If Japan thinks that the high percentage of Indians found in technical jobs worldwide is due to our memorising mathematical concepts instead of understanding them, it has got its sums all wrong. And we should not pat our backs, thinking that this formula works, says Surajit Dasgupta
A large number of Indians are under the impression that it is only in this country that children who find mathematics difficult can manage to do well in examinations on the subject, if they can learn all sums by rote. They will be surprised to study the contents of the textbooks of British schools (under the GCSE). Taking quadratic equations, for example, if the books published by NCERT, and those written by RD Sharma and RS Aggarwal have on an average seven exercises on the chapter, with about 20 problems to solve in each, the British books have one set of exercises each for positive and negative coefficients of x 2, x and the constant (in the expression ax2 + bx + c), with at least 30 sums in each!
So, presuming that our children are passing maths exams by virtue of sheer memory power, they are memorising the solution of 140 (20 sums x 7 exercises) quadratic expressions/ equations. Now, their British peers need to solve 30 sums with '+ax 2's, 30 more with '-- ax2's, 30 more with '+bx', 30 with '-- bx', as many with '+c's and an equal number of sums with negative constant terms. If you thought this total 180 is just marginally more than our 140, hold your breath; now will begin the exercises with random combinations of the above positives and negatives! Now, if the British students do not memorise sums, why do they need so many practice problems to rub the concept in?
The above was a prelude to my categorical disagreement with the inference drawn by a prominent national newspaper in its second editorial on January 3 from a report in The New York Times that it had carried on the front page the previous day. A news analysis by Martin Fackler with unflattering references to the Japanese was turned into an excuse for Indians' to pat their backs, for, as the paper saw it, this country's high production of technocrats owing to learning mathematics by rote.
Compare these statements from the article and the edit and you can judge the error of judgement. Some sentences from the article are: "Japan is suffering a crisis of confidence these days about its ability to compete with its emerging Asian rivals, China and India... Japan has grown increasingly insecure, gripped by (the) fear that it is being overshadowed by India and China, which are rapidly gaining in economic weight and sophistication. .. India's success in software development, Internet businesses and knowledge-intensive industries in which Japan has failed to make inroads has set off more than a tinge of envy... the aspects of Indian education they now praise are similar to those that once made Japan famous for its work ethic and discipline: learning more at an earlier age, an emphasis on memorisation and cramming, and a focus on the basics, particularly in math and science..."
And the editorial concludes: "India is, alas, trying to move beyond the rote formula." Alas? It should have been "India is, mercifully, trying to move beyond the rote formula." If the "rote formula" were right, why would Japan, despite following that formula once, now witness a slump in technocracy? And why would things come to such a passé now that the whole nation would suffer from insecurity? Moreover, why aren't the Japanese learning from the UK, given that the British method of teaching, which we inherited forgetting our glorious ancient age of Vedic mathematics, is more extensive to facilitate memorisation?
The answer is: Memory may give you a headstart and make you pass exams but won't take you ahead in any profession where you need to apply the concepts. Also to be noted is the fact that if Indians crowd the technology-related job market today, it's because the four to five per cent of brilliant students it produces per classroom make up for enough candidates for the whole world and more. But what about the remaining 95 per cent? In every batch of students I have taught in Delhi and Kolkata, I have found about five to six students jostling for space for the first three ranks in exams, followed by a massive 60 per cent who score about 70 per cent to 90 per cent of marks; this performance is not consistent. And the rest manage to pass... somehow.
Compare this with the scenario in the US, where children are given assignments to work on at home, which -- the honesty of the parents might surprise you -- the kids complete themselves (at least the US Embassy schools don't have maths textbooks; they are free to use reference material from any credible source). Unlike here, a 'good' student is one who scores 100 per cent. If it's even 99 per cent, the child loses his sleep for nights on end. And if it's a 'bad' student, he scores no less than 85 per cent. True, the progress in maths is slow by Indian standards. But when a given concept is imparted as education, a big chunk of the students follow it, not a gifted few with high levels of aptitude. Isn't this model -- more so because in science the US is still the top achiever in the world -- more worthy of emulation and also more democratic?
Back in India, it's the average students who later serve in offices. The brilliant either excel or perish, frustrated with their 'lesser' colleagues whom they look down upon, as they never spent time to learn about human relationships while staying glued to their textbooks for some 20 years of education. The lesser ones, in turn, scoff at the snobbery and 'impractical' outlook of the former. Well, that's about office management and organisational behaviour. Let's get back to Indians' knowledge of science.
How do typical educated parents face their growing child's inquisitiveness? "You know... I used to be good at calculus once; I've forgotten all of it now." How can you forget something you had once understood? Of course, you must otherwise admit that you had actually understood nothing; you'd rather crammed the whole of it. This is sham education. The epithet 'educated' is really doubtful. No wonder then that we receive requests on phone from doctors and engineers to carry their articles on sociology. Ask them to write on physiology, medicine, electromagnetism, thermodynamics or radioactivity in view of a recent development in the nation or the world, and they hang up or start mumbling at the other end.
The National Curriculum Framework, stressing the need for developing children's faculty of analysis and application, was crying to be created. When you were a child in 1988, and the then edition of your chemistry textbook had told you that "when 0.1 ml of potassium permanganate solution (1-300) and 1 ml of diluted sulphuric acid (1-20) are added to 5 ml of solutions of chlorites (1-20), the red-purple colour of the solution disappears, you are not likely to remember it in 2008. But had you bothered to visit the laboratory to add the above chemicals in that order, the sight of the red-purple colour vanishing would have lingered in your mind till now.
As for mathematics, say, mensuration, textbooks showing figures with several lines labelled as "height", "slant height", "radius", "circumference", etc are first, straining to the eyes; second, confusing; and third and most important, they don't resemble life as it is. A circle can never look like a real sphere; that's the limitation of drawing: A two-dimensional figure can at best create an illusion of being three-dimensional but cannot become one. Instead, try origami.
To understand cylinders, for example, take a rectangular sheet of paper; roll it along the length -- it's a cylinder. Then open it up; tell the child what was the length (l) of the rectangle became the circumference of the cylinder (2pr) and what was the breadth (b) of the former became the height (h) of the latter. Therefore, the curved surface area (CSA) of the cylinder, though sounds difficult, is as simple as the area of the rectangle of which it was made. This follows that since the area of the rectangle is l x b, the CSA of the cylinder is 2pr (in place of l) x h (in place of b), where p = 22/7 approximately. This is one of the ingenious ways of teaching maths and this is how the subject has started being taught in Indian schools now, thanks to the National Curriculum Framework.
If the "rote formula" has produced millions of technocrats, comprehension and application will produce billions of them. And then the mother won't send her child to the father for maths answers, who, in turn, won't send the poor little one to a private tutor; and yet claim they are 'educated' parents.
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