Much learning, both formal and informal will take place in the family home. Parents have an opportunity to share sometimes unique experiences and aptitudes with their children. Co-operative projects between schools and parents can be free from the traditional constraints of homework and provide new and creative ways to enhance learning and build stronger links between home and school.

Showing You're Working

A Project Using Former Pupil's Experiences to Engage Current Mathematics Students

Addressing the needs of disaffected mathematics students has always been an issue for teachers. The article seeks to explore some of the complex issues that surround such a topic, initially through a literature review, and then by examining a project that attempts to address in a small way, some of these issues highlighted. The purpose of this project is to provide answers to questions sometimes asked by frustrated pupils, such as, “What is the point of this, Sir?” or, “When will I ever use this in my everyday life?” By addressing pupils’ concerns through a range of examples, showing students how former pupils use mathematics in their daily lives, provided a hook that engaged those pupils. The diversity of professions also helped dispel many myths about the uselessness of mathematics. There have been a number of other benefits too which will also be discussed, such as current students’ attitudes to mathematics; which were tested during the study, and as a result of this initiative and several spin off activities, pupil’s perception of mathematics is now more positive, particularly with regards to the need of mathematics in potential future careers.

By examining a number of reports commissioned by the government in this review of literature, key issues will be discussed which in turn concern educationalists and industrialists alike today.

Let us begin by looking at why Mathematics is considered such an integral part of every child’s education. In his report on Mathematics Education Adrian Smith listed a number of reasons justifying mathematics’ prominent position; mathematics for its own sake; mathematics for a knowledge economy; mathematics for science, technology and engineering; mathematics for the workplace; mathematics for the citizen. Reading Smith’s report it is evident that Mathematics is a necessary part of our everyday lives, and the remainder of section 1 I will address relevancy in the mathematics classroom, but also explore some of the wider issues of the relevance of today’s mathematics curriculum to society, by examining several key reports that refer to aspects of Smith’s definitive list. Then in section 2 I hope to detail how “Showing You’re Working” could have a positive effect on the delivery of some of the government recommendations found in these reports such as the implementation of Functional Mathematics, and developing mathematical literacies in the workplace.

1.1 - Contextualising mathematics, mathematics for the citizen

“When will I ever use this in my everyday life?”

This is a phrase sometimes heard uttered by an exasperated student in my Year 9 bottom set last period on a Friday afternoon. As a mathematics teacher trying to justify my existence, I have often taken the bait, just like the Marlin in Hemingway’s Old Man and the Sea. Sadly, though, despite my very best attempts to provide an answer, there is always a pervading feeling that my comments make little impression on these disaffected students. I have no doubt that this is because, in discussion, they perceive me as an authority figure with little or no empathy for their situation and so, sadly, my response has little impact on them. So attempting to teach students through contextualised approach seems to address this problem, but there are also issues which are important when selecting suitable contextual material, summarised by both Southwell(1994), and Clarke (1990) who state that:

[teachers] need to find applications that are important and meaningful in the world of our pupils, and not just ones which get us, the teachers, excited.(Pg.34)

I am keen therefore to try to give my students examples that engage them but a balancing act inevitably ensues, as closer inspection of Smith’s many justifications in turn becomes almost an obligation that links the concerns of my learners to finding connections to everyday mathematics.

1.2 - Contextualising mathematics, mathematics for a knowledge economy

In 2004, Lord Leitch was commissioned by the Chancellor and Secretary of State for Education and Skills to lead an independent review to consider the skills base required by the UK by 2020 to maximise growth, productivity and social justice. The report was published in December 2006, and in its response document Numeracy for Employability (October 2007), The National Centre for Excellence in the Teaching of Mathematics (NCETM) outlined the aims of the report with particular reference to its Numeracy strategy. There are many issues which Lord Leitch seeks to address, some of which will be beyond the scope of the current 14 – 19 Pathways developments, and must be resolved by employers in the workplace through training initiatives. However, there are a number of school-based recommendations which Lord Leitch felt were necessary if the UK is to compete economically on a global stage. These are primarily to raise the level of “basic skills of functional numeracy (and literacy)”. The DIUS has asked NCETM to work with key stakeholders to develop a strategy to meet a range of ambitious criteria to enable our potential workforce of the future to be prepared for the new challenges ahead, through the successful implementation of Functional Mathematics for example.

