This is an article I wrote in 2016 for the Deccan Chronicle on the theme “Mathematics – 10 years from now.”
See, baby, one block, two blocks… barely has a baby learned a few words when we start teaching it numbers. Learning how to count is perhaps the first formal thing we learn, and yet, if we have to count out a sum of, say, 30,000 rupees in cash, we aren’t very efficient. We have to do it carefully and several times, and the moment the sums become substantial we’re better off with a machine. This is true not just of counting cash but of any algorithmic operation you can think of. (3256 times 8622, anyone?)
What then can we expect an education in mathematics to do for us? Of course we must master some algorithms. Efficient calculators or not, we need an understanding of arithmetic, fractions and percentages to be equipped for daily life and citizenship. Knowing how to divide a large number by another isn’t much good if you don’t know what you’re doing when you divide – on the other hand the theory of division isn’t very useful if you can’t find out – or estimate – the answer to an actual division problem. So teaching kids the nuts and bolts of numerical operations will remain a staple of mathematical education.
These nuts and bolts, however, don’t need fourteen years to master. There is plenty of time in school to move on to something closer to what mathematics is about today. Math classes in school feel nothing like what a mathematician actually does. How can this be true even of an “advanced” topic like calculus? It’s not the name of the topic that makes it mathematics – it’s what you are asking of a student. If all you require is the rote application of a set of formulae and a whole lot of drilling towards the quick and correct disposal of questions in under 5 minutes, then it’s just not mathematics. Mathematics is built around the notion of proof: a chain of reasoning, an argument that you have understood and then communicated, that shows why something must be true. Proofs are arrived at after digesting a problem, playing around with it, perhaps for a long time, and making many false starts. After a while a penny drops, and in a moment that feels rather like magic, you see why something simply *must* be true. Then you are in a position to construct a logical argument that convinces others and also confirms to you the correctness of your own idea.
Mathematics calls for patience, persistence, logical argumentation, acceptance of false starts and the seeking out of background knowledge. These are the very skills you need to be a good problem solver in any field. Instead of providing computational tools for students headed to technical fields, getting students to reason and problem-solve for themselves would be useful no matter what they choose to do. This isn’t simply the idiosyncratic opinion of a few – the most recent National Curriculum Framework, published by the NCERT in 2005, put forth precisely this vision. Yet eleven years on, its impact has been limited. A full implementation of this shift in the next decade would change not just the practice but the very goals of mathematics education.