That’s the title the editor gave to a letter I had published in the Education Age (21 May 07), commenting on an opinion piece by my University of Melbourne colleague Marty Ross. Since they don’t make the letters to Education Age available online, I’m putting it up here.
Marty’s piece generally was very good. He and I have no deep disagreement; but this letter puts into relief one point where we’d differ at least in emphasis.
According to Marty Ross, the purpose of teaching mathematics is “training in logical thinking, learning to reason about anything.” But mathematics is a poor way to achieve this goal, and there are better reasons to study the “queen of the sciences”.
Ross is recycling an idea as old as Euclid himself, for we can find in Plato the view that reasoning is like a muscle, which can be strengthened through training in some formal discipline such as mathematics or grammar.
The view is plausible, even appealing, but it is misguided. It violates a key insight of research into cognitive skills, known as the “problem of transfer”: skills learned in one situation “transfer” to other situations far less than we would expect. Studying mathematics may help students learn to prove theorems, but quite different kinds of reasoning are usually needed in everyday life and the workplace.
There is a better way. General “informal” reasoning skills can be taught directly, i.e., as skills in their own right. In recent years, some remarkably effective methods for doing this have emerged. Crudely, to Ross I would say: if you want to improve general reasoning, why not teach general reasoning? Why teach something else, in the forlorn hope that some general reasoning skills will result?
Unfortunately, effective direct approaches are not widely used. In addition to its mauling of mathematics, a major problem in the Victorian education system is its failure to systematically teach the fourth R, reasoning.
Lets not try to make mathematics carry a burden it cannot bear. Lets instead teach mathematics to give all students at least a chance to appreciate the profundity, and beauty, of the most magnificent achievements of the human intellect. Meanwhile, lets teach general informal reasoning skills using more direct and effective approaches.