An article from "Mathematics Competitions", Vol 15, No 1, 2002

A Programme of Mathematics Enrichment for Students from Grades 5 to School Leaving

Tom Griffiths

Tom Griffiths studied at Imperial Collge, London, UK and Waterloo, Canada. He has had extensive experience teaching mathematics to first year university level. He has had a long association with mathematics competitions including the US and Canadian Olympiads as well as the Descartes Competition and the Canadian Invitational Challenge. Tom has also been involved in many facets of mathematics education and curriculum construction.

I was a high school mathematics teacher for 34 years and retired in 1995. During my career I had considerable involvement with mathematics contests, both in preparing students, setting the papers and marking the solutions. I have been involved in various roles in the U.S. Olympiad, the Canadian Olympiad, the Canadian Mathematics Competitions Descartes and Euclid contests and the Canadian Invitational Challenge as Chair from its inception in 1988. When I retired it seemed a shame not to make use of this experience for the benefit of excellent mathematics students. I also wanted to give local students the opportunity to receive the appropriate coaching to work towards becoming members of the Canadian International Mathematics Olympiad (IMO) Team. I had been coach of the team to Finland in 1985, and have had one student on the team to Australia in 1988.

In January of 1996 I started visiting local schools on a weekly basis to help those students who were interested in taking a challenge to excel in mathematics. For the rest of that academic year I visited several local high schools weekly, for the sake of the few in each school who were interested. However, this turned out to be a very tiring experience, requiring much more effort than benefit warranted. Hence, I reconsidered my strategy and decided that it would be to everyone's benefit, especially mine, if all the students came to me. As it happened, the staff of the local University, the University of Western Ontario, (U.W.O.) decided at the same time that they needed to establish an outreach programme for high ability mathematics students. Fortunately, we managed to discover our mutual goals and agree to combine our experience, and I was delighted that they were willing to provide space to hold classes and give me free use of photocopying. It has been a win-win situation.

Shortly thereafter, the University also offered me an expense account through which I pay for travel, conferences and equipment for classes.

In October of 1996 I started with a two hour class every Tuesday night, and had six or seven regular participants for the full year, growing in number nearer the competitions as the students brought along friends and siblings. At the same time, a colleague in a nearby country asked if I would offer classes in her area. In October 1997 I continued the weekly senior classes at U.W.O. and offered weekly classes at a school in the nearby country. The class at Western continued to grow to a regular 12 to 15 students. I was also asked to help a young, and obviously talented, grade 6 student. I decided to coach him individually, and saw him weekly at his school. He has gradually developed into a possible member of the Canadian I.M.O team.

In the fall of 1998, the Tuesday senior at U.W.O continued, and due to the University and the local school board giving the class some publicity, it grew even larger. The classes in the nearby country had not flourished. After a period of alternating Mondays with that class and one at Western for grades 9 and 10 students, I changed to a cycle of two-hour, weekly classes for these students at Western. I had also had an offer from a retiring Maths Department Head, Walker Schofield, to join me, and we split the Tuesday night class between us, one hour each. Also in 1998 I started a two-hour session, one Saturday morning a month, October through April, for grades 7 and 8 students, and had a most encouraging first attendance of over 40. In the first hour I cover academic work and Gauss contest preparation. In the second hour Mrs Margaret Kemp specialises in more hands-on work such as studies using pentominoes, tangrams, tetraflexagons and Escher type art. Mrs. Kemp is a grade four teacher who coaches and also directs the selection process for the local area Ontario Mathematics Olympian (OMO) team for grades seven and eight.

Through 1998 we expanded in numbers, and improved our communication with the mathematical community, letting more students know of our existence. U.W.O. appointed a mathematics and science liaison officer, who has assisted us in publicizing our program to all the schools within an hour's journey of the university. However, the best communication is by word of mouth. I also picked up another two students to coach individually, and arranged for two other math teachers to coach other promising students.

In 2000 we added a two hour session for grades 5 and 6 on the Saturday afternoon. As with the morning sessions I share the time, one hour each, with Mr. David McMillan, a local elementary teacher. We use the same pattern as the morning. The first hour is academic and contest preparation, and the second is hands on activities. Two other retiring Math Dept. heads, Mr. Charles Scollard and Mr. Carl Silke, have joined me in teaching the Monday sessions. I have an hour every week and they share the other hour between them.

