The forgotten world of Mental Arithmetic
It has been such a long time since I last posted here that I guess no one reads this blog anymore! In a way, that is nice, since I am under no pressure to post anything useful or engaging, and can ramble on to my heart's content :-)
At roughly around the age of ten, I got drawn into the world of mental arithmetic. I had just been introduced to the world of Srinivasa Ramanujan, the enigmatic genius who tragically passed away at the age of 32 leaving behind thousands of results that researchers study to this day. Of course, I did not get to studying any of Ramanujan's brand of pure math, but I developed a great deal of awe and respect for that kind of thinking - the one that relies on leaps of intuition, and not merely plodding through pages of brute force boredom.
I think what makes people like Ramanujan special is the very thing that most of our schooling strips us of - unstructured thinking. If I were asked to list the single biggest problem in our methods of schooling, its this - It encourages one to come up with the 'one' right answer. It does not teach the art of approximation. Answers to questions in history exams will fetch one full marks only if the person gets the year exactly right. How does it matter if there is an error of a year or two if the incident occurred a few centuries ago? Students of electrical engineering compute a resistor value to 5 decimal places, without realizing that that kind of precision is impractical, and no one is going to/can manufacture a 121.238763 Ohms resistor for you. I think learning to come up with quick and dirty estimates is just as ( or perhaps more ) important than coming up a precise answer after a few hours of solving simulataneous equations in ten variables.
During those teen years, I picked up math tips from varied sources, built up my own bag of tricks, and had great fun learning to estimate results in my head. I got fairly good at estimating squares, and square roots quickly. For me it was purely a source of amusement, and at that innocent age, I wanted to, in my own humble way, emulate some of those math stars - Hans Bethe, Von Neumann, Enrico Fermi, and many more. To this day, I don't use a calculator unless I really need an exact answer, or if I need to double check a result that is really important. With easy access to calculators, one might argue that it is worthless to learn to calculate mentally. Maybe. But I think it is worth learning it, if for nothing else, then at least for the sense of thrill and challenge that is definitely brings !
I am surprised that this kind of 'math for fun' approach hasn't made it to most schools. Or maybe I just naively, but strongly believe in it. Also, how do we 'systematically' teach 'unstructured thinking' ? I don't know the complete answer, but in my opinion, the secret is to not always be systematic. Life itself is unstructured anyway, and I think its good to introduce youngsters to some of that from an early age :-) And I think it is this kind of unstructured approach that also uncovers latent talents in students. A bright, inventive mind might be lurking behind that dull, bored backbencher , just waiting for that right mind-teaser to wake him up, and spur him into exploring more of the magic on his own ! Students don't need to be 'taught' everything; often, all they need is a trigger to get them going ! Light a spark, and it will develop into a flame on its own.
Curiously, I got into the world of programming in a similar way, but that is a story for another day, or maybe, another blog :-)
