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The Roadshow currently comprises fourteen ‘Boxes’, each of 25 practical mathematical activities on laminated A3 baseboards.
Files on the CD are in PDF, except for the response sheets and the certificates, which are provided in Word to enable you to customise these for your own events. We request that, if you are making changes, you do not alter the headers and footers that provide the Roadshow logo and that give appropriate credits.
When asked, “Are you encouraged to talk about mathematics amongst yourselves in class?” school pupils’ responses, with few exceptions, are often “No”.
The prevailing view is that mathematics is a subject that you “do” (using taught skills, usually applying a given formula or mirroring a given example) and not a subject that you “talk” about (develop).
One element of the purpose of the Roadshow is the provision of a context in which discussion amongst participants, and also between participants and helpers, is non-judgmental and is participant-centred rather than teacher-led.
In general, talking about problems helps formulate questions. Indeed, it is often said that it is more important in the first instance to be able to ask the right questions than to know the right answers. Being able to ask the right question means that you have already ordered your thoughts appropriately and are therefore probably half way to finding the right solution.
It is for these reasons that we encourage the pupils to work together in FunMaths Roadshow sessions. These discussions lead to a more in depth understanding amongst pupils as they will learn far more from each other than from any teacher.
Selection of Appropriate Activities
Activities within each box of 25 have been selected to provide for a wide spread of abilities within the intended age group. They have been selected with some or all of the following criteria in mind:
Accessible – participants will be able to understand what they are being asked to do. Attemptable – they will be able to make a start on the activity. Achievable – they will have a good chance of completing the activity, perhaps with help. Guidable – helpers will be able to provide a hint, without doing the activity for them. Discussable – there are important mathematical issues or concepts relating to the activity.
It is recommended that you bear these criteria in mind if you choose to work with sub-sets of the activities or adapt the material for use in other ways.
Freedom of movement & timing
Normally, participants work in groups of two or three. They take responsibility for the sequence of activities that they pursue and for their work rate. Neither is dictated by the structure of the event. These responsibilities are always readily accepted and contribute to the sense of ownership of the session and the achievement attained, whatever the basic abilities of the participants.
It comes as a surprise and a disappointment to hear that sometimes the nature of the Roadshow event has been changed to restrict the time allowed for each activity or to require participants to move on upon hearing a whistle blown or a hooter sounded. This approach demoralises the slower thinkers and deprives the deeper thinkers of time to explore particular activities in depth.
It is vitally important that participants have the freedom to explore the mathematics at their own pace. This leads to them having ownership of the task, and of the solution. Teachers will know their own pupils, and will identify pupils who are ‘swinging the lead’ and as such need to be moved on. The use of any sort of timing restriction for individual activities is strongly advised against.
There is a strong temptation to encourage pupils to take part with a prize for the most activities completed. We have found that this can be detrimental for a number of reasons. The more able pupils tend to focus on easier and faster-to-solve activities, and then rush through them without taking time to think things through. The less able become disillusioned as they know that they can’t compete with the more able.
If you feel it is necessary to have some level of competition to motivate your students, we would recommend the phrase ‘a prize for the people who do best’, perhaps emphasizing that ‘the best’ does not mean ‘the most’.
Use of older pupils as support staff
Observation on schools visits suggests that many teachers have little experience of this “sharing” of responsibility and are somewhat hesitant in its use. Nevertheless they are invariably pleased with, and sometimes express their surprise at, the outcome.
The use of older pupils in this support staff role has many benefits. It provides further opportunities for discussion of mathematics, as mentioned above, with the addition that explaining the mathematical concepts to the younger pupils has a considerable effect on the older pupils’ understanding of those concepts. It also allows teachers to maintain an over view of the session, and also in most cases reduces the chances of pupils becoming disengaged whilst they await assistance.
The FunMaths Roadshow of the Liverpool Mathematical Society was originally created to celebrate the Society’s Centenary in 1999. The first edition of this CD - Version 2 of the Roadshow - was the culmination of a review of the Roadshow material undertaken during 2003. Subsequent versions have appeared every two years, up to Version 5, produced in 2009.
Changes made in V2 were mostly cosmetic other than some revision of Box 4 and the addition of boxes 5 to 8. V3 included two new Boxes, 9 and 10, which are aimed at A-Level students, as well as translations of the original eight Boxes into French, Welsh and Scots Gaelic. A few minor amendments were also made. V4 contained two new ‘Reality Maths’ Boxes, 11 and 12, and a translation of the original eight Boxes into Spanish. Again, there were some minor alterations to existing material.
Version 5 saw the addition of Boxes -1 and 0 to cater for the needs of Years 1 to 4. A number of activities from Box 1 were moved down to the two new primary Boxes and replaced by new material, while refinements were made to some other activities, based on experience of using them in schools.
