|
|
The aim of this article is to provide assistance for parents, teachers and children who appear to have better than average ability in mathematics. It is not meant to be the total response or even the best response to the pleas above. However, it is meant to be a first stop where you can get some ideas and find out who might be out there and willing to listen to you.
How do you know?
What makes you think that this person is mathematically talented? There’s no simple test to determine this. My own philosophy is that if a child sticks with me in a specialized programme then they are gifted. But my programme may not suit all mathematically gifted children, so it’s not a failsafe test.
While we are waiting for the perfect test here are some litmus tests. You should be encouraged to keep finding a programme for the child if you can answer “yes” to a number of these questions. (On the other hand, you should keep looking even if you don’t but you have a “gut” feeling about the child.)
- Is your child fascinated by patterns?
- Is your child fascinated by numbers?
- Does you child like arguing logically?
- Is your child bored in school?
- Is your child a nuisance in school?
- Is your child’s hand writing atrocious? (As opposed to what they actually write.)
- Does your child get involved in things and work on them for hours on end?
- Does your child have a “clever” sense of humour?
- Does your child only perform at an average level in school but wins prizes in maths competitions?
- Does your child think of unusual ways of doing things?
Who can you contact?
The following people are not necessarily experts in gifted mathematics students but they are people who are prepared to talk with you and make some suggestions.
Mathematics Departments
- Professor Rob Goldblatt, Department of Mathematics, Victoria University of Wellington, phone: 04 472 1000, ext. 8320; Rob.Goldblatt@vuw.ac.nz
- Professor Ivan Reilly, Department of Mathematics, University of Auckland; Phone 09 373 7999, ext. 8786; i.reilly@auckland.ac.nz
Other Contacts
What help might you want?
There are lots of things going on for students with mathematical talent. In the Appendices at the end of this article, there are many things you might find helpful. You can find out more about them by contacting the people involved in these organizations.
|
In class |
But first, maybe it would be a good idea to have an IEP, an Individual Education Plan. If the parents and teachers of a student agree that they have a bright cookie in their midst then sit down with each other, the bright cookie, and an expert and come up with a plan to help the student in maths periods. A general plan might be to think of a mathematical project that the child might enjoy. In class, after the child and the teacher believe that the regular class material has been mastered, the child can work on the project. This will probably mean that the project will be under way long before the rest of the children have completed their work.
The special project should be something that the student wants to do. It may be based on any of the things in one of the appendices or it may be a library/web project. For instance, the student might like to find out about Pythagoras, say. So the project may be a poster, or a 2000 word illustrated essay. I once had a student who worked his way through a geometry text book. He had to solve all the problems and make up a question after each chapter on the material of that chapter. He soon produced problems I couldn’t solve! On the other hand, the project might involve programming a graphics calculator to do something else that they find interesting.
The scope here is pretty wide. The one thing that you need to insist on, however, is that there is some output. If it’s something that can be put on the web, it will be gladly added to the Bright Sparks section of the NZMaths web site. If it’s something that you think might appeal to teachers, then maybe it could go to the New Zealand Mathematics Magazine (the editor is Dr. Mike Thomas, m.thomas@math.auckland.ac.nz). If it might appeal to a wider audience, then try Tall Poppies, the publication of the New Zealand Association for Gifted Children. If it might appeal to other students at the school, then perhaps the school magazine is the place to go. Try to think of some way of publicizing the student’s output and making it accessible to as wide an audience as possible. (Possible audiences include other students, teachers, parents.)
|
|
On the web |
There are an apparently infinite number of web sites that have something mathematical on them. Two particular sites have problems that the student might like to tackle.
The NRICH site in England is managed by Cambridge University. It’s essentially a problem solving site but it has articles too. The problems cover a wide area both in difficulty and topic. If your bright cookie is turned on by solving problems, then this is the site to go for. Nrich has been going for a considerable time and they produce new problems at several school levels every month. The “old” problems are archived and by pressing the appropriate buttons you can access them.
Students are encouraged to send in their solutions and these may be added to the web the next month, with suitable acknowledgements. There is also a club that can be joined. Just in case parents and teachers feel that they might be left behind, there is a section of the NRICH web site that gives tips and suggestions for them too.
