ATM People • Geoff Giles

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Geoff Giles, a member of ATM for over 40 years, died suddenly on 04 Aug 05. He was a regular contributor to MT and wrote the recent ATM publication Proof in Elementary Geometry. Many will remember, and still use, his DIME materials and also the ideas gained from his inspiring workshops at ATM conferences.

Geoff has been living and breathing mathematics education for a long time. When he joined the University of Stirling as a lecturer in Education (Mathematics) over 30 years ago, he was already certain that children could understand and enjoy mathematics if they could access it in the right way. He began work on his own specially written booklets, and, in particular, on the use of ‘concrete’ materials. A short time later he started DIME Projects – Development of Ideas in Mathematical Education – to allow the development and sale of his ideas in the form of experimental literature and teaching aids. Within a few years DIME Projects had an income from the Scottish Education Department alone of £12,000 for school material supplied to three major curriculum development schemes. At the same time the publication of the 24 booklets, originally written by Geoff for the Fife Mathematics Project, began. And when a major London curriculum development involving over 100 secondary schools, the SMILE Project, started using the DIME booklets, it became clear that a new stage had been reached. Since then they have sold all over the world.

The first items in the range of ‘concrete’ materials to be developed were the ‘DIME Solids’ (used with the ‘Build Up’ booklets), ‘Rotagrams’ (a device used for comparing ‘angles’), the ‘Probability Kit’ (giving a wide range of practical experiments in probability), and ‘Taktiles’ (which makes possible practical, discovery work in shape fitting and symmetry). The latest example was the book ‘Algebra through Geometry’, which uses ‘TakTiles’ to give meaning to algebraic simplification. This has been taken up officially, and forms the basis of a lesson on the Key Stage 3 National Strategy ‘Mathematics 3 Day Conference’ videotape that has now been released for use in in-service teaching sessions.

But Geoff will be remembered not just for these concrete manifestations of his contribution to mathematics education but also as an inspiring man who infected so many others with his enthusiasm. Here are some tributes from his many friends and colleagues.

ATM

I am sat here in my math room in the Caymans, Googling to fill in a bit of spare time before the Easter break, and I thought for some reason of Geoff. I am saddened to hear of his death. Geoff was my tutor, friend and inspiration for nearly five years at Stirling. He basically ‘conned’ me into working in East London in a SMILE school, and hence placed me in the career I Have followed for over 20 years. I will always remember the Gandalf style caricature he had of himself on his office door. Math Wizard it proclaimed. Never a truer phrase written. God Bless Geoff. I will remember you fondly. Andy Allom, class of 80-85.

Andy Allom

Geoff Giles was my great uncle and I saw him at least once a year on holidays up to Stirling. Since I was little I can remember him teaching me his sort of work and how I was to work things out for my self. I am only a 14 year old girl, but I could solve a Polish maths puzzle this summer that my brother who is nearly 18 years old, could not manage.

Geoff taught me in a way which made me so interested in it all, I always asked him to give me something more challenging, and he would find it for me in his workshop.

Considering I wasn’t very linked with him, as he was my father’s uncle, I felt almost that I was linked to him more that the rest. During his last months, I was with him as usually on holiday, but we wouldn’t quite do like I was when I was young, I would find things myself for him to solve, which he always did in record time, but we would just sit, and read, or do a hard puzzle. Also that same holiday, relatives had come over from Canada, people who hadn’t been over for some time, and so he was able to see some of the family before he died. But me and my family were unable to attend the funeral as we were seeing my mother’s part of the family abroad and could not come back home for the funeral.

I can say that every time I do well in a maths exam or even just a class, I can almost say to myself, that I might not have done so well, if it hadn’t been his wonderful puzzles.

These last days I have been looking for professional views of him, and have not been able to find very many, but the ones I have found are of people who knew him just professionally, and I thought that it would be good for people to see what he was like with his family, and with younger children.

His own grand children, whom I like very much, I think did not think much about the maths like I did, I really enjoyed finding out how it was done and the logic and mathematical terms behind it, while they enjoyed the games and puzzles but thought not much more.

He was a happy man, he always saw the light in dark problems and could solve nearly everything you put in front of him. I can just hope that maybe one day, I can try and do the same thing.

