General Session Abstracts

For your convenience, the codes below indicate the area of interest i.e. Primary(P), Secondary(S), Post-16(P16), Further Education(FE), Higher Education(HE) or General(G).

Session 1 Monday 3.45pm

There are no limit processes as such in classical Greek mathematics but by expressing some of Archimedes' arguments algebraically, one can see how his methods led to the notion of limits in the 17 th Century. Then we can consider how this historical development may be suggestive for teaching.

1.2 John Dabell
Maths on Fire: spark creativity through matchstick puzzles P, S

Maths on Fire will show you how to use matchsticks to generate puzzles and milk mathematical moments. The puzzles are designed for the 7-14 age group. They provide a wealth of opportunities to model mathematical concepts, motivate and challenge learners and enhance mathematical thinking. Ideal for starters, plenaries, whole class sessions, extension activities, homework, Maths Clubs and displays.

1.3 Gerry Leversha
Taking an Euler line for a walk G

In every triangle, four major centres always lie on a line. Moreover, the distances between them are always in the same ratio. In this talk, I use the Euler line as an excuse for undertaking various explorations of triangle geometry. What other triangle centres also lie on the Euler line? What can be said about a triangle which has a specified Euler line? Are there any other collinearities which mimic the properties of the Euler line, and it is possible to generate such Euler-clones by general procedures?

This talk is suitable for anyone who can remember at least some Euclidean geometry and who delights in mathematical beachcombing and the search for unexpected connections and coincidences. It is certainly not related to the national curriculum.

1.4 Janice Simpson
Learning Styles in the Classroom

Ever felt that teaching Maths is like speaking a foreign language? How would you like to be able to discover and teach to each child's preferred learning style? Come along, enjoy the experience and see how you can really make a difference.

1.5 Bill Richardson
New to conference

An introduction to the conference for those attending for the first time (and anyone else who would like to know more).

1.6 Adam Unwin-Berrey
Session title awaited G

Abstract still awaited.

Session 2 Monday 5.15 pm

2.1 Margaret Brown
Post 14 Pathways and Functional mathematics S, P16

An update and discussion of the proposals of the QCA Pathways project undertaken jointly by King's College and Edexcel following the Smith Report. This includes proposed changes in 2009 to the mathematics curriculum and assessment structures in schools and colleges, including Functional Mathematics (Entry to level 3), GCSE , AS /A level.

2.2 Rachel Gibbons
It's your responsibility P, S, P16, G

Those who appreciate mathematics should be sailing with the neglected minority - the non-A to C group. What will interest them? What do they need? How do we help those non-mathematicians who do teach them? A workshop on preparing appropriate materials for this group at all ages.

2.3 Susan Hickman Pinder
Hands On Maths P, S

A largely practical session based around Millennium Maths Project's Hands On Maths Roadshow, using activities from NRICH. Come along to discuss how such activities can be used to enhance lessons, Maths clubs, parents' evenings, open days, primary liaison events, summer schools - but mainly to get a taste of the activities themselves.

2.4 Nick Lord
Intriguing integrals P16, G

In this talk I shall look at some unconnected problems whose solutions hinge upon the evaluation of some intriguing integrals. En route we shall encounter integrands such as exp(-x^2) and sinx/x and their relatives!

2.5 Sir Christopher Zeeman
The achievement and limitations of the theory of proportion in Euclid, Book V G

Book V achieves a rigorous treatment of ratios (without the reals). Its main limitation is not to define ratios of ratios: hence no projective geometry, group theory or dynamics. The lecture replaces subtraction with a new axiom that implies Book V and allows the definition of ratios of ratios.

2.6 Mathematics Education Centre, Loughborough University
The Magic of Mechanics -development, delivery and evaluation of workshops for school students S

Modelling the real world with mathematics in practical, physical situations is an experience which few school students have the opportunity to explore. Within the Mathematics Education Centre at Loughborough University a programme of workshops has been developed through which pre- and post-GCSE pupils have the chance to carry out hands-on mechanics experiments which illustrate the laws of Newtonian mechanics, and which enable them to apply a range of mathematical techniques such as the solution of equations, gathering and analysis of data, algebraic manipulation, and graph plotting, in real world contexts. Staff in the Centre have extensive experience in the field and the Centre has access to some of the countries leading experts in the field of mechanics education.

