Learning how to count is perhaps the first formal thing we learn, and yet, if we have to count out a large sum of, say, 30,000 rupees in cash, we aren’t very efficient. 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? To begin with our students must of course master *some* algorithms. We need an understanding of arithmetic, fractions and percentages to be equipped for daily life and 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 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. (It’s worth pointing out we are still more efficient than machines at quick estimates).
These nuts and bolts, however, don’t need 14 years to master. There is plenty of time in school to move on to something closer to what mathematics is about today.
The truth is that a contemporary mathematician would not even recognise what students learn in school as mathematics. How can this be true even of students in class XI and XII studying 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 many false starts.
After a while a penny drops, and 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, acceptance of false starts and the seeking out of background knowledge. Getting kids to reason and problem-solve for themselves would be useful.
And this isn’t simply the opinion of a few — the most recent National Curriculum Framework, published by the NCERT in 2005, put forth precisely this vision. Yet 11 years on, its impact has been limited. A full implementation in the next decade would change not just the practice but the very goals of mathematics education.
The author is an Asst Professor of Mathematics at Ashoka University