Over the last two years, the only change in the programme is the addition of an extra hour, making three, on Tuesday nights. This enables me to concentrate on preparing students for the Olympiad level material and the American Regional Mathematics League Competition (ARML), held at Penn State in State College Pennsylvania, an eight hour drive away for us. With Peter O'Hara, a local high school teacher, my wife and I have taken students to this for the past three years. Last year we took a complete team of 15.

This school year, 2001/2002, we have a total of 128 registered in the grades 5/6 sessions, with an average attendance of 90. Of these registrants, seven are in grade 4 and one in grade 2. I think that this offers an opportunity for students to meet math peers regardless of age, and provides an atmosphere that encourages having fun with mathematics. Many of these students have no mathematical peers in their own classrooms, some even in their own school. Forming a peer group for these talented young people is possibly the most important role of the programme. The students involved are allowed to feel that they are not the only people in their world who love mathematics. For these students' regular teachers, there is a very useful spin-off in that the books that we offer on behalf of the Waterloo Competition Group, give these students something useful and productive to do when they have finished their regular school work, which often takes the better ones a very short time. With a total registration of 76 students in the grades 7/8 sessions, we are enjoying an average of 60 per session. There are a regular 40 at the Monday sessions and 30 at the Tuesday sessions. Not all students come for every session due to other commitments. There are actually about two hundred and eighty students registered in all.

The material we use in the sessions is mainly the Canadian Mathematics Competitions from the various grades as well as the MATH Contest book from the U.S. Math League. Both organizations have kindly given us permission to copy the materials. As we study the questions in these papers we often digress into interesting areas. We also teach the students the basic concepts needed for the material. Frequently we have some of the students who are ready for concepts years before they would usually study them in school. We attempt to enable them to continue mathematically at their natural pace. Where appropriate we also have students sharing ideas they have recently learned in their own studies.

This year for the first time I have also started charging the students \$20 for the year. This money is to pay for sending them to Mathematics Competitions, as last year I had to raise a total of \$7000 to send the students to OMO and ARML. The students who went did pay some of this, as did the Provincial Mathematics Association and a very supportive local company, Trojan Technologies, which has sponsored the junior Olympiad team for several years. We also offer a snack to the younger students at the mid-time break on Saturdays.

The rewards for our efforts have been the excellent and improving results that our students have achieved on contests. Last year some students wrote contests through our Math Challenge programme, others wrote in their own schools. The ones who wrote with us scored among the top ten teams in Canada in three of the five high school mathematics contests. We are regularly having students invited to write the higher level contests, and achieving excellent results. A personal reward has been that I have been given an honorary position in the Mathematics Department, with the title of Mathematics Co-ordinator. Another very important benefit to me is that my wife Marlene, has become progressively more interested and involved in the programme, and now takes care of all the business and attendance. This means that we work as a team, with Marlene at many of the sessions taking attendance and collecting money. For a retired couple this is a great opportunity to spend time together sharing a common interest.

For the University, the benefit is that the top mathematics students in the areas become regular visitors to the campus from a very young age. The University is also given names and addresses of the students, and they send copies of relevant information and newsletters to them personally. As a mark of their gratitude, last year the Dean hosted an appreciation dinner for the team.

I believe that a programme like this could be started in other places given the appropriate ingredients. First, you need a university which is willing to give its support to such a programme through accommodation and photocopying. Second, the university needs to help finance materials and equipment, especially for the junior students, and in publicizing the programme. You need a retired mathematics teacher or teachers who are interested in passing on their expertise and experience. I have been delighted to find that, once we got under way, the offers for assistance came in steadily, and the assistance is much appreciated. We also have three other high school and university staff who are willing to take classes for us when necessary. Peter O'Hara now also leads the ARML team, as well as assisting with covering classes when required. One benefit of this is that as a team no individual is indispensable, and as retirees we can take time off for vacations and have the others cover for us. I am hoping that when I am no longer able to run this programme there will be others willing to carry it on.

One of the most appreciated comments that we have heard is that some of the youngest students have gone straight from the class to McDonalds, where they and their friends are engrossed in mathematics, and that they stay that way for the rest of the weekend.

I hope that this may encourage others to start a similar programme. I will be pleased to assist with advice and moral support.

I would like to take this opportunity to thank the University of Western Ontario and my colleagues for their assistance and support in this programme. Without this the programme would not be possible. I should also emphasize that all participants are unpaid volunteers.

Tom Griffiths
985 Thistledown Way
London, ON N6G 4L6
CANADA