The best description of the problem I've read is Lockhart's Mathmatician's Lament since it really touches on the fundamental problem that we (as a society) have created:
Maths should be taught as Art, just like Music or Painting , instead of the current 'force feed abstract non-real-work complex set of instructions and concepts'
If you have not read his amazing paper (and you can just start with the first 10 or so pages), do it NOW since it might change how to think about Maths and how they are taught in school.
Bret Victor has the pdf available on his site, so you can read it directly below using the embedded pdf reader (or if like me you prefer a print version of this book, you can get one from here):
After two great analogies, Lockhart provides this description of the problem:
The first thing to understand is that mathematics is an art.
The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.
Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound.
In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?
Part of the problem is that nobody has the faintest idea what it is that mathematicians do.
The common perception seems to be that mathematicians are somehow connected with science— perhaps they help the scientists with their formulas, or feed big numbers into computers for some reason or other.
There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe).
Mathematics is the purest of the arts, as well as the most misunderstood.
Basically kids should learn about the beauty of Math, about how to appreciate the beauty of a particular formula/rule and more importantly the history of that formula/rule.
And I can see this problem in action in my kids (aged 8 and 10) where they can already do quite advanced maths but they fail to understand the root origin of a lot of the math's concepts they use. Basically they are lacking in Math's Basics and Math's History.
I specially find it very surprising their lack of ability to break harder maths problems into small ones, which are easier to solve and provide faster resolution paths.
This is very related with programming, which is a lot about finding simple solutions and understating how things work under the hood (i.e. there are a lot of parallels between Maths and Programming). I think that passion for programming is very connected with passion for Maths, and if we want to create a new generation of programmers that loves programming, we have to make sure they are not jaded by 'Maths' in school.
But, since Lockhart's does a much better job than me at describing the problem (and includes really amazing examples), I definitely recommend that you give that a read (btw, when in Turkey last year I meet a local professor in a cafe which recommended the A Mathematician's Apology book as another good read on this topic (I have not read that one, so if you have, let me know what you think of it))
And what about Zero?
Finally, for a great example of what I mean by learning the 'History of Math', what are your views on the number Zero?
Do you know (I didn't) that Zero has a number (and concept) has a really amazing/controversial history, and for a long time (event up to the 16th century) it was not accepted by large parts of our society.
I'm currently reading the book Zero: The Biography of a Dangerous Idea which is a great and interesting Math's history lesson (here is a good review about it)