As a current Head of Mathematics, I have one eye very much upon looking after my existing crop of students as they pass through the system. However, I am very aware that the future planned developments for mathematics, such as the introduction of Functional Mathematics, has a role to play in the successful implementation of Lord Leitch’s recommendations, and in a recent article Ken Boston emphasised his belief in basic skills, stating that basic literacy and numeracy were the right foundation for young people’s future success .

Thus, the successful implementation of Functional Mathematics and hence the work of NCETM will be central to much of the work leading to the attainment of World Class Skills for the British workforce before 2020.

1.3 - Contextualising mathematics, a historical perspective

The importance of the philosophy underpinning the teaching of mathematics in Britain to the success of Functional Mathematics cannot be underestimated. Casting an eye over the current school curriculum, I feel certain that a balanced approach to the integration of contextual applications that include all of these would be desirable.

However, this idea is not a new one, as Monroe (1994) points out:

The need for mathematical connections was articulated as early as 1902 by E.H. Moore in a presidential address to the American Mathematical Society:
“…everything exists in its relations to other things, and in teaching the one thing the teacher must illuminate are these relationships” (page 371)

Indeed, in his paper Using and Applying Mathematics in Education, DeLange (1996) charted the development of application and modelling within curricula. Based at the Fruedenthal Institute in the Netherlands, DeLange developed a school curriculum called the Theory of Realistic Mathematics Education (RME.) that sought to utilise and integrate application within the Dutch education system. Many other educationalists over the past twenty years have also championed the relevance of the curriculum, and a number of national initiatives developed in Britain in the 1970’s and post-Cockroft, due to an awareness of school leavers’ inability to transfer those techniques learned at school to the workplace (Boaler (1994)). These included the Mathematics Applicable Project (Ormell (1975)), The MEI scheme, Integrated Mathematics Scheme, The Spode Group, Kent Maths, The SMP scheme, and more recently, the LAMP and RAMP projects, and Enterprising Mathematics (Burghes and Hobbs, (1989), to name but a few.

Many of these initiatives were highly successful in engaging disaffected students and providing examples and connections for students to understand the links between mathematics and aspects of our daily lives. Many of these initiatives fizzled out, as other educational priorities gained importance, but more recently things have come full circle and, in the past few years, DeLange’s RME approach has gathered momentum here in Britain and a variant continues to be piloted with great success in pathfinder schools in the Manchester area.

Given the positive benefits in terms of enhanced motivation and raised pupil perception in making connections with the everyday world that were seen through these projects, it would follow that recognising applicability of skills could in turn enhance the learning in the classroom. This might suggest that such approaches could help deliver some of the benchmarks suggested by Lord Leitch in his report, and that this link is not just an aspirational one.

1.4 - Contextualising mathematics, mathematics for the workplace

However, looking at the problem solely in the school context by treating the learning of each individual student as a “potential member of the economy” would be imbalanced without input from the employers, and those who understand the needs of the workplace. Although, before I discuss the nature of the research conducted, I think it might be pertinent to suggest that teasing out explicit mathematical usage from employers can be an extremely difficult exercise, as contextual problem solving and reasoning skills are often not viewed as mathematical in nature, but are associated with a more generic wisdom akin to “common sense” .