I’ve already mentioned the NZMaths web site. This is essentially designed for teachers and, among other things, consists of lessons that can be used across all Strands and Levels of the maths curriculum. But there is a problem solving section that teachers can retrieve problems from (the section contains solutions so don’t despair). Of course, you could also just send your student there but they may also find the solutions on the site easier to access than finding the solutions for themselves.
But there is one part of the NZMaths site that doesn’t have the answers and that is the Bright Sparks part. This is designed especially for able maths students. These all contain a problem in a slightly animated setting. Here the children are on their own to try to master a task and get through a series of challenges.
One special feature with Bright Sparks is that students are encouraged to send their written solutions in to Derek at derek@nzmaths.co.nz. He’ll then engage them in a dialogue that aims to encourage them to write out their solutions in full (or at least tell him the arguments they used to get through the maze of questions), and to learn to extend the problem as far as possible.
But the internet has a great deal of information. If your student is interested in history and the lives of mathematicians, then they should access the St. Andrews site (see Appendix A). It’s easy here to chase up Pythagoras (for that 2000 word essay) or find what Gauss did when he was a boy. You can also find the details of the mathematician who died in a duel!
And then there are Pythagorean Triples, Golden Rectangles, Fibonacci sequences, Knight’s Tours and pretty well anything that you would ever want to worry about.
|
|
Books |
These are old-fashioned things with pages. They hold as much if not more information than the web but sometimes they are harder to find. We have listed some books in Appendix B but clearly the thing to do is to get down to your school and local library and see what they have or what they can get for you.
|
|
Outside class |
In Appendices C to G we provide lists of several resources provided by various people. These include correspondence courses, school visits, and maths sessions.
If you’re near a university, give the Maths department a ring and see what they have to offer. If you’re not near a University, give one a ring anyway. Most Universities will be willing to help by either making suggestions or by flying in for a short visit.
In many areas, local cluster groups operate. Here students from several schools are invited to attend one school for a day or so a week. There may be one in your region. If not may be someone could be encouraged to start one.
On a similar line there are the George Parkyn One Day schools (Appendix G), and the Gifted Kids Programme (Appendix F).
|
|
Competitions
There are several maths competitions available to New Zealand students. These are listed in Appendix D.
If your bright student likes this kind of activity they might set their sights on representing New Zealand at the International Mathematics Olympiad (IMO). This is an international competition held every year for secondary students. To get selected for the New Zealand team you need first of all to do the September Problems (see Appendix D). Students who do sufficiently well on these problems are invited to attend the NZIMO training camp in Christchurch in January. At this camp the team of six, plus two reserves, is chosen for the next IMO. In 2003 this was in Tokyo and in 2004 it will be in Athens. So there are some fun places to go for the really bright problem solvers. For more information on the IMO programme, write to
- Professor Ivan Reilly, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland
- Dr. Michael Albert, Computer Science Department, University of Otago, P O Box 56, Dunedin
- Mr Alan Parris, Linwood College, P O Box 24034, East Linwood, Christchurch 6
This PDF download describes how the Olympiad is run and provides a lot more information.
The beginning?
We hope that this information has been useful.
If you need more help, then please contact the Department or someone listed in this article.
Similarly, if you have information that we haven’t included and that could be useful to others then please let us know.
Appendix A: Websites
- This book provides resource materials and information that are available on the internet for teaching mathematics: Ameis, J. A., & Ebenezer Jazlin V. (2000), Mathematics on the internet: A resource book for K-12 teachers Upper Saddle River, NJ: Prentice-Hall.
- NRICH site
- The Maths Week site contains resources and ideas for teachers, competitions for children, and information for parents. Although Maths Week (held in August) is a week to highlight and celebrate mathematics, activities from previous Maths Weeks are archived on this site. Activities such as the Survivor Series are a popular challenge that would be suitable for gifted students.
- NZMaths site
- St Andrews’ site
- This NCES site has 20 middle school mathematics items and 20 middle school science items for students to use in self-testing their knowledge and comparing it with international peers.
