PISA from Shanghai, part 1

Students from Shanghai scored No.1 in PISA tests. While this result seemed to cause a sensation in other countries, it creates a wave of criticism in China. A typical online comment in China is something like, 'So Chinese are good at examinations. What's new? When will we have a Nobel prize winner(in science), or a Bill Gates or a Steve Jobs?'

This is not exactly a news for people who are familliar with China's school system. Mr. Finn was very very mistaken when he said, 'if they can do this in Shanghai in 2009, they can do it in 10 cities in 2019, and in 50 cities by 2029.'

Shanghai and Beijing students are by no means representatives of all Chinese students. They are considered underperforming 'spoiled' kids. Because of the state's policy favor, students from Shanghai and Beijing can get into colleges much easier than the rest of the country, which raised calls of unfairness every year. While Shanghai has her own examination system, Beijing students, who join the nation wide college entrance examinations, are usually outdone by students from other provinces by a margin of 50 to 100 points on a scale of 750. It might be a great underestimate to say there are at least 50 cities that can outdo Shanghai in PISA tests right now.

On the other hand, in spite of the stellar performance of Shanghai high school students, most Chinese seem to be underwhelmed. Some education researchers go as far as to say the high scores are a testimony of China's education reform failure. China's high schools have been long criticized for being too examination oriented and neglecting overall development of students. An example often cited is the IMO, International Mathematical Olympiad. Chinese high school students have been dominating IMO since joining the competition in 1985, with 15 team championships and more than 100 gold medals. While in developed countries, many of those young IMO gold medalists have become ground breaking mathematicians and scientists, including 2 Nobel price winners and 7 Fields price(often called Nobel in math) winners, few of China's gold medalists can brag even a moderate academic achievement so far. In fact, many of them are not in even in the field of science and math anymore. When Terence Tao, an Australian Chinese and also a former IMO gold medalist, won the Fields price three years ago, the question was raised again: What's wrong with China's school system?

Well, I think China is probably being blessed and cursed by the same thing, standardization. But before we move on to the controversial topic of standardization in education, I want to address a commonly held misconception, at least in elementary level math.

Understanding is overrated

Von Neumann, the inventor of modern computer, once said 'in mathematics, you don't understand things, you just get used to them.'

After all, what's the meaning of understanding? People use abstract concepts to understand specific concepts, not the other way around. When someone tells me something like 'three apples', I must have these abstract concepts like, three and apple ready in my mind to understand what he's saying. The point is you use abstract concepts like 'three' to understand more specific concepts like 'three apples'. You don't use more specific concepts like 'three apples' to understand abstract concepts like 'three'. It is said some native Australians don't have concepts of numbers above three. If you take away 1 stone out of 5 behind them they would notice there are less stones, but they wouldn't know how much less.

Understanding abstract concepts is difficult. That's why math is difficult. It took human thousands of years to abstract the concept of three away from 'three apples', 'three stones' or 'three xxx'. Every small step towards a higher level of generalization in mathematics took human hundreds of years or hundreds of mathematicians' work. You might wonder how difficult it is to invent concepts like zero and negative numbers. The truth is most great Greek mathematicians didn't understand them. How difficult can it be to understand an equation can be made of alphabets not numbers? Well, the lack of algebra, which is invented by Arabians, is considered one of the most important reasons why calculus didn't develop in China. Adults use these concepts like numbers, multiply and divide freely, but we shouldn't forget how hard it was when we were kids, trying to learn them. (Well, most of us.)

The objective of elementary school math should be to hard wire these abstract concepts into children's head until they can use them freely without much effort. The only way to do that is through a large amount of repetition. Call it rote learning if you want to. It is the method used by most people in history and it works. In fact, it's the only method of learning fundamental skills in almost every field. I remember a football coach once said, 'Football is all about fundamentals and hard work.' Now try to tell a football coach he shouldn't let his players do too much passing or footwork or a basketball coach he shouldn't let his players do too much shooting, because that's rote learning!

Of all reasons often cited for the decline of math education in America, I think the lack of training intensity is the most direct one. Teachers and parents are important, but do you really need a college math degree to teach long divide? All a kid needs is a disciplined classroom and some homework time without TVs and video games. Sometimes, I can't help to think American schools can probably do a better job if they let their football coaches to teach math classes, seriously.