PISA from Shanghai, part 2

Standardization

How many people can make a tastier hamburger than McDonalds? How about making a million of them and guarantee every single of them Ok, not good, just Ok?

The good thing about McDonalds is whenever you walk into a McDonald restaurant in Berlin, Delhi or Beijing, and buy a big Mac, it tastes the same. The bad thing about McDonalds is whenever you walk into a McDonald restaurant in Berlin, Delhi or Beijing and buy a big Mac, well, it tastes the same. The secret of scalability in management is standardization. You can be the best hamburger maker in the world or you never put your finger on a hamburger in your life. McDonalds don't care. If you are making hamburgers for McDonalds, you have to do is to follow their standardized recipe. This is probably not the best way to make state of art hamburgers, but it’s the only way to make a large amount of hamburgers of stable quality.

Most Chinese students are using standard textbooks, studying standard curriculum and taking standard examinations. There are many advantages of this. Standard textbooks make teachers' work easier. When people do something again and again, they tend to do it better and better. Do does teaching. The whole point of specialization is that when people are specialized on something they will do a lot better than when they have to deal with a lot of things at the same time. It makes evaluations of teachers, students and principles' performances easier. It arguably makes students' competition fairer. How well you do in the examination are more important than how well you are connected or how how much those who give you scores like you. In China, the combination of standardized education, large population and limited higher education opportunities created immense pressures on schools and students to improve their performances in examinations.

In America schools, standardization seems to be something everybody wants to avoid. Education researchers don't want it, because it will leave them no space for researches. Teachers don't like it, because it means their performance will be compared with other teachers. Students don't like it because it means more homework. I'm afraind it's probably a necessary evil that nobody likes. For example, the charter schools are often considered new hopes by many. In a recent research, CMO leaders complained attaining scale with consistent quality and without standardization, a challenge(Section 5, I'd rather call it an impossibility).

There are of course many disadvantages, the most important of which, it kills innovation. What is innovation really? For individuals, innovation is all about talent, but for societies, innovation is all about diversity. Think of a thought experiment. There are two groups of people searching for something in an unknown territory. Both of them have 10 people. One group demands everybody must stay together no matter what happened. The other encourage everybody out there to do their own search. Which group is more likely to find their target? It actually depends. If no special obstacle exists, I'd bet it's the group gives its member more freedom. America is a much more diversified society than China. That's why America is a great source of all kinds of innovations from pop music to physics.

But the purpose of education, at least basic education, is not for innovation. Every now and then an American high school student will do some works that can put mose graduate students to shame, but the average standard of secondary education is something deplorable for a developed country. Kant believed education was for the mediocre. The geniuses can find their own ways. The idiots are hopeless. The target of education should be to give the horde in the middle enough knowledge for a job in the modern society. Besides, anybody really believes when given total freedom most high school students will spend their time on finding new ways of doing math? Some of them will, probably only 2-3% according to some research. For these students a standard education is a total waste of time. They have a natural desire for knowledge. It's better to leave them alone. They will turn out something amazing in time. Dragging them through a standard education only put out their natural desire for knowledge. The point is education and innovation are two different games. If you have ten researchers, one of them made breaking through contributions, it’s a great success. If you have ten grade school students, only one of them can do long divide, it’s a disaster.

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.