From January 2013, Version 6 became available as a download. The primary Boxes (-1 to 3) have been translated into Welsh and are also available as a download. Work is progressing on further translations.
We recommend that much of the material, such as dominoes, tangrams, counters, etc, be obtained from educational suppliers, a ‘shopping list’ is included in each template pack. Much of this equipment may already be available in school. However, in almost every case, we supply templates, so that schools can put together their own sets at low cost. The baseboards should be laminated coloured A3 card, the baseboards for a given Box all being of the same colour. The colours suggested are green for Boxes 1, 5 and 9, yellow for Boxes 2, 6 and 10, pink for Boxes -1, 3, 7 and 11 and blue for Boxes 0, 4, 8 and 12.
An amazing feature of the Roadshow has been that equipment is seldom, if ever, lost. Virtually every event on record has been a success, with pupils of all ages and abilities often disappointed when time is up.
Sample certificates are provided for all participants and there are special certificates for student helpers to recognise their support for their peers during the session.
How it all Started
The Liverpool Mathematical Society (LivMS) was founded in 1899, principally as a meeting place for grammar school teachers of Maths and University Staff. In the mid 1970’s, James Taylor came to the University of Liverpool as Professor of Pure Mathematics. He recently had been Chairman of the Joint Mathematical Council (JMC) and felt that there was need for greater contact between the University and teachers of Mathematics in local Secondary Schools. He sent round a MEMO inviting all Heads of Maths in Merseyside schools and colleagues in other Higher Education establishments to a meeting at the University. That was the beginning of what became quickly known as Mathematical Education on Merseyside (MEM). This was designed to be independent of the University and to complement the LivMS rather than to replace it. It has for many years enjoyed Charity status.
The first MEM CHALLENGE take-home competition for 12/13-year-olds was circulated to schools in May 1978. The format has proven successful, and continues largely unchanged to the present day. The cartoonist, Peter Ackerley, has illustrated every paper over that period. His logo for MEM of a planet orbiting a cube bearing the letters M E M inspired the title of the termly newsletter - the MEM Orbiter, which continues to be circulated to almost all schools within Merseyside, Cheshire, the nearer parts of Lancashire, most of North Wales and the Isle of Man, as well as to many schools much further afield. If you or your school would like to be added to the circulation list, at no charge, just let us know.
The next relevant event was the national Popmaths Roadshow, which travelled the country in 1989/90, visiting around 20 venues, the first of which was the University of Leeds in September 1989. The Liverpool show, in May 1990, was hosted by both the Liverpool Cathedrals. The main activities were sited in the Lutyens Crypt of the Metropolitan Cathedral, complemented by a glorious selection of John Robinson's abstract sculptures in the nave of the Anglican Cathedral. A local add-on was a competition for children involving solving at least 10 out of around 50 puzzles set out on trestle tables around a maze. This was put together by staff from what is now Liverpool Hope University.
How It Evolved
The Liverpool Mathematical Society celebrated its centenary in 1999. Girobank, based in Bootle on Merseyside, and subsequently part of Alliance and Leicester, gave a grant of £2000, provided it was spent directly on children at local schools. We were aware that two teachers, Mary White and Frances Sibert, had taken up the idea of the puzzles on trestles. They used the material mainly for open days at Secondary schools when Primary children visited. Mary White was a Special Needs teacher, and she ensured that the mix of activities was accessible to everyone. In 1998, we approached them to see whether their material could be used as the basis of a local maths roadshow. Thus was the Funmaths Roadshow born. A committee of 12 teachers and Higher Education staff and students met, put together the first 100 activities. These 4 boxes were roughly graded as being accessible to School Years 5, 6, 7 and 8, respectively.
1998 – 2000
During the Centenary Year 1998/9 the Show attended over 100 venues all over Merseyside, Cheshire, North Wales and the Isle of Man. In the following year it went to quite a number of places further afield including, Preston, Fleetwood, Ulverston, Wells and Wycliffe College near Stroud, and even Inverurie, north of Aberdeen in Scotland to name but a few. We had a presence at MathFest North West at Maine Road, Manchester on July 1, 2000 and in September and October of that year the Roadshow was in Edinburgh for two weeks, while in November it was at Wareham, Dorset and Poole for a weekend.
Boxes 1 to 4 were made available to buy at the Joint Easter conference of the MA and the ATM in 1999. The conference, held at Liverpool Hope University College, celebrated the centenary of the LivMS. For each Box, there was a pack that contained A4 copies of all the baseboards along with templates, solutions and an equipment ‘shopping list’. The packs sold so well that reprints had to be ordered twice during the 3 days of the conference.
