learn how to use our Disk Compass (the Rolls-Royce of Geometry sets). Delve into the many shapes and patterns in our book Fun Art and Geometry to present geometry in a fascinating light. Find out why our new Cutting System based on the disk is taking the craft-world by storm.

3.2 Corbyn, Graham Specialist Schools In Mathematics And Computing [S]
This session is intended to provide delegates with an overview of the Specialist Schools Trust and specifically to discuss the role of Mathematics and Computing Colleges and their vision for raising the profile of mathematics nationally. This session will provide an insight into the developments and progress made within these Specialist Schools during the initial phase of designation. As a subject, mathematics remains a core subject for all schools and this session will also highlight some of the developments and plans that have supported and will continue to support mathematics across the whole of the Specialist School network, as well as mathematics across the curriculum.

3.3 Dale, Leanne The MOLE—Manor Online Learning Experience [S]
MOLE is Manor College Technology’s powerful virtual learning environment which offers all students their own ‘log-on’ to quality curriculum materials. MOLE has three ‘key’ advantages: 1. Staff can author appropriate and focussed curriculum materials. 2. MOLE records all student responses, which provides accurate diagnostic assessment. 3. Staff can monitor students ‘live’ on-line or retrospectively.

3.4 Imrie, Jane Improving Teaching And Learning In Mathematics [16+]
The DfES Standards Unit was established in January 2003 as part of the ‘Success for All’ strategy and mathematics is one of the priority areas. A team of secondees and consultants from the Unit are working with teachers in the post-16 sector to improve teaching and learning of mathematics. This session will update on projects and future plans.

3.5 De Villiers, Michael The Role And Function Of Experimentation In Mathematics [G]
This session will investigate what the role of experimentation is in mathematics, reflecting on some historical examples, as well as some personal mathematical experience. The functions that will be discussed and illustrated are: § conjecturing § verification § global refutation § heuristic refutation § understanding.

3.6 Crawford, David It’s A Kind Of Magic! [G]
In this session I will demonstrate a selection of tricks which may seem magical at first sight but which are all based on mathematics (no sleight of hand - honest!) The tricks will involve both numbers and cards and there will need to be plenty of audience participation. For those who have seen past sessions, there will be some overlap but I will also be trying to introduce some new tricks.

3.7 Robin, Tony Problems That Have Interested Me [G]
We shall look at some geometrical problems, which as far as I know, are not discussed elsewhere. Like, what is the greatest distance one has to travel to visit a hundred sites in the UK (or the world)? What is the greatest distance one can explore in a large desert? What is the capacity of a crisp bag? This session should be of general interest using only fairly elementary algebra and calculus, not geared at any particular course.

3.8 Lewis, Barry Maths On The Web [G]
A journey in to the mathematical web: come across a number sequence and want to identify it; need an animated mathematics dictionary for Key Stage 2; where are the best maths games ? This session provides the answers and more.

4.1 Pumphrey, Liz & Piggott, Jennifer Exploring Triangles In An Enriching Way. [P/S]
Text book tiredness can kill any taste for triangles. This practical workshop will explore one example of linked curriculum materials designed to support pupils working on “triangles”. Through tackling problems in a variety of enriching contexts pupils can improve their mathematical knowledge alongside their higher order thinking skills. Problems will all be taken from the NRICH website.

4.2 Henson, Katharine Concept Mapping As An Aid To Understanding Mathematics [S/16+]
Progress in mathematics hinges on the ability to make connections between ideas, yet many students have a very disjointed image of the subject. Concept maps can be used as a diagnostic tool to find out whether students are making important links and as an ongoing method of encouraging a more flexible and robust understanding of the subject. The content would be of interest to anyone looking for ways to promote their students understanding of mathematics, although most of Katharine’s examples will be taken from KS4 and Sixth form topics.

