Why do I say this is "required" of all mathematics teachers at all levels? Read on. Then, please, please read Friedman's book.
Then (my final request), get hold of the documentary film Two Million Minutes.
I received an invitation to see a private screening of this film in Palo Alto late last year, where its conceiver, financier, and executive producer Bob Compton talked about why he made the film and answered (many) questions from the audience. Compton is a highly successful venture capitalist, whose work takes him frequently to India and China, as well as all over the USA, giving him an opportunity to see up close the educational systems of all three nations, and how suited they are (or are not) to producing the kinds of people who will be successful in Friedman's flat world.
The film's title refers to the length of time a student spends in school from the 8th grade to graduation from high school. It follows three pairs of high school students, one in the USA, one in India, and one pair in China, as they go through a typical day, at school and at home.
Compton freely admits he did not set out to make a dispassionate documentary. He has an angle and he has made sufficient money in his career to be able to put out his views as a one-hour movie. So he gets to choose what is in the film. But he leaves it to the audience to reach whatever conclusion they may after seeing it.
I suspect that the "intended" readers of this column - college math professors - will reach the same conclusion as I did after seeing the film, and in fact will not need the movie to tell them what they already know. When it comes to mathematics education, the USA became an also ran to India and China long ago, and in the future we will have to commoditize and outsource most of our mathematics and engineering just as we already do with manufacturing, customer support, financial services, and software development.
Of course, the familiar comparison I just alluded to is not as simple as that. In the USA we took the tack of structuring and providing education for all students. China and India have vast populations, most in considerable poverty (though China, in particular, is changing rapidly in that regard), and only a small percentage are getting the math-rich education you see in Compton's film. But a small percentage of such huge populations still generates a large number of young people mathematically superior to the average American college graduate.
A simplistic response to the mathematical divide portrayed in Two Million Minutes (a divide that, on the aggregate, national level, we are on the underdog side of) might be to try to revamp our education system to compete with India and China, but I don't see that as feasible on several counts.
First, while the current US President may well mark an all-time low in math and science ignorance and illiteracy among our nation's leaders, the entire Congress is hardly awash with scientific and technologically knowledgeable individuals. The government won't and can't fix our education system because they don't know how and, since the 1960s, have demonstrated over and over again that they are not prepared to listen to those who do and follow their advice.
Second, whatever we do at a national level, there is no way we can create the huge personal need and family support it takes to motivate a young person to spend the enormous amount of time and effort required to master math and science. (That doesn't mean that we should not try to provide the support and resources to meet the needs of those American children who do have that drive; but government won't do that either - "No Child Left Behind" cashes out as "All Children Kept Behind".)
China and India are going to capture the market in doing the world's mathematics just as they already have in other spheres. But that does not necessarily mean that the USA will lose the one lead it clearly does possess: innovation and risk taking. Silicon Valley, where I live, is largely fueled by Asian-born engineers, and the main change being brought about by the global communications of Friedman's flat world is that many of them will no longer have to uproot themselves and their families and go through the hostile procedures of the US Immigration Service in order to carry out that work. But the bulk of the work that will go overseas in that way is the stuff the can be commoditized. In the case of mathematics, that means "Do the (routine) math required to make X possible." We can still hold on to the crucial first step of dreaming up the X (and its uses) in the first place.
Or can we? Is my scenario realistic? Can we commoditize and outsource math the same we do manufacturing or financial services. I don't know. For some mathematical tasks, for sure. Indeed, for some it has already happened. But the outsourcing issue is never as simple as it is often portrayed. If the outsourcer does not understand, at a deep level, what is being outsourced, then it's only a matter of time before the entire enterprise moves overseas.
Outsourcing mathematics strikes me as particularly tricky, since "understanding at a deep level" seems tightly interweaved with being able to do math (i.e., solve mathematical problems). But I don't think we have any choice. In terms of sheer numbers, India and China already dwarf the USA in terms of young people who can solve difficult mathematical problems. The only thing we have left as a nation is coming up with those problems (and the applications for their solutions) in the first place and making good use of the answers when we get them back.
The good news is that, because our society provides great individual freedom and we have a cultural tendency to innovate, entrepreneurial individuals can always sidestep government inadequacies and obstructions. As a result, we have an enviable track record on the innovation front. I believe the time has come to look at innovating the way mathematics is used in the real world and, correspondingly, how it is taught.
I gave up on the country of my birth (the UK) twenty years ago when it told me it no longer had need for people such as myself (not far from an exact quote from the Vice Chancellor ("President") of the university where I taught, acting under government pressure to reduce its mathematics department by 50%). Having lived through the decline of my home country as a world powerhouse in innovation and economics, I am not about to give up on the country that welcomed me with open arms. Perhaps that is why I care so passionately that we re-conceptualize the way we use and teach mathematics to ensure that the USA remains a world intellectual and economic leader.
What form will such re-conceptualization take? At the K-12 level, I have opinions and ideas, but little expertise or experience, so I'll leave that to others. But I do have a lifetime experience teaching math at the college level, indeed, experience in teaching the kinds of mathematics courses I think will be essential to our survival as a major player on the world stage. I'll write about that in my next column, a month from now.
But here is a clue. When we teach English, the primary goal is to make people literate, able to read critically, and to use language effectively. We do not set out to produce novelists.