- Figure This! provides interesting mathematical challenges that middle-school students can do at home with their families
- Robots are a great way to inspire students to learn about math, science, and technology. The local science centre may be able to provide Lego robots for your students to use. The site gives historical information about robots, offers challenges for students and provides a forum for asking questions and sharing ideas.
- The NZAMT site is the New Zealand Association of Mathematics Teachers site and it has an online competition for students, some teaching material, intermediate level questions and some Olympiad level questions as well, along with some cool sites links.
Appendix B: Books
A few titles are listed here; for more titles see National Library Service.
- Bolt, B. (1985). More mathematical activities: A resource book for teachers Cambridge: Cambridge University Press.
- Bolt, B. (1987). Even more mathematical activities. Cambridge: Cambridge University Press.
- Davis John. (2000). Famous mathematicians: Learning from the lives of key thinkers. Birmingham: The Questions Publishing Company.
- Gardiner, A. (1987). Discovering Mathematics. Oxford: Oxford University Press.
- Gardner, M. (1990). Mathematical carnival. London: Penguin.
- Hilton, P., Holton, D., and Pedersen, J. (1997). Mathematical Reflections. New York: Springer-Verlag.
- Hilton, P., Holton, D., and Pedersen, J. (2002). Mathematical Vistas. New York: Springer-Verlag.
- Holton, D. (1997). Problems to ponder. Leicester: The Mathematical Association.
- Langdon, N., & Snape C. (1984). A way with maths. New York, NY: Cambridge University Press.
- Snape, C., & Scott, H. (1991). How puzzling. New York, NY: Cambridge University Press.
- Snape, C., & Scott, H. (1992). How amazing. New York, NY: Cambridge University Press.
- Stokes, B. (1993). Stretch, bend and boggle. Hamilton: University of Waikato.
- Thiessen, D., & Matthias, M. (1992). The wonderful world of mathematics. Reston, VA: National Council of Teachers of Mathematics.
The Mathematical Digest is a student periodical that can be ordered from this link or by contacting Bill Ellwood, Box 11-235, Christchurch. This resource provides interesting topics, puzzles and challenges.
There is also a magazine called Mathematical Digest that is published in South Africa. You can contact it via the Editor, Department of Mathematics and Statistics, University of Cape Town, 7701 Rondebosch, RSA, or access the web site.
Appendix C: Other Resources
Certificate Course |
Auckland University runs a correspondence certificate course based on some problem solving books produced at the University of Otago. This is a combination of problems and written material. Students submit about 6 pieces of work for marking during the year. This course is usually taken by secondary students though very gifted intermediate students might benefit from it.
There is a charge for this course.
(Prof. G. Hookings, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland.)
|
|
Correspondence Problems |
Both Canterbury and Otago provide this service for school students. If students write to one or other of the people below, they will be sent a set of problems to work on. When they have solved the problems they may send their answers back to be marked. The marked work will be returned with the next set of problems. The earlier problem sets are suitable for bright primary and intermediate students.
This service is free.
(Dr. R. Long, Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 1; Mrs L. Grant, Department of Mathematics and Statistics, University of Otago, Box 56, Dunedin.)
|
|
Development Band Certificate Course |
This course is available from the New Zealand Association of Mathematics Teachers (www.nzamt.org.nz). The purpose is to assist teachers with the provision of a quality extension and enrichment programme that enables a student to work independently on modules featuring open ended investigations on topics such as bridge building, magic squares, and topological tricks.
|
|
Talks, etc. |
Most universities have someone in their mathematics departments who is interested in assisting bright maths students. Different universities are interested in doing different things but generally what they offer is free of charge. The activities range over the following:
- Talks or problem sessions in schools or in university departments
- Mentoring individual students
- Acting as a resource person
- Assisting at IEPs
To find out about what your local university offers contact the secretary of their mathematics department.
|
|
Appendix D: Competitions
Auckland Olympiad |
This competition is based on one that has taken place in St Petersburg, Russia for a number of years. After a preliminary set of questions has been attempted in Auckland schools, a group of students is chosen for each of two divisions, a Junior Division (Years 8 and 9) and a Senior one (Years 10 to 12). (However, intermediate students have been invited when the organisers know of such students who have exceptional ability.) This Olympiad lasts for two hours and students’ work is marked and prizes awarded in the same session.
