My Teaching Philosophy

Mathematics Education in India

Mathematics education in India is in utter shambles. The school system, for all intents and purposes, is dead. I served in an organisation where one of my responsibilities was to coordinate with the HOD of Mathematics at the school to deliberate over the syllabus. There is a divergence between the school and coaching syllabi, and the challenge was to reconcile the difference. After a few interactions, I learnt why there is a dearth of mathematical literacy at the grassroots level. There is a dearth of good teachers who are capable of elevating a student’s mathematical thinking. The result is an insistence on cramming endless formulae, results, and algorithms. A student begins to view mathematics as an enterprise that is heavily dependent upon formulae and tricks for quick resolution. A firm resentment begins to take root in a student with a sceptical bent. Why must I cram so many things just to get the answer? The next question is: is that all there is to mathematics? Many begin to antagonise the subject until they develop a phobia of it.

Coaching: Out of the Pan into the Fire

Let us say that, due to the student’s own innate mathematical ability or the awareness of his/her parents, s/he still has some inclination towards mathematics. This could be due to his/her engagement with non-routine mathematics or a variety of other factors. With this residual enthusiasm for mathematics, s/he enters a coaching institute, where an experienced teacher compounds the errors of the school teacher. The questions s/he encounters are more challenging, and yet the methodology remains the same. More formulae, more non-standard results, more cramming of problem-solving heuristics, and finally, more and more problems with each passing day. More and more of the same, essentially, just that the scope of the problems has widened. In such a case, when a student encounters a new problem that lies outside the ambit of his/her toolkit, s/he is unable to make satisfactory progress. The argument that teachers make in their defence is something along the lines of: this is a tried and tested method which has worked for many students. And they have indeed done well. However, this argument is incorrect on the following counts:

a) The students who performed well did so because they were extremely hard-working and possibly talented; it is not necessarily an endorsement of the method being employed.

b) If the method really worked, why did even bright students who were so rigorously trained remain unable to attack problems that escaped the ambit of the available toolkit?

My Philosophy

I am not claiming to possess a formula which will make every student fall in love with mathematics. The world would be poorer if everyone dabbled in mathematics. Indeed, from where would we get our share of poets, painters, musicians, and sportspeople? But to view mathematics as a formula-driven exercise, where success depends upon how many non-standard results you have crammed, is deeply flawed. This is not to undermine the importance of solving problems. Solving prob- lems is at the heart of mathematics. But solving a large volume of problems and believing that this is a substitute for understanding is an illusion which is shattered at the first encounter with a non-routine problem. It is as much about solving more problems as it is about meditating over a problem for some time—a problem to which there seems to be no immediate resolution. You learn more by sitting idly in the company of an unsolved problem that is not responding to your attacks than by swiftly razing through hordes of problems which reveal themselves at the first touch. Remember, any problem worthy of an attack proves its worth by fighting back. Mathematics, at its heart, is an exploratory exercise. An analogy would be a hiker with all her/his paraphernalia attempting to chart a treacherous peak. S/he knows that perhaps her/his kit and training are enough, but they might be inadequate because of the sheer novelty of the uncharted terrain. In that case, the hiker tries new things, tweaks her/his path, circumvents a path, punches a hole through, and sometimes invents a whole path by her/himself. No gym-rat or rock climber, however consummate, will be able to manoeuvre with such dexterity. This is exactly how we do mathematics. We take a problem, twist it, break it, dissect it, strip it to its bare bones until we recognise the underlying structure. Then we piece it back together and solve the original problem. If possible, sometimes we extend it or perhaps even generalise it, but this is essentially the art of problem solving. Formulae are important, and so is solving problems, but mathematics is built at the back of first principles and it begins where the toolkit ends.