China is a super power now. Be it technology, military or academia the growing might of the Chinese cannot be ignored. The gap between India and China in some of these is so huge that its really striking. However if we look closely, in a lot of the areas the two countries are compared on, the gap though huge is perhaps understandable, China although a communist country in name, is actually much more business friendly and that has resulted in multinational companies setting up their manufacturing hubs there giving rise to much more job opportunities, education and skilled labor . Tons have been written about this and I don’t really want to harp on the self explanatory in this blog.
However, one area where the gap seems really strange is academia and global competitive exams. China publishes a lot more research papers than India and also does much better in competitive examinations like International Mathematical Olympiads (IMO). The first can be chalked down to lack of funds in Indian institutes. The second one however is much more perplexing. India is a country with a population over a billion, yet it seems to way lesser medals than countries with less than one-tenth our population.
In the list of countries sorted by medal count in IMO, India stands at a rather unimpressive 31, while China stands at, yes you guessed it right at #1. What however is more perplexing is India ranking below countries like Romania, Thailand, Poland et all. Perhaps China is the exception in the Asian context ?No really, Asian countries seem to do well, South Korea is #5, very impressive for a country of its size and population, Vietnam is #8, Japan #12 and Thailand stands at #18. A good though perhaps unfair metric, is counting number of medals per 1 million people. Hungary is stupendous, with 8.3 gold medals per 1M people, USA is 0.8 per 1M, Germany 4.5. India ? 0.1 per 1M people. Of course for a developing country with a massive population its very hard to provide uniformly great quality of education unlike a country with small population like Hungary or a developed country like Germany but we are so far behind even developing countries like Thailand or a country with equally huge population like China that excuse alone doesn’t suffice. For a country that is credited with inventing zero and making much of higher mathematics possible this is indeed a sad situation. What’s really going on here ?
To succeed in IMO, even if you are one of the most brilliant person , you will need someone who can guide you. Doing it alone is hard, and this is made harder by the fact that your peers in countries like Russia, USA or China will be getting it in plenty. Now, Indian school or college teachers seldom have spare time, expecting them to help with preparation of strenuous exams like IMO is futile. This had led to the growth of private tutoring centers across the country , which cater to students wanting to do well in competitive exams. There are towns like Kota where the whole economy perhaps sustains on providing private tuitions to students aspiring to clear JEE. May be something similar can be done for IMO, if one is willing ? So I tried to see how many teachers are available in my city who can help prepare a student for IMO. I tried to do some research and the results were disappointing to say the least. I could find tons of teachers for JEE , however for IMO, there were slim pickings. Even the ones who are willing to teach IMO almost always also advertise themselves as teachers of JEE too. Not surprising, since JEE aspirants to IMO ones will be in the ration of 100 to 1 or more. That also means that even for the teachers who will guide you for IMO, few are really good at it, most probably spend most of their time teaching JEE and perhaps won’t be of much help with tougher IMO problems. Its a really sad situation, even if students are interested, finding a top class faculty to guide him seems preposterously hard.
On the opposite side, for a student who is good enough in mathematics and who could perhaps do well in IMO given guidance, there is the dilemma that IMO is inherently very risky, you are competing globally in an exam where if you fail to reach the final stages you will get nothing. Contrast that with JEE, where even if you don’t get the IIT’s you have the NIT’s and a great pool of other colleges to choose from. JEE is the safer option and there is no surprise which one most students choose to take. But surely if you get a Gold Medal in Olympiads, the rewards are sky high in India ? Well, if you get a Gold Medal in IMO, you will get direct entrance to Indian Statistical Institute — B.Math course and a cash reward of, wait for it, 5000 INR. Trying to crack “Kaun Banega Crorepati” (India’s version of “Who Wants to Be a Millionaire” )seems a much more rewarding and dare I say also a more practical prospect. For a student trying to judge the risk reward for IMO versus JEE, the math's is tragically rather uncomplicated.
Now the other advantages of countries like Russia or China (who do really well in Olympiads) have is that children from a very young age are encouraged by their schools to participate in Olympiads, more ever the teachers are generally available (more so in countries like Austria or Italy) to work with the students. They also have a vast experience of solving IMO problems and as such are able to guide young aspirants pretty well . Good luck finding an Indian school who will do that for your kid. You might get the odd suggestion that your ward can and should take part in the Olympiads, and that's about it. You are then responsible for teaching and guiding him and try and help him in on problems he is stuck, in a world where parents are already struggling with their work loads, few take up the offer. Given the pathetic teacher to student ratios in even the best schools of India, I must say any thing else would have been more surprising.