Not only do students learn a great deal about mechanics and the modelling process, they are encouraged to work in teams during their full-day or half day workshops, and are required to present their findings to their peers and to groups of parents and staff.

This talk will describe the experiences of developing and delivering these workshops and the lessons we have learnt from their evaluation. There will be an opportunity to see at first hand a sample of resources and equipment used, and for delegates to suggest ways in which activities like this might be developed across the school-university interface.  

Session 3 Tuesday 9.30am

3.1 John Dabell
Concept Cartoons in maths G

Find out how you can use these powerful formative assessment tools to inspire dialogue, promote participation and probe learners' misconceptions. If you're looking for ways to integrate thinking, learning and assessment then this is the session for you.

3.2 Gareth Honeyford
The Good Ship IT - Sailing through primary mathematics P

From Babbage & Turing to Gates & Jobs there has always been a link between maths and computing, but ICT and numeracy in the primary classroom is IT really worth it? We will journey from BBC micros to interactive whiteboards and on line learning and chart the significant landmarks. We will look into the horizon and ask what lies ahead?

3.3 Doug French
Some Thoughts on Learning about Fractions S, P16

Fractions are an important for all students and yet many fail to develop either fluency with essential skills or the understanding to use fractions effectively in solving problems. This session will present a variety of ideas designed to stimulate students' interest and build their understanding as they acquire and use the necessary skills.

3.4 Adrian Oldknow
New, computer-aided, discoveries in the geometry of the tetrahedron S, P16

Sir Christopher Zeeman's presidential address at the MA Easter conference in York in 2004 was about 3-dimensional geometry for schools. It included extensions of results in triangle geometry, such as the Euler line, to tetrahedra. This stimulated me to revisit my own discoveries about the Soddy circles, centres and line of a triangle to see if they extend to tetrahedra. Using the newly released Cabri 3D software I was able to devise constructions for so-called 4-ball tetrahedra and to discover 3D analogies to the results established in the plane. Working with Michael Fox, John Rigby and Sir Christopher Zeeman we have now established all the main results using a variety of geometric techniques. My talk will present the discoveries and also show how easy it is to set up exploratory models using Cabri 3D software. John and Michael will also give talks which between them cover most of the theoretical underpinning of the work - as well as links with unexpected pieces of geometry, such as Steiner chains.

3.5 Chris Pritchard
The Elementary Geometry of the Cyclic Quadrilateral G, S

Many teachers are aware of just one theorem relating to the geometry of the cyclic quadrilateral (that 'alternate' angles are supplementary) but there are many beautiful results associated with the shape and some of them are certainly suitable for secondary students.

3.6 Tony Robin
Some interesting problems G

We shall look at a few problems like Is it possible to manoeuvre that large wardrobe around a certain corner? or How are the numbers 5, 4, 6, 4, 14 linked to 2006, 2007,2010.

3.7 Peter Thomas & members of Post 16 Subcommittee
Post-16 Open Session , P16
The session will be an opportunity to be briefed on current developments in post-16 mathematics education and on the work of the MA's Post-16 Subcommittee. There will be plenty of opportunity for discussion of the issues and to suggest future action.

Session 4 Tuesday 2.00pm

4.1 Steve Abbott
How to teach mathematics well - the value of deeper subject knowledge P, S, P16, G

The campaign for real mathematics. Does your school teach students to understand mathematics?

The most effective teachers understand how mathematical concepts are built up over time and make links that reinforce students' understanding. As a result they can 'assess for learning'. They adopt teaching styles and use teaching resources that help students to think mathematically and to use and apply their knowledge in new contexts. This session will illustrate the importance of teachers' subject knowledge and explain how to teach students to think mathematically for themselves.

4.2 David Crawford
Mathacadabra! P, S, G

In this session I will look at some seemingly magical tricks all of which can be explained using relatively simple mathematics. The tricks fall into 2 main categories: Number tricks, which I use with my younger pupils to generate a bit of a wow factor in the classroom and to motivate them to practise mental and written arithmetic algorithms, and Card tricks (no slight of hand required!) which can generate a desire to understand how the tricks work and so lead to an interest in proof.

4.3 Adam McBride
Problems! Problems! S, P16, FE, HE, G

A look at some favourite problems which only require the ability to count and think straight, plus a dash of insight.

