I saw a really cool presentation by a fellow named John Mighton, who is a successful playwright as well as mathematician. He founded the JUMPMath program - a way that you can teach math to everyone. The way he does it is not complicated, but the results are incredible.
Case study: A grade 4 class. Their average and standard deviation on a standardized math test were 66 and 12. Such a high standard deviation essentially meant that the level of math ability spanned 3-4 grade-levels among the students. After doing JUMP for a year, the class took the next year standardized test, and had an average of 98, sd. 1.2 ...and some of the children in the class had previously been classified as learning-disable (in fact, he has taught fractions to kids who, weeks prior, couldn't count by twos on their fingers).
He has consistently repeated these kinds of results with other classes, and is training teachers to use these methods too. Many thoughts come to mind on this topic:
Some school boards have actually banned JUMP. One of the main principles of JUMP is that everyone can learn to do math well and understand it. Modern-day schooling supports the idea that some people just "aren't as good" as others in math. The truth is that they just aren't as comfortable with the way it's being taught, or even that very early on they had a bad experience (or bad teacher) and have distrusted math ever since. Anyway, apparently school boards don't like the idea that everyone could succeed.
What if everyone succeeded? JUMP can teach the material far faster than our present system manages to not teach the material — at this rate, students could be doing calculus by grade 8.... and loving it. That's the thing — one of the reasons the JUMP philosophy is so successful is that it makes kids enjoy math. Just imagine if students could learn so much more math by the time they reach high school? What about other subjects? Doesn't it seem like all of us have been (and are being) cheated out of an education we could have easily had?
What are tests for? Mighton suggests that tests should still be used in math, but that everyone should gets As. The test should be a test not of a student's "ability", but of the success of the education system in teaching the student! After all, JUMP has proven empirically thateveryone can learn math well. How then, can we still pretend that failing grades in elementary school represent a failure of the student?