Over 70 years ago in Manchester, New Hampshire, children learnt no formal arithmetic until grade 6 (about age 11). In the fall of 1929, The program's creator, Superintendent Louis Benezet, decided to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - "my new Three R's," as he called it. "And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language.
"In the first place, it seems to me that we waste much time in the elementary schools, wrestling with stuff that ought to be omitted or postponed until the children are in need of studying it. If I had my way, I would omit arithmetic from the first six grades. I would allow the children to practise making change with imitation money, if you wish, but outside of making change, where does an eleven-year-old child ever have to use arithmetic?
I feel that it is all nonsense to take eight years to get children thru the ordinary arithmetic assignment of the elementary schools. What possible needs has a ten-year-old child for a knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years' study by any normal child."
Benezet picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade. To read more about what happened go to the following link:
http://www.inference.phy.cam.ac.uk/sanjoy/benezet/index.html (a three part essay).
In brief, the results were that kids who had no formal math ended up much more knowledgeable about math concepts (measurements, estimations, logic etc) then those who were forced to learn say multiplication tables, etc with no context. Since the teachers focused on reading, discussion, story telling etc the kids ended up being more articulate, more engaged and eager for learning than their counterparts following traditional curriculum.
Today, those of us who follow the unschool route, can attest to the success of this method. My oldest daughter started school this pass fall in grade 8 for the first time ever,and she gets nothing but the highest marks. She had very little formal math instruction. My 11 year old who also started in the fall in grade 6 insists that she doesn't have a brain for math (meaning she is simply not interested in math at this time) but is managing to keep up.
Kids need less math instruction, not more. In the mean time, I think showing kids the beauty of math rather than the utter dryness of computing would be vastly more beneficial to the appreciation and understanding of the subject mathematics.