4.4 Elena Nardi
Towards a new pedagogy for undergraduate mathematics HE

'You look at these students, you look at their faces, you know they are lost...':

In this interactive session we will examine samples from a book Elena is currently working on. The book explores the experience of learning and teaching mathematics at university level from the perspectives of mathematics undergraduates - what they find difficult, rewarding etc. - and of the mathematicians who teach them - how they believe their students learn, what their difficulties are, how they help their students overcome these difficulties, etc.. The samples are in the form of fictional but data-grounded dialogues between a mathematician and a researcher in mathematics education.

4.5 Janice Simpson
Mind Mapping in the maths classroom G, S, P16

Would you like to ensure that regular revision of facts and formulae is taking place? Come along and learn, by experience, how to teach effective mind mapping to your pupils.

4.6 Wendy Singleton
Setting Sail P

This session will look closely at mathematical development in the late foundation stage (YR). The focus will be on counting skills and the early use of the number line. Consideration will be given to both the Curriculum Guidance for the Foundation Stage and the Framework for Teaching Mathematics.

4.7 John Rigby
The Soddy spheres of a tetrahedron P16, HE

Sir Christopher Zeeman's 2004 presidential address was the inspiration for an investigation, by a small group of enthusiastic MA geometers, of the 3-dimensional analogue of the Soddy circles of a triangle. I shall show how techniques and concepts such as 3-dimensional inversion and basic pole-and-polar properties of a sphere can shed light on the topic.

Session 5 Tuesday 3.30pm

5.1 Tony Croft
Supporting your students with mathematics & statistics at the transition to University P16, HE

What is not always appreciated in schools is that a huge proportion of school students will be required to study mathematics or statistics upon arrival at University. Apart from the obvious and traditional users of mathematics such as engineers and physical scientists, increasingly many other groups, such as nurses, psychologists, biologists, and social scientists are required to use mathematical and statistical methods too. This talk will outline the ways in which staff in the Mathematics Learning Support Centre at Loughborough are supporting your students once they arrive at University, and there will be an opportunity to explore some of the many resources we use to do this.

5.2 Michael Fox
Going round in circles G

We shall study some unfamiliar properties of tangent circles including (possibly) some new results. And we see how geometry software can suggest properties wee might not otherwise notice. If you are interested in classical geometry, this session might stimulate your imagination.

5.3 John Holden
Enhancing Excel as a Teaching Tool S

Excel does not cope well when required to graph continuous data. This session will show how using an Excel Add-In teachers and pupils can produce histograms, frequency diagrams and box-whisker plots easily. Other areas of mathematical functionality that will be shown include sampling and decision mathematics capabilities. The Excel Add-In used for the session will be the NAG Schools Excel Add-In (N-SEA)

5.4 Paola Iannone
The power of the number line P

One of the teaching aids that are strongly supported by the National Numeracy Strategy for children of all ages at primary school is the Number Line. In this sessions I will draw on an ESRC funded study to discuss the National Numeracy Strategy suggestions about the use of the number line in Year 1 mathematics teaching, and how the number line is in fact used as an aid to elementary calculations and development of counting strategies in five Y1 classes.

5.5 Wendy Singleton
Setting Sail P continued

A continuation of session 4.6

5.6 Open 11-16 Session

Session 6 Wednesday 11.15 am

6.1 Colin Abell
Navigating the Primary Mathematics Challenge P

Abstract awaited.  

6.2 Martin Bailey
Modular Origami G, S

Come and experience some of the wonders of Modular Origami. I will attempt to squeeze a 3-hour year-8 G&T masterclass into 75 minutes. No previous experience required!

6.3 Keith Eames
Use of PowerPoint in delivering Mathematics at Eastbury Comprehensive School S, P16

The session will involve how Eastbury Mathematics department set up and used Powerpoint at KS3, KS4 and KS5 to include GCSE revision on past papers. People that attend will go away with a number of Powerpoints to try out themselves.

6.4 Ray Huntley
People Maths - Seeking Submerged Treasure P, S, G

The session will explore some mathematical activities using people games, some well-known, some new. You can test out kinaesthetic learning styles by engaging in practical problem solving and see if they work for you and for other learners. We will also explore the hidden mathematical depths below the surface of some of the activities. This will be through group work with support, since a little bit of subject awareness and follow-up can help all learners to get the treasure beneath.

