Tuesday, March 11, 2008

ROTE AIN'T THAT BAD: PARANJAPE VS HARDY

Sunil has a post in which he muses over the merits and demerits of the American and Indian systems of education. With all the flaws we have in the Indian system, it's still hard to compare the two. I have usually come to the conclusion, even if not wholly satisfactory, that at least for motivated students our system is better till the end of junior college (high school in the US) while the American system can sustain a creative mind much better during the college and university years, with its opportunities for collaboration and research.

This comparison inevitably makes me think of one of the most common criticisms leveled at our system- the great emphasis on mostly mindless rote memorization, usually essential for getting good grades. Interestingly, this system is not just deeply embedded in our way of educating people. It used to be endemic in many European and American schools before progressives took over. I remember many biographies of scientists- Einstein being one- where they had to go through the humdrum of rote and usually ended up getting disgusted. Sadly, the European and American systems have largely outgrown this tradition while we still are steeped in it.

But rote memorization can sometimes serve a useful purpose, and there is one absolutely remarkable story that I always remember as an example of this.

My father's school mathematics teacher and close mentor- a man of great learning and wisdom- once wrote a letter to Wrangler R. P. Paranjape asking for advice on how best to do mathematics. But a brief digression here. Most of you probably know that the title "Wrangler", and especially "Senior Wrangler" was and to some extent still is an esteemed honorific that one can acquire in the famous and highly regarded mathematics Tripos examinations at Cambridge University. The Tripos, successful negotiation of which secured the title of Wrangler for those who dared, was the benchmark for marking geniuses, and some of the greatest scientists in the world, including Lord Kelvin and James Clerk Maxwell, have secured their position as Wranglers through this examination. The passing rate was notoriously low. Scholars at Cambridge in the nineteenth century could be divided among those who had cleared the Tripos and those who had not. The Tripos guaranteed one a place among the Cambridge elite and brought great intellectual and strategic benefits.

India can boast of two such personalities, Wrangler Paranjape and Wrangler Mahajani, who distinguished themselves through this difficult examination. Paranjape, who was a Professor and Principal at Fergusson College in Pune long ago (yes, that time standards were slightly different from now), enjoyed great prestige among Indian intellectuals and in fact was the first Indian to become a Wrangler. Incidentally he lived very close to our place, along the road that runs next to our house. His house today is marked as an important historic structure.

In any case, as a student, my father's mathematics teacher Prof. Godbole was curious about how best to go about studying mathematics and decided to write a letter to the great man asking for his advice. Paranjape wrote back and suggested some tricks, habits and techniques. But one thing in the letter stood out for Prof. Godbole, Paranjape's emphasis on rote memorization, the same rote memorization that we look down upon. Why did Paranjape hold this depressing habit in such high esteem?

In the twilight years of the nineteenth century, Paranjape had gone to Cambridge to appear for the infamous Tripos. He took the Tripos, and to his delight, scored the highest grade. But it was when he found out who scored below him that his pulse began to race and he indisputably trembled. It was none other than G H Hardy, best known as Ramanujan's mentor, and undoubtedly one of the greatest pure mathematicians who ever lived! Paranjape, gifted as he was, knew that he was no match for Hardy's formidable intellect. What on earth could have made him do better than Hardy in the Tripos?

Believe it or not, but it was rote, as Paranjape himself said in his letter. The Tripos examination is designed something like the IIT entrance test. One needs to tackle and solve a certain number of problems in a given amount of time. While creative solutions are applauded, efficiency is more important than genius. Hardy, that doyen among mathematicians, decided to apply his mind and come up with novel solutions to the problems. When he could not remember certain equations or formulae, he derived them in a stroke of brilliance. But all this took time. Paranjape who was steeped in the Indian system on the other hand, instantly remembered equations and formulae. He had memorized them and in fact entire problems beforehand through practice. Whenever he saw problems similar to ones which he had seen before, he recalled the necessary technique and solved the problem in a flash. Through sheer memory and the benefit of rote, Paranjape managed to solve many more problems than Hardy could, even if Hardy had shown creative brilliance in solving them.

