Thursday, May 15, 2008

Kudos to NCERT

For those not of the Indian origin, NCERT (National Council of Educational Research and Training) is a government body which publishes textbooks for students upto 12th grade apart from doing 'educational research and training'.

When I was in my high school years (9-12th grade) I enjoyed reading NCERT books. Being quite concise they took less time to study and most of all they were not at all boring like other textbooks (published by non-government publications) which just included solved examples and drill problems.

Well to my utter excitement these NCERT books have improved their standard much beyond what I had seen in my time (1995-1998). First let me remark on the physical design (well, because it is remarkable enough!). These books use color for diagrams to make it more attractive, contain very less misprints, use wide variety of fonts to draw attention, and paper is watermarked with NCERT logo (check their site for logo) to prevent counterfeit copies. And they happen to be quite cheap compared to other textbooks (probably because of government subsidy).

The things which I mention might not seem remarkable to foreigners, but if you actually go to a bookshop and get a textbook (other than NCERT ones) you will find that NCERT books are remarkable for their physical design alone, leave aside their content.

But the reason they have won my heart is primarily because of the content. This summer I had a chance to have a glance at NCERT Mathematics textbook for 9th grade (I pick maths because its my favorite subject and so readers beware! the opinions expressed in this post are primarily based on math texts). The book is really fantastic. These books focus on concept building and not problem solving. You have to read them and not start by working out problems.

The concepts are explained by simple examples, experiments and proofs (where possible) and many explanations contain historical notes or references to related interesting topics. Like while mentioning euclidean geometry they specially mention the history of the 5th postulate (which was the basis of non-euclidean geometries discovered later). And this is exciting enough for a 9th grader.

Now to the real test of a 9th grade book: the introduction to irrationals. Here NCERT goes beyond words and explanations and brings out diagrams in color. The real line is depicted by zooming in various sections to illustrate the concept of denseness. This zooming is by the way perfomed by using the image of a convex lens (commonly called the magnifying glass). What a nice way to express the fact that a small section of the number line is big enough to contain an infinite number of points (which represent numbers).

A point 'A' corresponding to an irrational number will seem to match with a rational point 'B' if you actually do the geometrical constructions. But when you zoom in, you will see that points 'A' and 'B' are different. No matter what rational point 'B' you choose you will be able to zoom the line sufficiently so that point 'A' is different from point 'B'. This zooming in is the essence of 'Mathematical Analysis' and the informal equivalent of espilon-delta.

Unfortunately and shamelessly R. D. Sharma (famous nowadays for IIT-JEE books, although I am not sure he is the same guy) copies these diagrams (its a xerox copy, the same line, the same magnifying glass) and that too in black & white. And it contains lot of examples and problems. Sadly most of the answers to the problems are wrong (printing errors probably), so the student has no way of knowing (apart from his confidence in case he has) whether his answers are correct.

Finally the NCERT book had some appendices discussing the importance of proofs in mathematics. This part is quite well written and is expected to motivate readers to appreciate proofs and develop skills to provide proofs.

Let's congratulate NCERT for bringing out such nice textbooks and hope that they do an even better job in future.


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