6.5 David Knowles
Mathematics and Computing Courses at the Open University FE, HE

Mathematics and computing courses and qualifications at the Open University, with particular reference to the following: -

Overview of Open University s Courses available in the Mathematics and Computing Faculty s Young Applicants in Schools Scheme s Graduate Diploma in Mathematics Education.

6.6 Bill Richardson
UKMT S

A chance to see and try some recent and less widely available questions. Definitely a 'Key Stage free zone'.

6.7 John Rigby
From Primary to Penrose: Tilings for Tiny Tots, Teenagers and Teachers G

A set of four tiles (a regular pentagon and other more unusual shapes), derived from Islamic interlacing patterns, will be described. These tiles can be used by young children for making patterns, but there is plenty of underlying mathematics (including the ubiquitous golden ratio), leading up to Penrose-type tilings. Other shapes of tile will make brief guest appearances

6.8 Charlie Stripp
Further Mathematics Network P16, FE

Abstract awaited.  

Session 7 - or leave for Trip Wednesday 2.00pm

7.1 Francis Bove & Jane Imrie
Improving learning in mathematics: challenges and strategies P16, FE

Mathematics education faces several challenges. The number studying the subject post-16 is declining and there is a perception that mathematics is difficult and fails to excite and motivate learners.

The DfES Post-16 framework, 'Improving learning in mathematics', disseminated nationally from Sept 05, was developed to meet these challenges. Building on successful practice, it explores approaches which encourage more active learning through group work, discussion, and open questioning. Learners are encouraged to 'have a go', to become more independent and reflective, to learn to think mathematically rather than simply learning rules and, most importantly, to enjoy mathematics.

This hands-on session offers the opportunity to experience, explore and develop approaches which encourage active learning.

Using Interactive Whiteboard, John Ellis, retired teacher and author of Living Worksheets for mathematics, will demonstrate and discuss the use of some of the range of interactive lesson starters the he has written for KS3 and KS4 use.

7.3 Doug French
Proportionality at Key Stages 3 and 4 S

Proportionality is a fundamental idea that pervades many areas of school mathematics and it has a surprisingly wide and interesting range of applications to everyday situations. This session will examine some of the difficulties that students encounter with proportionality and will present a variety of classroom approaches.

7.4 Gerry Leversha
What is to be done? S, P16

It has become increasingly clear over the last few years that the standard fare offered by GCSE and modular A level is inadequate for developing either real mathematical skills or inspiring talented students to perceive mathematics as exciting and stimulating. The performance of our students in all kinds of diagnostic assessments, be they standard multiple choice tests or the more demanding challenges posed by the UKMT, is woefully disappointing compared with those who join our educational system from other countries. Teachers in universities are increasingly concerned about the inability of our students to tackle a whole range of skills, ranging from basic algebraic manipulation to the appreciation of logical structure and the ability to construct arguments. The government's insistence on acceleration rather than enrichment as the panacea for educating the more talented is only contributing to this problem.

In this talk, I look at various strategies for enriching the standard curriculum. I criticise the tendency of some textbooks to rely entirely on algorithmic procedures and suggest ways of introducing key ideas at all levels from GCSE to A2 level which provide students with a much deeper understanding and appreciation of what mathematics is really about. These ideas have all been tested in my own classroom and I am sure that they can be used in your own. I hope I can persuade you that it is high time to launch the Campaign for Real Mathematics.

7.5 Barbara Linton
QCA Secondary & Post-16 Update S

The purpose of this session will be to share the latest insights into the current curriculum and pupil performance; new developments aimed at strengthening teaching and learning; and recent progress with projects relating to government initiatives.

7.6 Jenny Ramsden
Mathematics of Navigation S, G

In this talk, I will run through what I teach about latitude and longitude calculations at a Year 9 Masterclass for the gifted and talented. I will aim to show how this topic, sadly no longer on the secondary school curriculum, can be introduced at various levels and used to stretch the most able pupils. No previous knowledge is required, but bring a calculator to join in the fun!

7.7 Charlie Stripp
Further Mathematics Network P16

Abstract awaited.

Session 8 & Trip Wednesday 3.30pm

8.1 Francis Bove & Jane Imrie
Improving learning in mathematics: challenges and strategies P16, FE

Double session see 7.1

8.2 Bob Francis
Computer Workshop S, FE, HE

Title and abstract awaited.

