By Ellie Olivier
There is a famous anecdote about a renowned mathematician, John von Neumann. A friend of Von Neumann gave him a problem to solve: two cyclist A and B, at a distance of 20 miles apart, were approaching each other, each going at a speed of 10 miles per hour. A bee flew back and forth between A and B at a speed of 15 miles per hour, starting with A and back to A after meeting B, then back to B after meeting A, and so on. By the time the two cyclists met, how far had the bee travelled? To his friend’s astonishment von Neumann gave the correct answer in a flash by summing an infinite series.
Prof Man Keung Siu, in his paper, The good, the bad and the pleasure (not pressure!) of mathematics competitions apply the story to explain that there are several ways to go about solving a mathematical problem. The process of first calculating when the cyclists met is slick and captures the key point of the problem. The other way of summing the infinite series is slower and goes about systematically solving the problem.
The first method, which has been going on in the classroom of most schools, is to present the subject in a consistently organised and cautiously designed structure complete with exercises and problems. Another approach, which goes on more predominantly in the training of mathematics competitions, is to confront learners with various kinds of problems and to train them to look for multiple ways to solve the problem, thereby acquiring a host of strategies and techniques. Each approach has its separate merit and complements each other.
Learners who shine in mathematical Olympiads and competitions are not all-natural problem-solvers, but exceed because they have good teachers/mentors who expose them to problem-solving over some time. The problems in a mathematics competition are more complicated and stimulating than the usual exercises of the classroom, giving promising young mathematicians chances to expand their horizons and show their potential.
Since mathematics provides the foundation for many desired career paths, the improvement of mathematical problem-solving skills is essential for our country’s economic growth. We have to empower learners to become independent, creative and critical thinkers to interpret and critically analyse everyday situations and to solve problems and develop future leaders and influencers in the science, engineering, technology, economic, financial, and management sciences space.
It is pleasing to see that many teachers understand and recognise the significance of mathematical competitions giving the fact that more than 176,000 primary and high school learners participated in the first rounds of the Old Mutual South African Mathematics Olympiad (SAMO) and the Nestlé Nespray South African Mathematics Challenge (SAMC). More than 86,000 Grade 8-12 learners from 1,200 schools participated in the SAMO and more than 90,000 Grade 4-7 learners from 1,096 schools participated in the SAMC.
We want to thank teachers for allowing their learners to go beyond the curriculum and the provincial education departments, especially Western Cape, Kwa-Zulu Natal and Mpumalanga, for encouraging schools to participate. Learners who achieved at least 50% in the first rounds will advance to the second rounds in May.
Learners who develop their mathematical problem-solving skills over some time have an advantage over learners who only write the different rounds of the competitions. We, therefore, invite learners who have qualified for the second round of the SAMO/SAMC to register for our Olympiad Training Programme - https://www.samf.ac.za/en/olympiad-training-programme-2. The ideal outcome is that you foster a genuine interest in mathematics as a subject, but that you should also enjoy the extracurricular activity. I conclude with a poem by Prof Siu:
The good, the bad and the pleasure of mathematics competitions
Are to which we should pay our attention.
Benefit from the good; avoid the bad;
And soak in the pleasure.
Then we will find for ourselves satisfaction!