Indian schools also now focus more on teaching English to students. This has its pros and cons, and to be fair in the Global economy there are perhaps more pros than cons. But recently I was reading the book “Outliers” by Malcom Gladwell. There he tries to find out the reason behind the supposed superiority of the Asian cultures like China, Japan in mathematics. There are a lot of interesting theories (like stating that working in paddy fields for generations have made people of these cultures particularly disciplined and hard working) . The one which caught my attention however was his assertion that Chinese students seem to learn counting much faster than their English counter parts. After extensive studies , it was later on found out that this due to English number names being absurdly long (containing much more alphabets) than Chinese ones. This led to a serious gap after sometime, where the Chinese student soon could remember much more numbers than their English counterparts. Now, this is perhaps also applicable in India. A similar study perhaps could be done, for at least some Indian languages I know number names are much shorter and contains almost the same number of characters compared to English. Lets take a look shall we 1 is “One” in English , 6 is “Six” , both of three characters each, but 7 is “Seven” and 21 is “Twenty one”. Now lets check the equivalent in Bengali, 1 is “এক”, good but not that great an improvement, seven is “সাত”, 21 is “একুশ”, thirty one is “একত্রিশ”. If you are not a Bengali you have to trust me when I say that the Bengali names are inevitably always shorter than the English. Not convinced yet ? Try this slowly say the numbers 1–20 in English, measure the time taken from start to finish and then do so in any Indian Language you are comfortable in (As far as I could determine for Hindi , Bengali and Marathi the time taken is invariably shorter than English , however for Tamil or Kannada might not be that different). Think of it like this , assume a kid can store only 100 characters in memory. Now you have a kid being taught counting in English and another in Chinese or Bengali, which one do you think will remember more numbers ? Not the English one for sure.
In fact, after ten, most words in the English counting system consists of two words and this in itself places an additional cognitive burden on kids. As Malcolm Gladwell says in his Outliers book, this means that kids learning counting in native Chinese often learn twice as fast as their English counterparts, and that gap grows as time progresses (The better you get at counting , the sooner you tackle other problems). Our Indian languages could have perhaps also provided such an advantage, but its gradually eroding. This doesn’t mean that making students learn counting is a panacea, infact without fixing the other deep rooted problems stated above, it’s merely a better launch pad in a marathon not a 100 metre sprint. But its still a start.
A lot can be done to improve the state of our mathematics education, and jotting down every thing will make this article impossible to finish. However some things can be and should be done in the near future if our children are to compete in the global marketplace like, improving teacher student ratio, funding universities so that more research happens, encouraging students to participate in IMO et all, and proving them with better risk-reward scenario than what it is now (5000 INR for Gold Medal ? Seriously ? That barely fills up one week of Petrol now a days ), for most of us tend to choose the safer alternative. A more adventurous step is perhaps to conduct some studies on whether choosing a native teaching medium for math's helps young kids to get better at things like counting faster. If a native language does provide the benefit (not all native Indian languages perhaps are terser than English) try to choose that for a set of kids, and if not stick to English. This might have some unexpectedly good results if Malcolm Gladwell is to be believed (keeping in mind that quality of teachers, school conditions etc. are same and only the language used as teaching medium varies).
A lot of the suggestions above seems to place the onus on others and if you have a kid who is now going to school or one who wants to take the IMO, chances of him being benefitted from any of the above is lesser than you winning 10 million INR from lottery. So what do you do ? If you are a parent who has a young kid and want to help her develop good mathematical skills, and you are willing to put in the time and effort then honestly helping child solve elementary arithmetic shouldn’t be hard and as far as I can tell that alone places your child in a more advantageous position than most other kids (As I read some where, the greatest un fair advantage in this world is to have kind educated parents who are willing to sit down with you and help you learn). Firstly you have to believe that preparing for IMO is not that bad an investment, mathematics is needed everywhere, someone who is good in it will have much better chance of cracking any competitive exams, it also helps with being a better software engineer, and learning to code will soon become a mandatory skill for everyone. What you can do is encourage your kid to participate in Olympiads from a very young age, there are a good collection of books on this subject (try Amazon) and there are some good platforms where they can try out their skills for example. Encourage him/her at least to take part in the National Olympiads from a young age (this starts from class 1 and goes to 12, they also provide a set of books and conduct mock examinations ), yes it will be a time investment on your part, but if not a IMO medal, you can be assured that your ward will have better foundations than other children.
If you are some one who is preparing for IOI/IMO consider doing the following courses online, they have much better study material than what you will get from most private tuitions in India.
When choosing between YouTube video's and MOOC like Coursera always try to go for the later, as you can engage with other students in the forums, which is invaluable. Having trouble in understanding really difficult Maths problems? Subscribe to 3BlueBrown in YouTube. Once you watch some of his videos, you will have a much clearer understanding of most subjects and also see the beauty and elegance of Maths (See his video on Fourier Series for example). Internet is a great leveler, perhaps the greatest democratization of education has happened due to it, if you want it, its there.
What do you think can be done ? Feel free to comment below.