The Australian Mathematics Competition (AMC) is not simply a stand-alone exam. It is the first step in a complete program of enrichment designed by the Australian Mathematics Trust, which enables students to explore their talents and develop them to their potential. The programs run by the Trust extend to the Mathematics Challenge for Young Australians, enrichment courses, and up to international competition.

Above all, the AMC truly meets the definition of being a Competition. It is the only broad based mathematics competition in Australia which fulfils the definition, as outlined below.

It was back in the 1970s that the first major Australia-wide school competition, the Australian Mathematics Competition (AMC), was introduced. Since then, the Australian education scene has seen a proliferation of many similar events, not only called competitions, but sometimes challenges, assessments, etc.

These events might be run by large organisations, small organisations, some from within professional societies, others clearly of a commercial nature, some for individual students, some for teams, some quite broadly pitched, others narrowly focused, and in all the major school subjects.

These events are often seen as similar in what they offer, but they can be quite different, and it really is worth asking what role they have in the school's academic program.

First it should be noted that competition might not be the best word. We were hesitant about using this word, as it can be taken in a context different to intention, but in the end we settled on it because there were precedents for its use in Canada and the US.

I should also note our intention with the use of the word "competition". We do not mean to emphasise students competing against each other. Instead we see it as the student competing against the problems. In other words we see the AMC as a personal challenge in which the student can try to solve problems with the knowledge that if they fail, it has not counted against their personal assessment, but if they succeed there is personal satisfaction and recognition. And if one can solve one mathematics problem it is not only satisfying, it also provides the motivation for wanting to solve another.

We see a competition as not only an opportunity to assess and diagnose, but this is still a major feature of the AMC. This was the original Australian competition, which, because of the large entry numbers, and optical reading of the answers, was able to provide detailed feedback.

The AMC is carefully moderated by experts from each state to ensure that the mathematical content is within the scope of the regional syllabus. Most of the paper, particularly the first half, is what might be called "Curriculum bound", that is set in familiar classroom context. Towards the end of the paper questions might be set in contexts new to the student, albeit still using mathematics known to the student.

This means the AMC is really testing a little more than normal classroom mathematics, identifying students who can apply their knowledge to new situations. The AMT issues a "Mathematics and Problem Solving" Proficiency certificate to students who would otherwise not receive a credit but who have nevertheless indicated satisfactory ability in problem solving (which the AMC measures) and skill.

It has wide appeal also because there are questions of all standards, beginning with quite easy questions, which all students should be able to solve, the questions become progressively harder until the last 5 questions which are for very talented students. Students of all standards have an opportunity to achieve and be challenged during this time.

In fact the concept of challenge is of contemporary interest in the profession of mathematics education. An ICMI Study Challenging Mathematics in and beyond the Classroom is currently in progress. This international Study is in fact being co-chaired by Trust Executive Director Professor Peter Taylor.

We also see a competition as being an event which is part of a much wider experience. This experience enables a student to spend time in the weeks before the event practicing problems of the type which will be encountered (and all past problems are classified and available). Afterwards there is significant benefit in discussing the solutions, particularly following up the ones they could not do on the day. Any discussion, whether among students or with the teacher, is beneficial. This is why we provide fully worked solutions for our problems.

On top of this the most important thing is that a student who has experienced all of this may want to do more. The AMC is just the first in a range of activities run from within the greater mathematics profession of Australia, leading to possibly representing Australia at the International Mathematical Olympiad.

Certainly the next step is to participate in the very popular Mathematics Challenge for Young Australians, which includes course work which substantially develops the problem solving skills of the student.

At the end of this, students who participate well in the AMC and the Challenge can be invited to participate in more advanced work, which might be under the tutelage of local academics or former Olympiad team members.

In the real world, students will need to become problem solvers. In whatever undertaking they pursue they will encounter "problems". Generally, mathematical reasoning provides a model for problem solving on a wider scale. In the real world one might identify a problem, decide what are the variables which affect the outcome, identify interconnecting relations, and if solved in a mathematical sense, relate the solution back to the real world.

In the AMC we set problems in the real world to which students can relate. They learn mathematical skills per se in the class room, but in the more advanced AMC problems, they apply additional problem solving skills.

It is a major aim of the AMC to give students an opportunity to use these skills of problem solving, and the experience both before and after provides an opportunity for this to develop.

A good competition should provide real educational outcomes, enrich classroom learning and allow further development. The AMC is designed to achieve these aims.

Peter Taylor
Executive Director
Australian Mathematics Trust
April 2008