Much educational research has taken place, focusing upon the mathematical needs of the workplace, such as the text Schools Mathematics and Work Ed. M. Harris (1991) and, more recently, Mathematical Skills in the Workplace (Celia Hoyles, Alison Wolf, Susan Molyneux-Hodgson and Phillip Kent – June 2002, Institute of Education and STMC). Through a series of case studies, the report detailed how the mathematical needs of industry have changed due to advances in Information Technology, but the recommendations emphasised that the need for mathematics was still critical. The report redefined the need as being a mathematical literacy and, through their four recommendations, detailed how these literacies might be developed. The recommendations examined how to raise awareness of mathematical literacy; the need to generate workplace CPD opportunities to promote and develop these competencies; to investigate further the core concepts within the mathematical literacies, and the need to communicate to employers how particular qualifications relate to these competencies. Interestingly, looking at the international perspective, Lakoma (2002) cites similar findings based on his experience in Poland, when looking at the school education system and implications for future engineers in the digital era.

1.5 - Contextualising mathematics, mathematics for science, technology and engineering

Membership of the MEI Industry Committee has given me an invaluable insight into issues which currently surround Mathematics education with particular reference to mathematical needs of the workplace, and also into curriculum development, 14-19 Pathways, and Functional Mathematics to name but a few.

Indeed, whilst attending a recent MEI/IET conference examining the needs of Engineering, it became evident that many delegates and speakers shared concerns over the dearth of suitably qualified individuals who would need to join the profession to address the current population dynamic found among engineering industry, thus replacing those due to retire in the near future. One glimmer of hope was the Further Mathematics Network initiative, which many felt provided an alternative route to facilitate the learning of Further Mathematics, and has been a major influence in the upturn in numbers taking mathematics in the sixth form since the dramatic fall in 2001-02. This concern was also reflected in Lord Sainsbury’s recent review (October 2007) where he sets out a map in section 7 to “Educate a new generation of young scientists and engineers”; granted many of his recommendations centred around the need to develop and promote the ‘S’ ‘T’ and ‘E’ elements of STEM. However, there are a number of STEM initiatives that aim to put the Mathematics (or the M) into STEM, as discussed by Adrian Fenton (of STEM), at the recent IMA “Mathematics Works 2007” Conference.

Having commissioned these reports, the government now needs to look carefully at the recommendations to decide how best to make sense of the needs of the workplace, preparing a workforce for the challenge they will face in a (information) technologically changing economy. Some issues are being addressed, in part, through the changes due to take place in GCSE mathematics in the coming years. This is dominated by the introduction of Functional Mathematics and the second GCSE qualification. The proposed changes to the 14-19 Pathways are also significant. Relevance of the curriculum, therefore, will once again become a hot topic in school mathematics, with specific reference to the workplace becoming increasingly emphasised.

When discussing mathematical literacies in particular, one aspect of the final recommendation of Mathematical Skills in the Workplace stated that the focus should be to:

Determine how educators could communicate this information more effectively to employers, including ways of enabling closer links between schools, FE, HE and employers (Foreword by Steering Group: 4)

As a teacher of Mathematics, this statement made me think about opportunities to forge links between the current student body and two major stakeholders in the life of any school; its former pupils and the parents of its current pupils. I had concerns, though, when reading a document entitled ‘Blueprint for Numeracy’ which was published for employers to help them understand the full implications of the Cockroft report. The booklet concluded with a message to employers to encourage those in industry to develop liaison schemes with schools. I agree entirely with these sentiments, although given the final recommendation quoted above, I question whether there has been a successful sustained link between industry and schools at a national level since the publishing of the Cockroft Report in 1983. I must clarify this query by stating that I am sure that at regional levels and through LEA appointments in the past of schools/industry liaison officers there has been some success. Nevertheless, at this particular point in time, I don’t feel there have been national initiatives which have built, maintained and sustained those links with schools. Therefore, in some small way I wanted to develop a project that had the potential to enable schools to approach industry proactively through credible use of former pupils to encourage links to develop naturally.

