Not all imagainations are useful. Some are useless and some are harmful to the society. Useless imagination is still useless. Until now, math like 1+1 = 3 serves no purpose and does no good to the society. I don't think a kid of 5 should be taught to create useless math like 1+1 = 3. Innovation requires good foundation to build on. Many of the useful technological advancements are incremental, and build on the existing one. As a Ph.D., you should know that many of the research results are based on the past research results. It is almost impossible to create something out of nothing.
what if 1 + 1 = 3 is a solution for the problem at hand? you're obviously getting a strange answer, so that should lead you to rethink the question itself.
If I had a silver dollar for every time someone starts an article/conversation/thread/book/etc. with "U.S. Headed For Economic Disaster"...
As i said, till now most of us haven't found it useful yet. Why teach something that are known to yourself as useless as of today? I don't support a public school to teach a new theory without any supporting evidence. Scientific research and advancement is not only about new ideas, but the evidence of its usefulness.
'Real' Americans do have a lot of 'communication' skills, mainly in the area of relentless arrogant self-promotion. They do not have science degrees - no need to - just get some MBA, English or journalism or 'free arts' major, and you can run any US corporation, like Carly Fiorina ran HP. Any American Idiot has good communication skills and ready to run anything, including the great state of Alaska, or the US of A itself (remember George W?) Titanic already hit the iceberg, the living standard going down with the bankrupt Uncle Sam, who passed a point of no return. American Idiots will have to learn to leave according to their means in a hard way, paved for them by the rulers from Goldman Suchers etc. Americans also have an inherent love for individual freedoms - this is why they supported whole-heartedly the Gestapo methods that can be applied to _any_ non-citizen deemed a 'terror suspect', and feel good about pinpoint drone bombings of wedding parties in Afghanistan and Pakistan. Yes, Treasuries will be worthless, and the US dollar too. However, USD denominated real assets go down with the dollar, and Chinese are loading up on them, buying good startups in the valley and other places and moving them to PRC. They are also the cash buyers of a prime residential RE. This is to the question of whether Chinese or other non-Americans can manage money, and do business, or they need an American MBA who learnt creative thinking 1+1=3 to run their enterprises for them. Math is hard, it is for Asians, American kids want to do sports, music, ... or pot, beer and vodka. They absolutely do not get it that you do not need a calculator to answer the question what is the difference in areas of a circle 2" in diameter v 1" in diameter. Their future is bright and getting brighter.
Students in China, Japan, South Korea, Taiwan and many Western European nations are far more proficient in math and science by the time they reach high school as many Americans are by the time (and if) they enter university. Our public primary school system in this country is a patchwork that varies wildly from state to state, county to county and city to city, but on average, it's just abysmal. While everyone is pointing fingers at the teachers and administrators of public schools, the real problem is a cultural one in that many kids have parents, whether single or married or divorced or whatever, that just are not willing to do whatever it takes to motivate their kids to excel in school, and discipline them when they don't apply themselves. The teachers' union and public school administrators response to weak performance going back to the 60s now is to ask for more and more money and larger and 'better' buildings, computers and other 'things.' This, of course, is akin to 'throwing money at the problem,' and does not address the root cause of our primary school system's mass failure. On top of these problems, parents who are engaged and involved with their children, and who have the financial means, are likely to send their kids to private schools, which simply amplifies the existing problems at public schools. In Japan, the schools are absolutely stark in comparison to U.S. schools, and many aren't even heated or cooled in particular prefectures. Their are no janitors, because the students are charged with cleaning the schools - the same is true in Singapore. They have simple structures and yet have rigorous standards and superior results. Our problem is a cultural structural one. Waiting for the university level to 'fix' all the imperfections of our primary schools is very inefficient and is akin to spending health care dollars by the bucket load to try and keep an unhealthy 75 year old alive in the hospital, when prevention would have cost 3% of treatment ex post facto.
Which answers? Like 1+1=3 ? Or maybe : The Earth lies on three whales? It has nothing to do with imagination.If you get the right answer in a different way that is more simple ... You have used your imagination. Like (maybe i'm wrong with the hero) Ferma. When teacher asked his class to sum all the numbers from 1 to 100 he made it this way: 100+1=101, 99+2=101... So 101*50= 5,050. While the others were puting together: 1+2+3+4... Maybe any "imaganable" kid said at once: A million! I like it. If you can't solve some equation... It's ok! Use your imagination! Put any number and the problem is solved. How many Nobel prizes in Economy have Americans won? For the last 10 years? And what is the result? Endless turmoils,crisises and like that. Maybe this nobel show all political?