4.3 Murphy, Bernard Teaching Advanced Mathematics [16+]
The aim of this project is to provide a course to support teachers who wish to acquire the skills to enable them to teach AS/A level mathematics. Many of these teachers will not be maths trained themselves, but will be teaching maths in schools which have been unable to recruit maths teachers. The first cohort of teachers will enrol on our course in June 2004 and will use the MEI distance learning website to study 8 AS/A level modules and take part in 7 days of workshops at Warwick University. Although this is an MEI initiative we will not be concentrating solely on the MEI syllabus.

4.4 Fox, Michael Unexpected Connexions In Geometry [G]
We find links between some apparently unrelated geometrical results. A chain of deduction takes us from a well-known theorem to a set of nine inter-related conics touching the nine-point circle. We watch a parabola gyrate round a triangle. This isn’t in text-books, and will stimulate your geometrical imagination.

4.5 Rao, Shantha Moving With Mathematics [G]
Indian Classical Dance evolved many hundreds of years ago and the choreography of this ancient dance form celebrates the symmetry of the human body. A unique combination of intricate rhythmic patterns of footwork and movement explores all dimensions of space. This is a valuable contribution from Indian culture to the world of Mathematics. Shantha Rao will illustrate the basic principles of this highly evolved art form through the use of dance movements, spoken rhythmic syllables and a display of geometric Rangoli patterns.

4.6 Forster, David Michel Chasles And The Development of Synthetic Geometry [16+]
Michel Chasles was one of the most important geometers of the 19th century, introducing the concepts of cross-ratio and involution, and making full use of the principle of duality. This talk will examine the advances he made in his TraitÉ de GÉomÉtrie SupÉrieure and subsequent works.

4.7 Visit   York Brewery Tour
York Brewery Tour - Within the ancient walls of the City of York, beer is being brewed commercially for the first time since 1956. The brewery produces top class ales that have resurrected a Traditional York Industry.

5.1 Piggott, Jennifer & Gilderdale, Charlie Exploring ‘Being Systematic’ [P/S]
We are often encouraging pupils to ‘be systematic’ but how can we help them to develop this illusive skill? The aim of this session is to explore one example of curriculum materials designed to support pupils in recognising what ‘to be systematic’ might mean and apply that knowledge in the context of a variety of interesting problems from NRICH. This is a practical workshop where participants will engage in ‘being systematic’.

5.2 French, Doug Geometry At Key Stage 4: Congruence And Similarity [S]
Congruence and similarity are two key ideas in geometry. This session will look at ways of introducing these ideas in interesting ways, including the use of dynamic geometry software, and will show how they can be applied to a wide variety of stimulating and accessible problems.

5.3 Stripp, Charlie Using web-based resources to support AS/A level Mathematics and
Further Mathematics [16+]
MEI is extending and enhancing its web resources to support the whole of Maths AS/A level. The resources are suitable to support all AS/A level Maths specifications. They are not syllabus or textbook dependent. The structure of the resources means that they can be used by both students and teachers. You can use them to supplement and enhance your existing teaching, or you could use them to revolutionise the way your students learn Maths!

5.4 Perkins, Sarah All Triangles Are Isosceles, And Other Mathematical Truths [16+/G]
It’s amazing what you can prove if you put your mind to it. Starting with a simple demonstration that 0=1, I’ll show you some of the classic fallacious proofs. I’ll use every inch of my mathematical guile to deceive and mislead you, so beware!

5.5 Leversha, Gerry A Journey Around Pascal’s Triangle [G]
Pascal’s triangle is one of the most familiar of mathematical structures. In this talk I undertake an exploration of this configuration, beginning with well-known results accessible to pupils in year 9 and developing different interpretations of the numbers in it. The triangle is generalised and extended in various ways, and, in the course of our exploration, we will encounter results associated with Euler, Fermat, Leibnitz, Bell, Catalan and Sierpinski, and will visit such areas of mathematics as number theory, combinatorics and fractal geometry.