After graduating, and securing a Mathematics teaching post at Kingswood School in Bath in 1994, I maintained links with Exeter University’s School of Education and, during that time, I spent a summer vacation visiting a range of businesses and industries, conducting interviews for a research project examining the mathematical needs of industry . My interest in teaching mathematics and making connections with every day life took a different turn between 1999 and 2001 when I completed a Masters degree in Philosophy, which focused on using sporting contexts to increase motivation in the mathematics classroom. I think, looking back, that I was very fortunate to have David Burghes as a supervising tutor; he inspired me to look for mathematics in everyday life. To quote Sir James Lighthill, I was someone who picked up ‘Maths at Work’, by Howson and McLone (1983), who became an interested reader of the book, and:

…was recommended to use every opportunity to become conscious of as many examples as possible from those unexpectedly vast areas of life today where, with great effectiveness mathematics is being put to work (Maths at Work, Foreword vi)

Given my background and commitment to applications in mathematics I find it especially frustrating when, as a teacher of mathematics, I have heard “What is the point of this, sir?” As discussed in 1.1 we must be mindful of our students’ interests and values, but also some unlikely inspiration can come in the shape of some people who can make that all-important impact on the students. In September 2006, I was lucky enough to host a superb talk by Paul Shepherd for sixth form students on stadium design, which made a great impression on the students present – so much so that, recently, a few students referred to it in a Physics lesson when discussing resonant frequencies. My final inspiration was seeing the fantastic range of mathematical applications represented by the speakers at the IMA “Maths Works” conference held at Birmingham in October 2006. I came away buzzing with enthusiasm to create a work-related project that could reach out to the students who are most disaffected by the whole mathematical experience in schools, although the challenge was how to package the information so that the students relate to it, and deliver the material in an engaging way?

The timing of the conference was fortuitous as the Autumn half term provided a brief interlude in which I was able to jot a few ideas down and think more formally about how I could structure the project to involve both target audiences naturally linked to schools, i.e. parents and former students.

I decided to concentrate my energies initially on contacting former students, and I was able to access e-mail addresses of a number of our ex-pupils, so a circular was sent asking them to indicate if they would be prepared to take part.

Approximately 5% of ex-students responded; these were sent a specific list of questions. I was a little unsure about the nature of the questions at first, but after reading Mathematical Skills in the Workplace Final Report to the Science, Technology and Mathematics Council, I thought that some of the questions in the on-site guidelines for observation and interview would be an ideal starting point to open up a dialogue with our ex-pupils. So I approached Alison Wolfe to seek permission to incorporate some of the questions into a template. This was sent to former pupils; one such example can be found in Appendix I. The completed answers were returned by e-mail, and a booklet of the ex-pupil responses was then compiled. In addition, several former pupils said that they would be happy to return to Kingswood to chat to the students about their experiences.

The booklet was distributed to pupils by e-mail, and an abridged version sent in a weekly newsletter to current parents. The launch included a poster campaign to match up their profession with the statement: “I need maths to….”

As stated in the review of literature, I felt that students should see industry and workplace links as integral to the relevance to their everyday lives, but balanced with other elements detailing the importance of Mathematics, such as the aesthetic qualities of mathematics and abstraction – the final of Smith’s categories from section 1. Therefore, the launch of the project was one of many aspects of a mathematical awareness week held at school in March 2007. This provided opportunities, linking seemingly disconnected topics, such as aesthetics and the nature of truth, but fundamentally promoting the ever-pervasive nature of mathematics underpinning aspects of our existence. In addition, I felt it was important to include lectures for pupils to see the power of mathematics in action, and how formal mathematical expressions could be considered both beautiful and engaging. I must thank Prof Chris Budd of Bath University, and Chris Sangwin who kindly allowed me to create a presentation based on their article entitled “101 uses of Quadratic Equations”. I must also thank Leekes Department store for kindly providing a number of wallpaper samples that were included in a lesson examining the 17 different types of wallpaper pattern.

Former students also visited Kingswood that week and gave a diverse series of talks on fields such as how mathematical modelling helped describe the Kings Cross Station tragedy, and how mathematics helped enhance the Outside Broadcast recording of the American Rock band The Foo Fighters live in Hyde Park – which the students thought was very cool. This afforded the students an excellent opportunity to see that the “fictional booklet” contained the experiences of real people, and it gave the project an immediacy that had a lasting effect on pupil perception of the relevance of the mathematics they experience at school.