8.3 Michael De Villiers
Using dynamic geometry to engage students in defining quadrilaterals themselves S, P16

A short theoretical perspective from the Van Hiele theory about the importance of actively engaging students in defining mathematical objects themselves will be given. Participants will then engage in a series of Sketchpad activities, e.g. exploring the properties of an isosceles trapezium and investigating several different correct, economical definitions.

8.4 Tony Gardiner

Tony confirms that this change does not affect his original session content.

New title: "Euclidean geometry in 90 minutes"

New description: The profession recognises the need for a coherent programme of more demanding provision for the top 25% or so. Euclidean geometry should be a natural part of such provision. But most teachers have never taken a course in formal Euclidean geometry. Here is your chance to correct this.

(Original title: An extension programme for Years 6-10 P, S )

(Original description: The future shape of secondary mathematics and its assessment remain unclear. But the Smith Report and the profession are clear about the need for a coherent programme of more demanding provision for the top 25% or so. We will discuss the issues in the light of draft material for Years 6-10.)

8.5 Donald Keedwell
Defining sets for ordinary and magic Sudoku squares G

Abstract awaited.

8.6 Peter Thomas & members of Post 16 Subcommittee
Advanced Revision P16
In this session several teachers will talk about approaches to revision for AS and A2 examinations. The emphasis will be on strategies that promote the active engagement of students. There will be an opportunity to discuss these ideas and to share other ones.

8.7 Pamela Wyllie
QCA Primary Update P

The purpose of this session will be to share the latest insights into the current curriculum and pupil performance; new developments aimed at strengthening teaching and learning; and recent progress with projects relating to government initiatives.

Session 9 Thursday 9.30am

9.1 David Acheson
√66 and all that G, S, P16

Square roots can help bring mathematics to life in many different ways, ranging from the number system itself to chasing the exact value of pi, exotic methods of proof, playing with the infinite, flying an aeroplane and even cooking a hot dinner.

9.2 Barbara Cullingworth
Japanese Logic Puzzles and Other G

There are many puzzles around, such as Hanjie (Tsunami), Enigma, Kakuro, Sudoku, etc., using different mathematical techniques. This session will explore some of these. I hope to stimulate participants and, possibly, also provide ideas for the classroom, though this is not the principle aim. Expect to get fully involved.

9.3 Michael De Villiers
Generalizations of the nine-point circle, Euler line, Spieker circle and Nagel line S, P16

My personal rediscovery of a beautiful generalization of the nine-point circle to a nine-point conic with Sketchpad will be given, as well as an associated generalization of the Euler line. Lastly, an analogous generalization of the so-called Spieker circle to a Spieker conic (and associated Nagel line) will be discussed. 

9.4 Jennie Golding
Go Creative in the Secondary Classroom S

We live in an age where the pressures to 'achieve' ever-higher results plague the classroom teacher, albeit we are offered ever more 'support' in the way of structured textbooks and electronic resources, all apparently designed to the same end. Teachers, and students, could be forgiven for thinking that the only important outcome is the final grade, even at the cost of the fascination, frustration, exhilaration and sheer fun that is our mathematical heritage. Not so: this workshop will be hands-on, suggesting and sharing ideas for how the teacher, and the student, can reclaim ownership of the creative culture that is mathematics. Much more than scissors, glue and coloured pens (and it needn't cost grades!).

9.5 Jenny Gage & Toni Beardon
Discovering of Maths & Science through video conferencing P, S, P16, FE, HE

This is suitable for teachers in primary, secondary and FE plus anyone else interested in using video conferencing in education, using discovery and experimental methods in mathematics, or forming links with the developing world.

9.6 Barry Lewis
Fibonacci numbers and trigonometry - two sides of the golden coin. P16, FE, HE, G

Fibonacci numbers are to the sine function as the Lucas numbers are to the cosine function - an exploration of this astonishing duality and in a generalised setting the constructive way it leads to unification and structure. Requirements: Euler's exponential formula for the trigonometric functions; Binet's form for Fibonacci numbers.

And look out for the Ian Porteous' Funmaths Roadshow

A brief history of the project, from its inception to celebrate the Centenary of the Liverpool Mathematical Society in 1999, to its current extensive scope in partnership with various SETPOINTs, The Ri and the Specialist Schools Trust.