5.6 Thimbleby, Harold Computers Unplugged [G]
Computers and the maths behind them are great fun, but somehow understanding computers has been turned into rote learning how to use commercial software. Very boring! This session describes how to get the excitement back into computers, by unplugging them and playing with the key ideas. The session will describe an international project to do this, and its success with all ages and levels of experience — from children through to postgraduates. Come and expect to get involved.

5.7 Continuation of Visit York Brewery Tour

6.1 Threlfall, John Shape And Space Challenges For Able Children Aged 9 To 13 [P/S]
We will show paper and computer mathematics materials designed for able pupils (from the ‘mathsinsight’ resource) at ages 9-13. We will consider pupils’ responses to challenging questions, and discuss teaching strategies to support the development of mathematical thinking in these pupils. The session is aimed at upper primary and lower secondary teachers involved with ‘gifted and talented’ pupils in mathematics.

6.2 Oldknow, Adrian Supporting Mathematics Teachers To Do X with Y,
where X = ‘Teach Geometry Effectively’, Y = ‘ICT’ [S]
The Association has been working, with DfES support, to develop guidance on ICT in teaching mathematics, and to use ICT to provide professional development for mathematics teachers. The illustrations will focus on teaching geometry (including the RS/JMC report and recent work for QCA), but the potential is far wider.

6.3 Kean, Stephen Handheld ICT – The Next Generation [S]
This session will introduce you to the Casio’s latest handheld mathematics tool, the ClassPad 300. This stylus driven PDA-like device includes a powerful Computer Algebra System, a ‘soft’ QWERTY keyboard with natural expression entry and an in-built dynamic geometry application. This will be a ‘hands-on’ workshop.

6.4 Jagger, Jan Generalisations Of Pythagoras’ Theorem [S]
This talk will include the dissection proof of Pythagoras’ Theorem given by the 9th Century Mesopotamian mathematician Thabit ibn Qurra, as well as other results associated with Pythagoras’ Theorem. Be prepared to do some mathematics.

6.5 McBreen, Gerard Using Interactive Physics™ To Teach AS/A2 Mechanics Modules [16+]
Interactive Physics™ for Mathematics Mechanics combines a powerful and intuitive modelling program with a gallery of 72 interactive models for teaching the AS/A2 mechanics modules. The session will provide an overview of this new product, showing how it can be used to teach Mechanics. The TES BETT 2003 review quoted: "It is one of the most useful programs for advanced mathematics teaching I have seen for some time".

6.6 Holton, Matthew The Game Of Go, Its Properties And Educational Benefits [G]
Go is an ancient oriental board game of great depth and subtlety, at which computers flounder and humans excel. Hugely popular in the far east and used there as an educational tool for many years. It is growing in popularity here in the west. How best can we use Go to aid education here?

6.7 Gardiner, Tony What Is Mathematical Literacy? [G]
Teaching mathematics is hard and success is inevitably elusive. Cockcroft encouraged us to assess what kids ‘can’ do, not what they can't: the 2003 outcome was Grade C for 16% on

Higher and ‘quantitative literacy’ and ‘mathematical literacy’. We examine what school mathematics should really be about.

6.8 Rigby, John An Islamic Interlacing Pattern From Turkey [G]
Thirty years ago I copied an elaborate interlacing pattern from a tiled wall in Konya, but I have only recently analysed it in detail. It is full of regular pentagons and decagonal stars, so there is no escaping the golden ratio. Come and hear also about Whirling Dervishes and a geometry lecture at the Teacher Training College.

6.9 Cooper, Peter & Youdin, David Careers In Maths [S/16+]
The community is developing careers materials to show the benefit of studying mathematics at schools, and how this can lead to stimulating careers and improve earning potential. Target audiences include KS3, KS4, Post-16 and Undergraduates. Printed and web based materials are planned.

7.1 Singleton, Wendy Exploring Shape And Space At Key Stage 2 (Double session into 8.1) [P]
Shape and space is an often neglected area of the curriculum, given the pressures on teachers to produce ‘numerate’ children. In this session we will explore some fun activities to help develop children’s thinking skills whilst at the same time increasing their understanding of the properties of 3D and 2D shapes. The activities will be suitable for children in years 3 to 6 in mainstream mixed ability classes.

