In defense of rote
Comparing American and Indian education systems can be a tricky endeavor since many cultural and educational specifics in the two systems are not transferable. But there is one feature of the Indian system not existing in the American one which seems to be universally criticized, and that is its insistence on rote learning. Any one of us who has run the gauntlet of Indian education does not need to be reminded what this is. The pounding of facts, usually accomplished by mindless repetition, is a mainstay of much of the time that we spend in the classroom and at home. When I was in school rote learning extended to everything from multiplication tables to Sanskrit adages. Such unpleasant exercises appear essential for good grades, and it seems there is no escape from them.
But rote is not exclusively an Indian invention. It was also a staple of European education in the twentieth century. Einstein recalls how he retreated into Kant and Darwin as a refuge from the deluge of rote that he had to face in the Gymnasium. In his biography of Linus Pauling, the English biochemist Max Perutz also describes having to memorize thousand-page chemistry books in his native Vienna; as he dryly remarks, such exercises gave him the kind of satisfaction one might get from walking between the two ends of Cambridge, but nothing more (Pauling’s highly influential book which provided a rational basis for hundreds of disparate chemical facts was his salvation).
However, rote memorization serves a certain valuable purpose which I want to describe here. This purpose is best exemplified by a rather remarkable story passed down by my father about the Indian mathematician and ‘Senior Wrangler’ R. P. Paranjpe, who was the principal of Fergusson College in Poona at the turn of the century. The story comes from an old mathematics teacher of my father’s, Prof. Godbole, an extremely wise and learned individual whose students went on to teach at leading Indian universities and technical colleges. He once wrote a letter to R. P. Paranjpe asking for advice on how best to do mathematics.
First, a brief digression. The title “Wrangler” was and to some extent still is an esteemed honorific that one can acquire in the highly regarded mathematics Tripos examinations at Cambridge University. Successful negotiation of the Tripos secured the title of Wrangler for those who dared and was a hallowed tradition that separated the boys from the men. As Robert Kanigel describes in his wonderful biography of Ramanujan, scholars at Cambridge in the nineteenth century could roughly be divided among those who had navigated the currents of the Tripos and those who had not. The Tripos guaranteed one a place among the Cambridge elite and brought great intellectual and social benefits. Some of the greatest scientists in the world including Lord Kelvin, James Clerk Maxwell and James Jeans made their names by cracking the Tripos. The highest rank was ‘Senior Wrangler’ with lower ones designated ‘Second Wrangler, ‘Third Wrangler’ and so on. For the very best students, anything lower than Senior Wrangler was tantamount to ignominy. The passing rate was notoriously low.
India can boast of a select few personalities who distinguished themselves through this difficult examination. R. P. Paranjpe was the first Indian to become a Senior Wrangler and enjoyed great prestige among Indian intellectuals . He was initially a professor and principal in Fergusson College and later held vice-chancellorship positions in Bombay and Lucknow universities.
As a student, my father’s 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. Paranjpe wrote back and suggested some tricks, habits and techniques for gaining mathematical facility. But one thing in the letter stood out for Prof. Godbole- Paranjpe’s telling emphasis on rote memorization, the same rote memorization that we look down upon. Why did Paranjpe hold this depressing habit in such high regard? To illustrate his point he told Godbole a story
It was 1899, and Paranjpe had gone to Cambridge to take the infamous Tripos. To his delight he got the highest grade and secured the coveted title of Senior Wrangler. But it was when he found out about the Wranglers in the previous few years that his pulse began to race and he indisputably trembled. Just a year before, the title of Third Wrangler had gone to none other than G H Hardy, best known as Ramanujan’s mentor, and undoubtedly one of the greatest pure mathematicians of the century. Gifted as he was, Paranjpe knew that he was no match for Hardy’s formidable intellect. What on earth could have made him outclass Hardy in the Tripos?
The decisive factor may have been rote, as Paranjpe himself said in his letter. The Tripos examination is designed so that one needs to tackle and solve as many problems as possible in a given amount of time. While creative solutions are applauded, efficiency is more important than raw 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 unexpected and brilliant ways. But all this took time. On the other hand, Paranjpe who was steeped in the Indian system 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 techniques and solved the problem in a flash. Through sheer memory and the benefit of rote, Paranjpe managed to solve many more problems than Hardy, even if Hardy had shown creative brilliance in solving them.