It would be nice if you could give me details on where I can find a full list of his puzzles and games, as I have not been able to find one.

Helen Giles

I saw Geoff in ICME5 at Adelaide University. He began his lecture, “I am a salesman. But my idea is free.” Honestly speaking, only his session was able to be followed for me, a participant from Far East who was not good at English. His idea is clear. And his works are friendly to children, in another view, provocative. After his session, I had a conviction that it is worth for me to have a training to speak and hear his language. I went an English Conversation School half an year, and wrote a fan-letter to him. “Can I see you at Stirling, when I went to Europe to take part in ICME6?”. To my surprise, his answer was “If you come to UK you should stay my home.”

So, I was a visitor to Bet and Geoff in Hillsfoot Road. A workshop was held only for me. He is a very teacher, a kind man. “You must visit” he introduced his friend Mr. Jenkins of Tarquin-Books, and added his joke, “But, in general, Scotsmen and Englishmen are rival each other.”, for a foreigner from Far East.

Later I read book written by Dr. Howson and Dr. Kilpatrick , in which DIME is introduced as a curriculum development of grass roots. It is a word that we aim to do in Japan. And I see why his works are attractive for us. I made and have published a book that introduces DIME to Japanese teachers.

Answering my question about the panorama in the rotagram project, he said “It is a landscape of a fictitious village, but you should make your own panorama about your city for your students.” His idea is still fresh. In his works, easily we can find many materials that we want to develop our own. But hardly can find a suitable phrase without “I miss him.”

Rio Showder, Associate Professor, Kokushikan University, Japan

I can’t remember which came first - my awareness of DIME when a participant in some locally-provided INSET or that led by Geoff himself. Whichever, I will never forget clutching that free packet of Taktiles from the session (and which I still might have!) and excitedly working on them with family, friends and pupils. When another session provided a free box of Build-up materials I was similarly moved to share them, and continued throughout my career to promote these and other DIME resources both in the classroom and for INSET.

I found that Geoff, ably-supported by Beth, was always willing to lead such sessions whenever he could and which were invariably a great source of enjoyment and enthusiasm, but rarely contentious as Geoff’s quietly-spoken demeanour led us quietly through his ideas via Socratic-like questioning.

He is sorely missed.

Harvey Blair

Geoff Giles was a great inspiration to Australian mathematics teachers. His DIME materials and his contributions to AAMT and Mathematical Association of Victoria conferences were legendary.

Only yesterday I was talking to some colleagues about his influence on us and bemoaning the fact that many young teachers have not had the benefit of learning from and with him. And what a great guy: funny, insightful, and genuine. He will be sadly missed.

Sue Ferguson

It was my privilege to know Geoff first professionally then personally when a second cousin took up a lectureship at The University of Stirling. While I helped Glennis settle in, we were frequent visitors to Bet and Geoff in Hillfoots Road, picking brains, socialising - and borrowing tools!

Needless to say, the touring maths lab which we set up at the end of the '80s and has been on the road ever since, was inspired, supported - and, by DIME materials, partly furnished - by Geoff. If we wanted to know whether an idea would work, we asked Geoff. As others have noted, wherever in the world you take your box of manipulatives, tip the DIME materials out first: you know they’ll work.

Paul Stephenson, p.p. fellow directors, The Magic Mathworks Travelling Circus

I had both enormous pleasure and stimulation from piloting many of Geoff’s materials and was excitedly impressed that Geoff would give consideration to each aspect of my pupils' work. Characteristically, he would incline his head, ponder for a few moments to digest their responses, their problems or their ideas and reflect on their progress with a slow nodding of understanding. The delight with which he responded to their work was infectious. The simplicity of the final product for learning, from a small rectangle of tin-foil for symmetry to a chess board for ideas of proof, has always been inspirational. In essence, he was an inventor of vehicles for learning, presenting the core of a mathematical concept in ways which are accessible to both teachers and learners.

At conferences, training sessions, or the occasional stop-over at my London home, Geoff enthused about children and the teaching approaches which, he was sure, would help them to enjoy Mathematics. In sharing his ideas for the classroom, he always had time to consider something new. Even in retirement, he was always searching for better ways to support learning and his infectious enthusiasm continued to inspire us all.