7.2 Dale, Leanne Vital Statistics [S]
Vital Statistics is a fully interactive software package linked to the AQA GCSE Statistics syllabus. The software is specifically written to engage young people, enhances student motivation and has built in self-assessment. This easy to use resource has a variety of applications; teacher-led presentations; whole class activities and independent learning opportunities, including access and diagnostic assessment via the internet.

7.3 Monaghan, John Downloading And Analysing Web-based Datasets (Double session into 8.3) [S/16+]
We are involved in a school-based project using the statistics SW package Fathom. We are exploring the possibilities, throughout the 11-18 age range, of downloading web-based datasets and using Fathom to analyse them. We expect to present some of the things we feel have worked as well as noting problems in such work.

7.4 Perks, Pat & Prestage, Stephanie Isosceles Triangles – The Way To Constructions [S]
This session will look at tasks to exploit the isosceles triangle and help students link the ideas of symmetry, reflection, perpendicular and angle bisectors, properties of polygons, circle, angle theorems and parallel lines. The isosceles triangle and dynamic geometry software and drawing facilities in Word will also feature.

7.5 Wall, Susan Interactive Teaching And Learning [16+]
In order to meet the challenges of AS level Mathematics, we have developed an interactive approach to teaching and learning. Students participate in a wide range of activities which involve discussion, connecting ideas, questioning, problem solving and no textbooks. Students are encouraged to ‘have a go’ and take more responsibility for their own learning.

7.6 Grant, Rudi Dynamic Teaching And Learning [G]
All education managers and teachers recognise the need to improve the quality of teaching and learning. Using the premise that learners who are motivated and who employ their preferred learning style will be more successful, and more likely to stay the course. This session explores the practical methods for creating dynamic learning experiences based on a variety of learning styles.

7.7 De Villiers, Michael Mathematical Treasure Hunting, Building Airports And
Rugby Goal Post Kicking [16+]
Transformation geometry will be used to solve and generalise a classical ‘pirate treasure’ problem. Similarly, the problem of finding the best position to build an airport in a number of different situations, and the best position for a kick to rugby goal posts, will be investigated.

7.8 Thimbleby, Harold Revolting Calculators: Weapons Of Maths Destruction [G]
Handheld calculators are impressive technology to get all that maths into a handy package. Except they can’t do maths. We should make better calculators, and we know how to do so. This talk reviews the state of the art in calculators, reviews the relevant maths, and shows how better calculators can work. Please come with your own calculator and see how it squares up.

7.9 Forster, David et al Mathematics - What Use Is It? [16+]
A variety of modern, real-life applications of A-level Maths, to use in the classroom to inspire and inform your pupils, and to answer the oft-posed question “What is it?”

8.1 Singleton, Wendy Exploring Shape And Space At Key Stage 2 [P]
This is a continuation of session 7.1. Please do not book as a separate session.

8.2 Anderson, Ian Check Digits In The Marketplace [S/G]
Whenever you buy the latest Harry Potter book, cornflakes or baked beans, pay for them by Visa card, visit the library or buy an airline ticket, check digits are hidden in the process. I shall discuss ISBN, IBM and EAN systems. These are real life applications of simple arithmetic ideas, easily within the grasp of school pupils, and yet giving rise to some interesting mathematics.

8.3 Monaghan, John Downloading And Analysing Web-based Datasets [S/16+]
This is a continuation of session 7.3. Please do not book as a separate session.

8.4 Ellis, Claire Code Breaking In The Classroom [S]
An insight into how secret codes and code breaking can be used in the classroom as one way of demonstrating the real life applications of maths. Cracking codes involves aspects of data handling, problem solving and logical thinking. During the session, Claire will demonstrate a genuine WW2 Enigma cipher machine.