I devised an assembly illustrating many of the careers, to use a visual approach to raise the profile of the project in school. This made a very significant impression on both staff and students alike as here was tangible proof that a vast array of careers uses mathematics in one way or another, but presented in a way that connected with each pupil personally. Each example was a Kingswood student who, like them, was from a similar background and had sat in their classrooms, studying the same subjects and even being taught by the same teachers! This empathy was extremely powerful and added a great deal of impact to the project. Here is one such example of a case study used. During the assembly I asked our students to raise their hands if they owned any of the devices they were about to see. Mini Disc players, MP3 players, mobile telephones, Nintendo DS, and Playstation PSP games consoles to name but a few flew onto the screen, and most students put up their hands. All of these devices are linked to former student Tudor Brown of ARM Technologies who detailed how he uses mathematics in the workplace. After leaving Kingswood, he worked in computing, and high speed devices such as graphics display controllers became his speciality. He then became part of the company that created the ARM microprocessor which now powers virtually every mobile phone, and many other consumer devices. This particular example showed the students how an ex-pupil of Kingswood stated explicitly how important mathematics is in his workplace and how his workplace and, particularly, these products impact so profoundly on our everyday lives.

Of the other professions I included in the assembly, there were contributions from a epidemiologist, bomb disposal operator, bridge engineer, lawyer, organic pizza company owner, professor of thermofluids engineering, research meteorologist, intensive care charge nurse, contract geologist, operations analyst with National Rail enquiries, agricultural adviser to Soil Association, and vet to name but a few.

From the outset of the project, I felt it was important to try to assess the potential effect that this initiative could have on the intended audience i.e. the current students. I wanted to assess pupil attitudes toward mathematics as well as the importance of mathematics to any future career plans students might have, and I used a likert scale, alongside a series of statements, that measured perception of confidence in Mathematics, as well as usefulness of mathematics. These are used with kind permission of Professor Jim Ridgway of the Durham SMART Centre. Pre-testing then took place, and the students completed a questionnaire during a tutorial session in March ’07. Rightly or wrongly, it was felt that teachers have much more influence on the perception of KS3 students. There was also awareness that option choices might well influence pupil responses in Years 9 – 13, and therefore we focused on analysis of data from Years 7 and 8 pupils – on average 75 / 76 students per sample. Please note: Year 7 students in year beginning September 2006, tested in March 2007, coded as 2006/07 Yr7, March ’07. The project has definitely altered the behaviour and attitude of some of the more disaffected students in the year group, and this is evident with recent post-test results where last year’s Y7 group were asked to answer the same set of statements (cohort “2007/08 Yr 8 Oct ‘07” in tables 1 to 5).

5.2.1 - Question Time The attitudinal data found in tables 1 – 5 (see Appendix) revealed a drop in many positive statements in responses by Year 8 pupils. I discussed this with other heads of department, as the variation might be due to simple differences between year groups. It was felt that this dip was a trend due to maybe a more apathetic phase as pupils progress through KS3. This mid key stage “blues” was the subject of discussion at a department meeting at the end of June, in preparation for the new school year. We decided to address this issue by supporting the students in Year 8, in a way, which would help them, collectively, think more about aspects of mathematics that interest them, as opposed to sticking to reinforcing techniques which they struggle to understand in the classroom. Mr Musto’s Year 8 Question Time was devised, and has been a huge success. The students were issued a challenge: if they can find a mathematics question which stumps Mr Musto, then they win chocolate bar prizes. Students submit questions. Then I devise a PowerPoint to answer as many questions as I can in the forty minute slot available. The most interesting questions that strike at the heart of mathematics have come from lower ability students. Some examples are: How many times do we use maths every day? What is the point of x? What is the perimeter and area of Bath? When do we ever use Pythagoras’ Theorem? Who was the greatest mathematician who ever lived? What is the biggest number you know? What is Pi? Did Pythagoras ever do anything for us in Bath ? These sessions have had a very positive effect on the students, because now they have a forum where they can vent their frustration about a topic or a particular bugbear they may have with mathematics, and I will try my best to answer their requests in an open and honest way.

