Peter Crippin
During the time that Peter Crippin taught at Woburn Collegiate in Scarborough, Ontario, there were more students from Woburn on the Canadian International Mathematics Olympiad team than from any other school in the country. In nine years, the Woburn team achieved the highest score in the Descartes math competition five times, in the Grade 12 Euclid math competition five times, and in the Grade 11 Fermat contest three times.
Many of these students have gone on to earn senior degrees in mathematics, science and medicine at prestigious universities. They credit Peter's teaching and his emphasis on problem solving for starting them on the road to success.
Peter has also contributed to the professional development of his colleagues, regularly teaching a specialist course at York University for math teachers.
Approach to teaching
"As a teacher, never say, 'I have the answer' to a problem."
The key to teaching problem solving is to teach the "how to" rather than to focus on the answer. Placing the emphasis on solving the problem rather than on the solution builds on students' existing knowledge. It also shows students how to appreciate other people and their ideas. If people are engaged, you can motivate them and offer insight by discussing ideas.
Although I don't believe that math is the be-all and end-all, nor that all my students should continue to study it, I do think that the problem-solving techniques of mathematical and scientific thinking can make the world a bit more sensible, and my students' lives more pleasant and productive.
I also do not believe that advanced courses and math competitions should be open only to gifted students. At Woburn, they are open to all students who convince me that they are willing to do the extra work involved.
Transferable experience
To coach students for math competitions successfully, you have to focus on the pedagogical need that these activities meet. Math competitions are valuable because they help people learn about problem solving.
This is particularly important for students-arriving in Grade 9. Many of them believe that mathematics is a mechanical process: you plug numbers in on one end and answers come out the other. Mathematics teachers have to show students that computations are only the raw material and that the creative reasoning required to solve problems is what this subject is really about. Teachers will not be able to do this unless they are personally excited by this process. I begin my Grade 9 classes by showing my own interest to the class. From day one, I take time to put up one or two problems for my students and we discuss them together.
At Woburn we supplement these in-class activities with the Senior Math League (grades 12 and 13) and the Junior Math League (grades 9, 10 and 11), which meet after school on a competitive basis. One of the surprising things about math competitions is how much teamwork and cooperation they require. No one teacher or one student can do this alone. To improve, you have to discuss problems and share ideas constantly.
Ultimately, you want to expand this approach beyond the doors of your school to include other schools and even other districts. You also want to discover what other resources are out there rather than trying to reinvent the wheel. The first step is to contact other teachers who are already coaching students for competitions. The University of Waterloo also produces some very good support materials that are organized according to topics and according to level of difficulty. Most established math competitions are inexpensive and easy to enter.
If you are really interested in problem solving, your students will pick up on your enthusiasm. They will see that you are listening to them describe how they are solving a problem and that you won't barge in and tell them how you do it. By listening, you are teaching students more than mathematics. You are teaching them to have open and inquiring minds.