8.5 Lewis, Barry Sequence Transforms [16+]
Martin Gardner described a neat construction for the Bell sequence, which he attributed to Professor Jeffrey Shallit. This construction is the starting point for this session, but along the way a range of famous sequences and number arrays will be encountered and explored – the Derangement, Fibonacci and Bernoull sequences, Stirling numbers and their generalisations.

8.6 Brown, Joyce Mathematics And Bell Ringing [G]
This session takes at look at the mathematics of change ringing, with an opportunity to have a go with a set of hand bells. With 4 different bells, there are 24 different “changes” that can be rung, but there are particular rules about the order of ringing these, which lead to symmetry, Fibonacci numbers, Pascal’s triangle and networks. Group Theory is involved, but this talk will not be at that level; the mathematics is accessible to all, and has been given to both primary and secondary masterclasses.

8.7 Golding Jennie Islamic Art In And Out Of The Classroom [G]
A hands-on session suitable for beginners, looking at examples of the cultural legacy of Islamic art and the perspectives it can give to the maths classroom. Participants will produce their own designs from ideas suitable for the Primary or Secondary classroom, or for their own living room. Materials provided.

9.1 Barbour, Robert Managing Transition [P/S]
Moving from one school to the next often causes a check in a pupil’s mathematical development. In Worcestershire this affects moves from first school to middle, from primary to secondary and from middle to high. I shall be describing ways we have explored with our schools to improve this transition.

9.2 Francis, Bob Exploring Geometry Via Excel And Word [S]
Bob will use facilities in Excel and Word to produce templates for exploring geometrical concepts such as symmetry, transformations, loci, conjectures, etc. Examples of classroom ready spreadsheets and worksheets will be available for delegates to explore and take home to use and/or modify to suit their teaching situation.

9.3 Dabbs, Mark Enriching Mathematical Thinking Via The Humble Triangle [S/16+]
Perhaps the most influential and regretful loss to our classrooms over the last 50 years or so has been that of pure geometry and the skills and insights it imparted to pupils. This talk will consider the most basic of geometrical objects, the circle and the triangle, and will establish some “elementary” and beautifully symmetrical, algebraic connections between them - namely the Incircle, Circumcircle, Excircles, etc. Of central importance in this work is to show pupils just how far they themselves can go with some basic algebra, trigonometry and above all else, ingenuity.

9.4 Thornber, Mark Mathematics And Chocolate [16+]
Inspired by a throwaway remark of Nick Lord, MA member at the 2003 Annual Conference, I plan to use a variety of tenuous links and laboured analogies with chocolate as an excuse to look at a range of topics from a sixth form perspective.

9.5 Stripp, Charlie The New GCE AS/A Level Specifications For Further Maths [16+]
The September 2004 changes to GCE Maths will have a significant effect on AS/A level Further Maths. Further Maths AS will become viable to teach in year 12, alongside AS Maths. This is a great opportunity for extending access to Further Maths to far more students, which could really raise the standard of Maths in the sixth form. This session discusses the 2004 changes in detail, along with their implications for the teaching and learning of AS/A level Further Maths.

9.6 Cullingworth, Barbara Logic Puzzles [G]
There are many new types of logic puzzle stemming from Tsunami, Link-a-pix and other Japanese based puzzles. This session will look at a few of them and some of the techniques needed to solve them. Expect to get fully involved.

9.7 Roper, Tom Anyone For Tennis? - The Geometry Of A Tennis Racquet [G]
Innovations over the last two to three years in the design of tennis racquets have produced claims about increased accuracy in serving and increased power of the serve thereby leading to even novices being able to improve their game. The new designs are controversial and have been threatened with bans on their use. But do the racquets do what they claim to do and how do they do it? The talk explores these designs using some GCSE mathematics and A-level mechanics. Improve your game here!


