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Dr. Jai Maharaj

Posts: 276
Registered: 1/30/06
Posted: Jan 8, 2008 9:53 PM
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Cram, sham maths -- Surajit Dasgupta

Forwarded message from S. Kalyanaraman

Cram maths, sham maths

By Surajit Dasgupta
The Pioneer
Monday, January 7, 2008

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.

End of forwarded message from S. Kalyanaraman

Jai Maharaj
Om Shanti

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