5.2.2 - Presentation at The “Maths Works 2007” conference
Section 2 through to section 6 of this article is based upon a talk I was asked to give at the IMA “Mathematics Works 2007” Conference. The PowerPoint presentation was one of many talks by industrial mathematicians and key figures within the IMA and ACME, examining the links between mathematics, schools and the workplace. Many attending teachers and other delegates spoke very positively about the booklet of responses I had produced and distributed and, as a result of that, I was asked to write this article.

Given the success that I have seen at Kingswood which stemmed from Showing You’re Working, I hope to follow up the project with the development of a potential parent and pupil project: a collaboration to create a show and tell activity, giving details of how their parents use mathematics in the workplace. I am fully aware that this idea is not new, and I feel certain that there are teachers nationally who have already achieved success in similar ventures. I felt it was important to keep up the momentum post project, and to provide an opportunity to utilise the School’s parental body.

It is also hoped that, through an extended network of contacts, both former students and parents, the school will be able to develop a programme of speakers for a range of year groups in the future. Similarly, to encourage aspirational students into mathematically (or STEM) related subjects, we might take advantage of this network of links to include work experience placements for mathematics students in key stage 4 or the sixth form.
Finally, I think it is important to the sustained success of such a venture to get members of the department on board, hence the attempt to create a day-release arrangement during examination leave for interested departmental staff. This will allow staff to gain experience of mathematics in the workplace and video mathematics in action in order to create a PowerPoint presentation that could be used at appropriate times within the programmes of study.

Despite having a full time teaching commitment, the opportunity to conduct research in school as a teacher has been invaluable. Through looking closely at and evaluating our current working practices, there have been definite benefits for the department and for stakeholders, such as parents and former students. The project set out to improve students’ perceptions of the usefulness of mathematics to their everyday lives and especially in the workplace. This has been achieved, but it has also provided so much more. I must thank Kingswood’s former students for answering my many emails, and for returning to the school to speak to the students about their experiences. Without their contribution, this project would not have been possible.

IMA Conference: Mathematics Works 2008
Given the emphasis on 14-19 Pathways and Functional Mathematics, I am sure that many school mathematics departments are now turning their attention to the relevance of the curriculum, and possibly forging links with local businesses, and industry. There is an IMA conference for teachers planned for July 2008, which will provide details of how teachers can participate in similar research opportunities in their schools. There will be opportunities to learn more about the curriculum changes, the implications for the introduction of Functional Mathematics, and how the latter will affect classroom practice. There will be examples of how best to make use of the many institutions and initiatives to encourage speakers into schools, and how to provide examples of interesting and engaging ways in which mathematics is used in the workplace. If any teachers are interested in attending as a delegate, please contact me for details.

Piloting Showing you’re Working in schools
I am piloting “Showing You’re Working” in several local secondary schools in Bath, and I am looking for other schools who would like to be involved, to find ways to effectively build links between former pupils and current Mathematics students. Therefore if there are any teachers who are interested in trying out this project in your school, or indeed FE College, please contact me via e-mail and I will happily help you in your endeavours in anyway I can, for example forwarding all of my letters, templates, questionnaires, assembly notes and the booklet of pupil responses.

I think this project has an ability to make an impact with current students the way that my experience and examples cannot, because pupil perception is the key. They perceive me as an authority figure, whereas examples of mathematical application in the workplace quoting former students who have sat in their desks, and being taught by their teachers is a hook that really captivates the current students, and must not be underestimated.

Sharing ideas or project information establishing and maintaining industry links
Similarly, if you have an idea for a project or indeed conducted a project in school that you would like to share with others then contact me, and maybe we can create a forum/web page for interested parties, or you could even become part of the IMA conference proceedings!

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