So many of us learn to ace the test without thinking of everyday applications for the things we learn. Isn't it a sign that we should change the way we teach? Remove the notion that math is the same as learning to do sample problems or calculating answers. Maths should be about solving problems, turning an unknown problem into a known one, thinking what data you need instead of having it supplied on a plate. Maths should be about tricks like the ones the "mathemagician" used to break down the problem into manageable chunks.
Not many Western schools teach the Vedic Maths of simplifying calculations, for example, and yet there is something inherently beautiful about the fact that the square of a two-digit number that end in 5 is always the product of the first digit and one more than the first digit, followed by 25. For example, the square of 75 is (7x8) followed by 25, or 5625.
Or the trick for multiplying by 11 (see tutorial 6). This is not calculating - this is playing with patterns.
In another excellent video clip, Dan Meyer suggests how to make maths problems more challenging and more fun for our students. TV has trained us that any problem can be solved “in 22 minutes, with three commercial breaks and a laugh track”, and his dream is to teach a patient way of solving problems.
For sure, not every learning style is suited to patient problem solving. Not every student will have a natural ability to perform complex calculations in their heads. But if these ideas improve the school experience for even one student, they are worth trying.