I have been thinking about the following problem recently: Maths.
In 2001, the bipartisan Hart-Rudman Commission warned that the failure of math and science education posed a greater threat to American power than any conceivable conventional war in the new century. In his 2005 book, and in later postings on his site, the conservative US politician Newt Gingrich, who was on the Hart-Rudman Commission, warned that “American high schools are obsolete”

The collapse of math and science education in the US and the relative decline of investment in basic research is an enormous strategic threat to American national security. … Keeping America competitive in the twenty-first century is dependent upon having increasing number of students studying math and science.[source]

David O’Meara, the CEO of Havok, the computer game and cinema physics company, raised Gingrich’s warning at the IIEA Digital Future Group in Dublin in early 2009. I had just completed The Next Leap report, and O’Meara’s Gingrich’s warning resonated.
The questions this raises are, first, what is the relative decline between West and East in innovation, and second, what might be its future trajectory? I approached two mathematics researchers at Magdalene College, Cambridge, with an idea for a new book to tackle these questions. We are currently in talks with Springer about a book deal to work on this project. If all goes well, we will be examining the historical role of mathematics in the prosperity of states and civilisations, and its role in our future as global competitors in a new era of innovation.
The answer to the question about the West’s decline, at least according to the Hart-Rudman Commission, is clear:

In 1997, Asia alone accounted for more than 43 percent of all science and engineering degrees granted worldwide, Europe 34 percent, and North America 23 percent. In that same year, China produced 148,800 engineers, the United States only 63,000. [source (p.39)]

While this is something that we will have to investigate more fully, these figures from 97 are interesting indicators. In Outliers, Gladwell grapples with the question of how mathematics is learnt in the East. When it comes to math, Gladwell says, “Asians have built-in advantage”:

The number system in English is highly irregular. Not so in China, Japan and Korea. They have a logical counting system. Eleven is ten one. Twelve is ten two. Twenty-four is two ten four, and so on.
That difference means that Asian children learn to count much faster. Four year old Chinese children can count, on average, up to forty. American children, at that age, can only count to fifteen, and don’t reach forty until they’re five: by the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills.

Gladwell also refers to Stanislas Dehaene’s The Number Sense:

Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is ’si’ and 7 ‘qi’) Their English equivalents—”four,” “seven”—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.

But a follow on question arises, to which I do not yet have an answer: is there an innovative spark in the Western system that is lacking in the rote-based system in the East?Is it fair to talk about an Eastern rote system at all?
More anon…

The closing point re “speedy” I’ll come to on the next page.

Looking at other comments, I especially like the idea of seeking “classroom” support from the technology world, especially as many leading companies there do have teaching facilities. Mobile learning and e-learning are also of course critical.

Third level is actually in better condition, and I really would get the first 2-3 levels fixed before wandering into invented country like “fourth level”.