2000 – 2001 Boxes 5 and 6
The success of Boxes 1 to 4 was such that the LivMS commissioned a further two boxes, aimed at Years 9 and 10, in 2000. A development grant was obtained from COPUS, the Committee on the Public Understanding of Science, based at the Royal Society in London. The chance to do a critique of the trials of this new material was taken up eagerly by Shaine Bushell, a final honours student at the University of Liverpool, who had met the original Roadshow in the early 1990’s at the school where Frances Sibert was then teaching. He says that the day he came up from his Primary School to visit the Senior School is one of the most memorable days of his school career. In the two or three years that followed, he was Frances’ ‘staff’ when she again used the material. After taking a PhD in Mathematics he worked as a secondary maths teacher, before taking up a post at the University of Chester. Trials of Boxes 5 and 6 were very successful, including the use of the material in Masterclasses in Liverpool, Wycliffe College, and the University of Glamorgan, as well as on visits to a wide variety of schools.
2001 – 2003 Boxes 7 and 8
Encouraged by the continued success of the Roadshow, the LivMS commissioned two Boxes aimed at Years 11 and 12, the transition from GCSE to A -level studies. A number of these activities feature geometrical ideas or simple algebraic proofs. Trials of these Boxes were successful, and they were on display at the meeting of the Mathematical Association at the University of East Anglia in April, 2003. These Boxes have been found to be useful in a cross-curricular setting as well as providing a break from routine in the regular Mathematics programme. In the summer of 2003, for the first time, all Boxes of the Roadshow were thoroughly revised, and the material put on a CD, ‘Version 2’ of the Roadshow.
2003 – 2005 Boxes 9 and 10
In the summer of 2004 we moved one stage further and created Boxes 9 and 10, aimed at A-Level students studying Maths and/or Further Maths. Activities include ones looking at the natural logarithm and the exponential function, as well as complex numbers and 2 x 2 matrices. But these more serious items are interspersed with more light-hearted topics. The material was trialled first at a University of Liverpool Maths Club session, then at UCAS visits at the University of Liverpool. The final trial was in February 2005 at Runshaw College, Leyland.
2005 – 2007 Boxes 11 and 12
What seemed now to be missing was material suitable for use with those Year 12 and 13 students who were not necessarily taking A Level in Maths. We developed the concept of ‘Reality Maths’ for these activities, which looked at the use of mathematics in contexts as varied as cycling, tennis, loan repayments and driving safely. As has been our practice throughout, students, lecturers and teachers were part of the writing committee, and on this occasion we have also had very positive input from several school students. Trials were held at the University of Liverpool Maths Club, along with schools all over the country.
2008 – 2009 Boxes -1 and 0
After requests from many schools for material suitable to work with Key Stage 1, it was decided to develop two new Boxes at the primary level. Primary teachers in Ellesmere Port, particularly the staff at Sutton Green Primary School, and staff from Liverpool Hope University were very helpful in the process of writing and trialling the new activities. Several activities throughout the Roadshow underwent some modification and the solutions to all of the boxes were upgraded to include more detail to help staff discuss the answers with students.
2010 – 2013
Following on from the successful addition of Key Stage One resources, further refinements were made to various activities throughout the Roadshow, based on teacher and pupil feedback and also our own experience of running events in schools. As ever, minor revisions and corrections were made to both activities and solutions, to remove potential ambiguities and errors.
To address a perceived lack of activities on handling data, a small number were written and replaced some older activities, principally at Key Stages Three and Four.
These and other changes were incorporated into Version 6, which was released as a download in January 2013.
Work is progressing on a new Polish translation of Version 6 in bilingual and stand-alone forms; it is hoped that this will be available as a download by the end of 2013. Work has started on an update of the Spanish translation. Translators for a new German version are being sought and other translations are also envisaged.
It is hoped that, in due course, translations of Version 6 into at least some of the other languages previously available will be completed.
Association with SETNET
The LivMS became an Associate of SETNET in 2003, and we have regularly been involved in activities of SETPOINT Greater Merseyside (now Maestro Services) since then, mainly at Anfield football stadium. SETPOINT North of Scotland has used Roadshow materials for some years. In the summer of 2003, the Roadshow was demonstrated to SETPOINT East London. In October of that year it was demonstrated to SETPOINT Hertfordshire at a school in St Albans, and we have heard that the material is to be used in schools all over that county. During March 2005, the Roadshow visited ten schools in Belfast at the invitation of SETPOINT Northern Ireland.
Although we usually set out the Roadshow with two Boxes, there are many occasions where space is at a premium, or an event has a particular theme and a smaller selection of activities would be more appropriate. Our solution is to present a selection of sets of four activities, usually chosen from different Boxes. For UCAS visits to the University of Liverpool we often use all of these, and occasionally we use one or two theme sets in addition to the fifty activities in use at an event. The current selection of themes we have created is as follows:
Working in 3D : 20, 44, 70 and 94 A mathematical breakfast : 38, 63, 89 and 101 Mathematical games : 31, 55, 117 and 198 Getting the hang of things : 169, 182, 217 and 244 Identity parades : 164, 189, 208 and 232 Reality maths : 265, 273, 299, and 300 There are, of course, many other possibilities and you can create your own to suit any event.