Prof. Godbole passed this story on to my father, and my father passed it on to me. And I have always remembered it. Sometimes rote can make one triumph even over more gifted individuals. While learning certainly does not end with rote, for all its drawbacks, rote ain't that bad.

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8 Comments:

Anonymous Kimberly Vance said...

I think the idea of rote memorization in the old American and European systems was to train the mind for the bigger tasks to come. As Dorothy Sayers would say, rote memorization was "intended to teach the pupil the proper use of the tools of learning". In your opinion is that a valid claim; does a system that includes rote memorization train the student in the ability to think, not just about the subject at hand, but about any number of subjects?

8:11 PM  
Blogger Ashutosh said...

I largely agree with Sayers. I think rote does have its value and its place in school education. It definitely enables students to thoroughly know the essentials and have them ready at their disposal for application. As you said, rote can train minds for bigger tasks. But there is a limit to which you can emphasize rote. In many Indian schools, the process becomes mindless and is emphasized overwhelmingly over critical thinking. That allows the student to get good grades, but fails to train him or her for independently tackling novel problems later in life. When solving these, rote can only take you so far.
Interesting site you have by the way.

7:52 AM  
Blogger Sunil said...

Ashutosh....I think a certain amount of "rote memorization" is really essential in order to be successful as a researcher. Basic concepts can be googled for, but if they are internalized then it is much easier to tie together diverse problems, or link different observations. A foundational knowledge is an absolute must. That said, it should not be done in such a way that any creativity in a student is lost. I'll agree partly with your comment on a combination of high school education in India and subsequent college education in the states. But I'll have to add that it has to be high school education in a "top" school in India (at least the best school in that city), followed by college education in the US. It is very hard to excel for a vast majority of the students in India because of the extreme mediocrity of the system (even when it comes to rote memorization!).

1:57 PM  
Blogger Girish Mallapragada said...

Ashutosh,

Nice post! I have to first admit that I was a champion roter in school. I tend to agree with you that there is some purpose to roting. I am not sure how it did contribute to my intellectual growth, but I sure do know that I would not have become the researcher I am without the roting of the school years.

8:59 AM  
Blogger Ashutosh said...

Sunil: That's true. In fact I was surprised at how some of my very smart friends managed to do so well in the rote-memorization system.

Girish: I can empathize...rote memorization that I did in school helps me too!

1:15 PM  
Anonymous Jiten M. Shah said...

Just a minor note. The story handed down to you from your dad about Paranjpye (official spelling) besting G. H. Hardy in Tripos may not be true. Paranjpye was the Second Wrangler in 1899; G. Birtwistle was the Senior Wrangler that year. G. H. Hardy had taken Tripos a year earlier in 1898; he was officially the fourth wrangler. Also, there are two parts to the Tripos exam, which makes it difficult to truly or unequivocally "rank" anyone.

Nothing said above is meant to disparage value of rote memory in your excellent blog. With best wishes,

Jiten

11:47 AM  
Anonymous Jiten M. Shah said...

Some corrections: My earlier comment today about Paranjpye being the Second Wrangler & G. Birtwistle being the Senior Wrangler is wrong. G. Birtwistle & R. P. Paranjpye were joint Senior Wranglers for 1899.

Similarly, as J. F. Cameron & J. H. Jeans were joint Second Wranglers, G. H. Hardy was probably the Third Wrangler for 1898.

Source: Masters of Theory by Andrew Warwick, University of Chicago Press; Pages 522-523. This book does not identify joint winners, thereby creating confusion. I regret this error & oversight on my part.

Please let me know if information gleaned from above source needs to be corrected and/or revised. Thanks.

Jiten

1:10 PM  
Blogger Wavefunction said...

Jiten, thanks very much for correcting the error and providing valuable references. Of course Paranjape might still have been surprised that he was Senior Wrangler while Hardy was Third Wrangler. The way Paranjpye is spelt is also interesting since around where I live we always spell it 'Paranjape'. I should now check out the book you have referred to.
Thanks again for providing valuable insight into an interesting anecdote.
Ashutosh

7:48 PM  

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