The Programme at a glance

Tuesday 13 April 2004

12.00 noon


2.00 pm

Opening Lecture - Cyril Isenberg

3.15 pm


3.45 pm

Session 1

5.00 pm


5.15 pm

Session 2

7.00 pm


8.30 pm

Icebreakers - Kjarten Poskitt


Wednesday 14 April

9.30 am

Session 3

10.45 am

Refreshments/ Publishers’ Exhibition

11.00 am

AGM / Publishers’ Exhibition

12.00 noon

Publishers’ Reception

12.30 pm

Lunch / Publishers’ Exhibition

2.00 pm

Session 4 or visits

3.15 pm


3.30 pm

Session 5 or visits

4.45 pm

Refreshments/ Publishers’ Exhibition

5.15 pm

Primary Plenary - Rob Eastaway

7.30 pm

Presidential Reception

8.00 pm

Annual Dinner
After-Dinner Speaker Des MacHale


Thursday 15 April

9.30 am

Presidential Address - Sir Christopher Zeeman

10.45 am

Refreshments/ Publishers’ Exhibition

11.15 am

Session 6

12.30 pm

Lunch / Publishers’ Exhibition

2.00 pm

Session 7

3.15 pm


3.30 pm

Session 8

4.45 pm

Refreshments/ Publishers’ Exhibition

5.00 pm

Teaching Committee: Open Meeting

6.30 pm


8.00 pm

Ghost Walk / Boat Trip


Friday 16 April

9.30 am

Session 9

10.45 am


11.15 am

Closing Lecture - David Acheson

12.30 noon



Registration Notes

Conference Arrangements

Conference sessions, all meals, and the Annual Dinner, will take place on the Campus of The University of York.
The Registration Desk will open at 12.00 noon on Tuesday, 13 April 2004.
Lunch will be available from 12.00 noon until 1.30 PM. The Opening Lecture starts at 2.00 PM.
Conference will close after lunch on Friday, 16 April 2004.
If your delegate requirements are not listed in the booking details of the Registration Form, we will do our best to accommodate you so please contact the Office Manager at Headquarters, who will be happy to discuss your requirements.
Resident price includes full board and ensuite accommodation, from lunch on Tuesday to lunch on Friday.
Non-resident price includes access to all sessions, exhibition, morning and afternoon teas/coffee, and all lunches. Evening meals and attendance at the Annual Dinner are extra.
An early bird discount is available for bookings received and fully paid before 31 December 2003.
Special Discount for NQTs - 25% discount on any price category allowed. If you fit the description, your application should be accompanied by a letter from a Headteacher or Course Tutor confirming your eligibility.
Students - 25% discount on any price category allowed and a complimentary one year membership to the Mathematical Association is included. Your application should be accompanied by a letter from your Course Tutor confirming your status.
Non-MA Members - Why not take advantage of a 10% discount on membership to the Association? Indicate on your booking form if you wish to do so, and you will receive a membership application form. Better still, telephone the Membership Secretary, Sally Bryan, on 0116 221 0013 and she will be happy to talk you through joining.
Visits - Please note that all visits take place at the same time, therefore only one needs to be chosen and paid for. We reserve the right to cancel trips if insufficient bookings are received. A refund will be made or, alternatively, if you indicate a second choice we can transfer your booking to this. (If you choose to go on a visit, then please be aware that sessions 4 & 5 cannot be booked as well.)

All accommodation is based on single room occupancy, ensuite or standard, on the University’s campus.

Partners are welcome, but may only attend sessions if they are registered as delegates. For those not wishing to attend Conference sessions, there is an option on the booking form to cover this (accommodation and meals).

Main Programme Component
The programme structure for MATHS TAKES SHAPE will have plenary lectures, regular lectures, sessions, workshops and discussion groups, covering primary, secondary, post 16 and general interest. In short something for everyone

Venue: All of the conference activities will take place on the campus of the University of York, located about 2 miles south east of York's city centre.

Getting there: The University and the city of York are well served by road and train connections from all regions of the UK. Manchester airport is the nearest airport with a train service to York.

Costs: There will be various delegate rates available, anticipated to range from £45 to £260.

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