Is there a place for competition in mathematics?

Context matters. Jonathan Jansen explains why mathematics teachers should use their professional judgement when it comes to co-operative versus competitive learning.

Illustration by Liani Malherbe

I liked two things about learning school mathematics – the opportunity to work together in small groups to solve a complex ‘word problem’ and the chance to compete with classmates to solve a quadratic question ahead of others. Both these contexts –cooperation and competition – provided me with valuable lessons in life and in learning. In life, I learnt that each context offered me ways of seeing the world as a complex place where team-work and individual effort both have their place. In learning, I found that the pooling of intellectual resources helped solve a wicked problem, but that applying your mind to resolving a problem on your own forced you to think hard and draw deep beyond what you thought lay within you.

As I watched my 18-month old granddaughter on the video-feed from New Zealand stand on her toes trying to open the latch on the door, it struck me that the easiest thing to do would be for one of her parents to rush over and do it for her or they could lift her up to do it herself. Better still, they could stand back, as they did, and watch her struggle to figure (sic) out the workings of the latch-door mechanism all by herself. Eventually, she did unlock the door and what happened next, I will never forget—a smile that conveyed a very powerful sense of individual achievement.

One day I would hope her parents enter the young child in a mathematics Olympiad. I would like her to compete with the smartest children in mathematics for three reasons. One, the young learner will never know how good she is until measured against the smartest children in the room. Two, when competing with smart children she will find herself stretched to do even better than what she might have thought possible. Three, she must learn the value of coming second or third or further back and then have the grace of going to a competitor and saying, ‘well done.’

Photograph by Nino Mekanarishvili

There is of course a compelling argument among critical theorists of education that competition is one of those values that prepares children for assimilation into a capitalist economy. The notion of winners and losers in an open market economy, the argument goes, derives from the ruthlessness of capitalist competition. By competing with others for the highest marks in a mathematics classroom, these academicians contend, children are also learning a set of values through what is called the hidden curriculum of schooling. This position gives pause for thought, but I think it is too cynical since a judgment about the value of competition depends on the context of application.

It is certainly the case that competition can be harmful when winning or losing becomes the absolute end and where human worth is assigned differential value depending on whether a child finishes first or tenth in a mathematics test. But that kind of outcome is not pre-determined in the curriculum. What matters is the kind of pedagogy exercised in the course of teaching mathematics. A good teacher would use a strong performance in mathematics teaching to build the self-esteem of a student lacking in confidence. A better teacher would take time to motivate a student whose mark jumped from 40% to 60% to help boost that child’s sense of accomplishment. Context matters.

One of the devastating practices of some of my white science lecturers in the first year of university was to tell the crowded class filling the amphitheatre to come down to the front of the room to collect their marked scripts. That act in itself had debatable merits except that the more than 100 scripts were carefully arranged such that the highest marks were at the top of the pile and the lowest marks at the bottom. Needless to say, by the time the lecturer called the names of those in the lowest quarter of marks scored, the class had already emptied. The goal here was racial humiliation not healthy competition among students doing the science degree.

In the same way, co-operation can be mechanical in its application and not signal the higher order values that one would expect from collaborative learning. This was perhaps one of the single most important lessons learned from an earlier curriculum experiment in South Africa called ‘outcomes- based education’. This progressive policy included the idea that students should learn through teamwork solving problems together rather than in competition with each other. We now know that simply working together as an organisational routine does not guarantee deep learning let alone the benefits of shared learning that comes from merely arranging children in groups. Put bluntly, competition no more prepares children for a capitalist economy than co-operation makes students oven-ready for a socialist economy. It depends on the context.

This means that the mathematics teacher should use her knowledge of the subject and her knowledge of how to teach to determine which problems lend themselves to co-operative learning among groups and which are more appropriate contexts for competitive learning arrangements among individuals. Choosing the context for learning is, in the final analysis, a case of professional judgement.

Prof. Jonathan D. Jansen

Distinguished Professor of Education,

Jansen is a curriculum theorist who studies the politics of knowledge as expressed in the social, natural and medical science disciplines.

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