In more recent years, I have had the delight of passing on his ideas and his resources to many other teachers. In whichever country that has been, teachers have received his methodology with appreciation and gratefulness - as well as a sense of wonder that learning can be so simplified. I have been honoured to broadcast his work.

From Nigel Langdon, Mathematics Education Consultant

My recollections of Geoff fall into two distinct but clearly related forms. The first concerns my reaction when first I came across the DIME materials. I was a relatively youthful teacher looking for something to scaffold my students’ learning in ways that the procedurally-focused texts around at the time did not. Someone suggested I look at the DIME materials and I was immediately hooked. Amazed and excited by the simplicity of the materials and the sophistication of the mathematics I have used them for nearly twenty-five years. The manner in which they expose the structures of mathematical entities, has informed everything I have done since. I shall always be grateful to Geoff for opening doors onto a hitherto unseen didactic world.

The second concerns Geoff the man and not the architect of mathematical thinking, although it is difficult to separate the two. I can’t remember exactly when I first met him although I know it must have been at one of my first ATM conferences. I had gone to one of his sessions in awe of his reputation but excited at the possibility of supping at the master’s cup. What followed completely over-turned any notion of master and pupil. His session was delivered in ways that shouted from the rooftops, “we are learners together and our collaboration will not only help us in our understanding of mathematics but through our working together facilitate our students’ understanding of mathematics”. We worked collectively on a number of algebra-related tasks and the excitement generated as we talked and shared was tangible. It was a magical example of how to run a session for colleagues.

I remember Geoff as a quiet, fundamentally shy but always approachable, man who transformed mathematics teaching not by shouting louder than the others but through the strength and quality of his arguments. Not only did he transform my professional life but also he showed me why ATM is the organisation it is. The world seems emptier now Geoff has died.

Paul Andrews

Geoff was almost unique in his view of the teaching of geometry. Some pure geometry lay always in the background, as shown by his more theoretical articles which produced some unusual and surprising theorems at an elementary level: see for instance the amazing theorem in MT 45. Tessellations were always a love, and again his approach was unusual; his overlapping tessellations (MT 71) were ingenious, and the Tess Tiles in the DIME series again ingeniously provided tiles that could build tessellations each in several ways. The whole DIME package was in fact a revelation as a simple and practical approach to complicated problem solving. The idea of providing a set of pieces that could be fitted together in several different ways to produce a symmetrical shape was almost mind-blowing.

His “Geometry for all&rdsquo; in MT 100 noted the disappearance of deductive geometry as it had been taught previously, and called for a rethink of what geometry was about, especially as a subject which no longer, he thought, should be confined to an elite section of the school population but could be made available to everyone. The many examples given in the article illustrate both his ability to invent construction problems which have several solutions, and his refreshing approach to elementary ideas. Somehow he gave a new meaning to looking at things from a different point of view.

"There are those who will argue that the ‘Geometry’ I am advocating has no substance, no body, and thus cannot be taken seriously. But they are thinking of mathematics as static content, and their geometry is entombed in textbooks. If the mathematics classroom is to be alive, then we must allow children to do their own mathematics. ... It is the ‘doing’ that is important, not what is done."

This was a plea in 1982. One may well consider what has happened in school geometry since then.

David Fielker

I have fond memories of Geoff’s many seminars at ATM conferences, which I often attended, always confident in the knowledge that his imaginative creativity would have generated something new since the last time. Geoff presented his seminars with infectious enthusiasm but he was also keen to listen to others' ideas and suggestions. I knew that the materials and ideas he offered us would support the development of fundamental mathematical ideas whilst also being easy to use and practical in the classroom; I used them for many years as a classroom teacher and still use them with our secondary maths trainees at university.

Anne Haworth

I first met Geoff at a ‘Mixed-Ability’ mathematics conference at Westhill College, Birmingham in 1975 and he was demonstrating his Tessellation Tiles. And over 20 years later I invited him to run a session at Lancaster where he continued to stimulate his ‘audience’ with his inventive manipulatives. Geoff’s ability to make mathematics something that happened in our hands to help us make sense of what goes in our heads was wonderful. Long after the National Curriculum and National Strategies have been forgotten Geoff’s ideas, his practical equipment and his enthusiasm for teaching will continue to make mathematics accessible to future generations.