This story is revealing but it’s probably not as startling as it sounds. While rote learning in the Indian system has rightly received a lot of flak, the criticism has also veered off to the other extreme and dismissed rote as having absolutely no value. There is a sense that ‘truly’ intelligent students don’t bother with rote. Such an attitude has also led to a perception of rote learning being completely divorced from creative problem-solving. But both these attitudes seem to be misguided. As Paranajpe’s story demonstrates, rote can undoubtedly be helpful even for navigating some of the most difficult exams in the world. And although I cannot attest to this, I suspect that a similar situation exists even with those most highly regarded exams- the Mathematics Olympiads.
What about our own notoriously difficult IIT entrance exams? Well, for one thing I remember many of my friends from the IITs stressing the importance of rote in their examinations. Rote learning certainly seems to be extensively utilized even by students in our top universities. But also consider this. One of my father’s friends is a mathematics professor at one of the IITs and for many years has been involved in formulating problems for the entrance exam. My father once asked him how he managed to come up with novel problems every single year. The friend honestly responded by saying that no, it’s just not possible to come up with entirely novel problems every single year and so even the exam committee is relegated to constructing variations of old problems from previous years. If that’s the case, is it any surprise that students who intensively train for the IIT entrance exam for an entire year often have little trouble in cracking it?
In reality, you don’t need to either love or hate rote learning to recognize its specific value; it’s just one more tool that students can use to master complicated concepts. Plus we are all supposed to leverage our strengths, and why shouldn’t someone with a good memory not take advantage of this tool? On the other hand, someone without a good memory could also use rote to get the extra mile out of his other abilities. Unfortunately in India, rote is too intimately tied to the examination system and this has resulted in reasonable criticism of rote also leading to its unwarranted wholesale condemnation.
It’s important to realize that rote learning goes far beyond exams. In its simplest incarnation, it establishes certain signposts in our brain which the brain can then quickly reference for pointing the way towards a solution. These days it’s fashionable to Google every single fact in the universe. This habit seems to have conveniently freed us from actually remembering things and is often lauded. But I think such an attitude carries a liability in not making it possible for the brain to connect ready-made facts and figures in order to tackle a complex problem. To me there seems to be a clear advantage in being able to have important numbers, concepts and definitions ready for disposal. Much of problem solving, especially in this interdisciplinary age, consists of forming links between seemingly disconnected facts and acquiring new insight from these connections. To me it seems indisputable that someone who already has all the facts in his or her head would find it much easier to make these unexpected connections compared to someone who has to look them up one by one. In the parlance of modern science, one could say that a collection of already available facts possesses emergent properties that are not inherent in the piecemeal acquisition of these details.
So before we consign rote to the dustbin, let’s not forget its benefits especially for this age of multidisciplinary research. Mindless rote learning certainly needs to be criticized, but let’s not throw the baby out with the bathwater. Perhaps a final story would illustrate the advantage of having all the facts in your head. The story involves one of the greatest scientists in modern history and tells us that even great scientists efficiently use rote memorization, and sometimes unconsciously so. During the Manhattan Project, engineers working on the plutonium production reactors used to often run into problems involving quantities which had not been measured until then; these mostly involved nuclear cross sections which indicate the probability of interaction of radioactive elements with neutrons. In frustration they approached the infallible Enrico Fermi. Fermi used to complain that he could not help them since the relevant numbers were not available. But the engineers would just smile and start reading out a list of numbers to him. When the correct number showed up, Fermi’s eyes would literally twinkle and the engineers used to know the ballpark estimates. Fermi’s eyes twinkled because he had a list of other relevant numbers in his head, and his brain could connect these numbers in different ways to arrive at a good estimate of the missing quantity. Now while that does not mean that Fermi actually sat down after dinner and memorized the list, it also does not mean that having the list ready in his head by rote memorization wouldn’t have helped.
What would the world have done if the great Enrico had said, “Hold on, let me Google these”? There’s a lesson there somewhere.