From the start we have taken the Roadshow to schools throughout North Wales, and it was not long before a Welsh version of Boxes 1 to 8 was commissioned by CYNNAL in Caernarfon. Trials were held in schools at St Asaph, Blaenau Ffestiniog and Caernarfon during 2005.
Following a visit to Plockton and Kyle of Lochalsh in NW Scotland in 2005, there was a request for a Gaelic version and SETPOINT North of Scotland, based in Aberdeen, arranged for this to be done.
A French version followed, translated by Andre Diatta from Senegal in Francophone West Africa, who was then a research student at the University of Liverpool. It was first trialled at two primary schools in Lancaster, in association with Ripley St Thomas C of E High School, a Languages Specialist College. In 2006, the British Council in Paris sent us an invitation to exhibit at the 8th Salon of Mathematical Games on the Place St Sulpice in Paris in the Spring of 2007, which we were pleased to accept. Earlier, in January 2007, five of the team visited Provence, presenting the Roadshow in both French and English to local Primary and Secondary schools.
During the trialling of the French version at St. Julie's Catholic High School, Liverpool, a request was made that there should also be a Spanish version, as many primary schools in the Liverpool area teach Spanish rather than French. A teaching assistant at that school who was from Madrid offered to do the translation, and Boxes 1 and 2 were trialled in three primary schools in March 2006.
There followed a request for Portuguese and so a Portuguese version was prepared in Portugal by a friend of a Colleague. Some of the Portuguese material has been trialled at a school in Thetford, Norfolk, where there is a considerable number of Portuguese speakers.
The idea for a Mandarin version sprang in part from the partnership between the University of Liverpool and XJLTU in Shanghi. This version was prepared by a Chinese staff member at the University of Liverpool. Part of the Mandarin version has been trialled at Calday Grange Grammar School in West Kirby, which has been teaching Mandarin very successfully for over ten years.
Up to 2012, the translations were all based on V4 of the Roadshow, with only Boxes 1 to 8 translated into each language. So that it was possible to consult the English original, Boxes 1 to 8 of V4 in English were supplied on disc 2 alongside the language material. The various language versions of the FunMaths Roadshow have successfully been used as a cross-curricular activity. Teachers of languages and of mathematics working together along with their pupils have really enjoyed the novelty!
In 2012, work started on translations of Version 6. The primary Boxes in Welsh were released as downloads in June 2013 and it is hoped that further Boxes will be available by the end of the year. A new Polish translation in both bilingual and stand-alone forms is in progress and should also be ready for release in the autumn of 2013. Work has started on an update of the Spanish translation. Translators for a German translation are being sought. Other versions are under consideration.
We have already acknowledged the pioneering work of Frances Sibert and Mary White. In addition, Janet Kermode and Anne Higginbotham both made major contributions to the first version. Throughout the development, the contributions made by Barry Grantham, Mary Stevenson and their colleagues, students and ex-students at Liverpool Hope University cannot be overlooked. Similarly Ken McKelvie, formerly of Liverpool John Moores University, has been a tower of strength. Amongst many others who have played a part, either in the development work or in visiting schools, special mention must be made of Chris Marchant, who as a final honours student at the University of Liverpool took responsibility for all the early visits to schools in Wirral and the Chester area and Shaine Bushell, responsible for the critique of the trials of Boxes 5 and 6 for COPUS.
Roadshow materials are now an important and regular feature at INSET days for Mathematics teachers with Jan O'Neill, Debi Evans and Kelly Rawcliffe being responsible for training sessions in Sefton, Knowsley and Middlesbrough LEAs. Barry Grantham, Mary Stevenson, Kelly Rawcliffe and Vishva Murtha have used Roadshow materials with great success at Mathematics workshops held in India, Malawi, and South Africa. Mike Hodgkinson has taken the Roadshow materials to Cyprus.
In 2005, the Roadshow writing group comprised Ian Porteous, Ken McKelvie, Mark Holland, Chris Sawer, Michael Jones and Michelle Thomson, the last three being recent graduates of the University of Liverpool. Mark was responsible for involving the University of Manchester in Roadshow activities when he held a Postdoc position there in 2002/3, and there has been strong collaboration with Barbara Grundy and John Begg (previously of UMIST) since then. Chris Sawer put everything on the first version of the CD, having also been responsible for the second edition, V3 of the Roadshow. By 2009, members included recent University of Liverpool graduate Lonnie Readioff, and school students Jon Tims and Iain Carson.
Acknowledgement is also owed to those unknown authors from whose original ideas some of our material may have unwittingly been sourced.
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