Mike Ollerton

It has been over thirty years that I have known Geoff. Thirty years in which to put to rights the mathematical world for school children.

Before DIME he always showed a keen interest in what we (then newly qualified) were doing in our classrooms. Back then we were suspicious of Durell and warmly embracing things SMP. It was Geoff that introduced us ‘southerners’ to what was happening north of the border with an emerging and flourishing SMG. In doing so he raised the debate about meaningfully and actively involving children in their mathematics.

Then DIME came into being and many young teachers got interested in the active research being done by him and his associates at Stirling. We gladly tried out the materials which always felt better than other things around at the time for he felt strongly that here should be no shortcuts, no pruning of ideas to meet budgets. Just prudent spending!

It was DIME that really focused our friendship back then and over the years at conferences there was always time for the inevitable question: “Now laddie, what are you doing with …” His interest in our classroom practices never wavered.

He would have appreciated that on our recent visit to South Africa in July this year it was DIME materials that were unpacked first. The responses of the teachers there would have said all that these words are trying to say. Through Geoff we had brought rigour and involvement to their classrooms - just has he did to ours years earlier.

Geoff is a sad loss to those who consider ATM a meeting place of kindred spirits.

Lyndon Baker

Geoff was a personal friend and a huge influence on my professional life. Our relationship goes back to the middle 70s when I was a young teacher and he was already respected around the world for his remarkable insights into mathematics education.

Sharing his expertise was all that Geoff ever wanted to do. In the closing paragraph of a 1978 Keynote Address paper written for the biennial conference of the Australian Association of Mathematics Teachers, he invited us all, and now invites us anew, to continue this process:

“If this miscellaneous collection of bits and pieces has convinced you that mathematics in school can be made more interesting, accessible and understandable I will be happy. Should it also motivate you to work with others on the improvement of mathematics education in the classroom then I will be delighted. But please don’t keep your insights to yourself. Share them and let them multiply.”

Doug Williams

My very first memory of Geoff is a vivid one of a seminar he gave. It was at the first ATM conference that I attended in Bognor and I was very uncertain of what to expect.

I was most disconcerted when Geoff handed out some strips of clear plastic which he said were off-cuts from some of his other materials. He told us we were to do some mathematics with them. I was struck by total panic, I was going to fail totally and make a real fool of myself! However I should have trusted him, the strips really did have a lot of possibilities and although I have quite forgotten what mathematics I did, I can still feel the sense of creation and satisfaction that it gave me.

Thereafter I looked forward each year to finding out what new and imaginative materials Geoff had produced and made it a priority to seek him out to ask about them. My favourites remain his symmetry puzzles which look so easy and can be so hard and Build Up. Build Up did more for my, up-until-then, low three dimensional visualisation ability than anything else and the set he gave me has had much use working with teachers Even in retirement is carefully preserved in the hope of new opportunities to use it. I think my grandchildren are now old enough to enjoy it.

Gill Hatch

I trained and began my teaching career in inner London and first encountered Geoff’s DIME materials through the SMILE project.

The range of materials, both in geometry and algebra, proved a wonderful addition to my classroom and I still regularly use them to this day. Meeting and working with Geoff at successive ATM conferences were marvellous experiences. The last occasion for me was Geoff sharing draft material from his Proof in Elementary Geometry booklet - memories I treasure. Geoff’s work on geometry, especially, is a fitting memorial to an inspirational mathematics educator.

Keith Jones, University of Southampton

Geoff was an enthusiast and really great teacher.

I was his first student at Stirling University and was able to benefit from his inexhaustible energy and insight into how human beings thought about mathematics.

In the three years I was able to work with him, many new doors were opened which have shaped my professional life for the last forty years! Without his influence I would not have become a mathematics teacher or teacher educator. Without the time he spent encouraging me to play with multicoloured plastic shapes, asking, changing and answering questions about geometry, my life would have been infinitely poorer.