(Prof. G. Hookings, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland.)
|
|
Australian Mathematics Competition |
The Australian Mathematics Competition for the Westpac Awards has been running for 25 years and has been very popular in New Zealand. Results of the leading students are forwarded to the New Zealand Mathematical Olympiad Committee to enable identification for their programmes and an experienced New Zealand teacher vets the paper as suitable for the New Zealand syllabus. The Competition is administered in Australia by a non-profit organisation based on the mathematical professional societies there.
The questions are multi-choiced. The easiest questions are very easy, and the standard increases through the paper until the last questions, which are very challenging even for the elite students, so students of all standards will be challenged in the competition.
(Prof. Peter Taylor, Executive Director, Australian Mathematics Trust, University of Canberra ACT 2601)
|
|
Eton Press Senior Mathematics Competition |
This is for year 12 and 13 students and done through schools. A preliminary paper is sat in May and the finalists all go to Christchurch in Term 3.
|
|
National Bank Junior Mathematics Competition |
This is a competition aimed at Years 9, 10 and 11 but intermediate students have taken part (and won prizes). The competition takes place just after Easter each year and consists of several problems that have to be solved in an hour in school time. Past competition questions and their solutions are available for a fee.
There is a small entry fee for this competition.
Full details: National Bank Junior Maths Comp
|
|
Problem Challenge Competition |
This competition is designed for intermediate students, though it is taken by a few younger very bright students. Five times a year students attempt sets of 5 problems in 30 minutes in their own class. Certificates are awarded for performance and the top students are invited to take the Final Challenge at the end of the year. Past competition questions and solutions are available for a fee.
There is a small entry fee for this competition.
Full details: Problem Challenge Competition
|
|
September Problems |
Each year in September, a set of problems is made available for students who want to participate in the New Zealand Mathematical Olympiad Committee’s annual camp at Rangi Ruru School, Christchurch. The main purpose of this camp is to prepare students for the International Mathematical Olympiad. This is a prestigious annual international secondary school competition. In recent years this competition has been held in Seoul, Glasgow, and Tokyo.
The September Problems cover secondary school mathematics but do so in novel ways. Students are given a week to work on the problems and then they submit them for marking. The problems are clearly aimed at secondary students but able intermediate students might like to attempt them.
There is no fee for the September Problems.
(Prof. G. Hookings, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland.)
|
|
Singapore-Asia Pacific Mathematical Olympiad for Primary Schools |
The competition is for any student up to (and including) NZ Year 8 and
runs in over twenty countries and provinces throughout the Asia Pacific
region. It provides valuable experience for further Olympiad Programmes
in High School education. The competition is in two rounds, the First
Round is held in each of the overseas centres (King’s Institute, Saint
Mark’s Church School and Cobham Intermediate in New Zealand), and the
top 10 students from each of the countries/provinces and the top 10% of
the students in Singapore and Malaysia are invited to the Invitation
Round which is held in the Hwa Chong Institution, Singapore.
Further information may be obtained from the King’s Institute, which organises the New Zealand Round of the competition or from the Hwa Chong Institute.
The people to contact in New Zealand are J.Powell or L. Hede.
|
|
Appendix E: School Support Services
One way to get advice at a local level is to contact the School Support Services in your region. They have Advisers there who will be able to assist you. Contacts are as follows:
Appendix F: Gifted Kids Programme
The Gifted Kids Programme (GKP) is committed to meeting the “special needs” of gifted children.
Over 500 children attend the one day classes that GKP provides each week in Wellington, Rotorua, Auckland and Whangarei, and many teachers participate in the Giftnet Professional Development workshops which are funded by a Ministry of Education TDI contract. Centres do not yet operate in the South Island. Their classes feature focussed provision for mathematically talented children, as they have a specific focus on talent development in areas of children’s strengths.
Learn more about GKP from their website.
Appendix G: George Parkyn Centres
The George Parkyn Centres cater for talented students largely at the primary level. They do not specifically cater for mathematically talented students though.
Other centres like this exist around the country. I hope to be able to add these to a subsequent version of this article.
The George Parkyn National Centre for Gifted Education:
|  |
GIFTED CHILDREN
