A wonderful article on Futurity. The authors investigated whether children learn algebra better when:
Physically moving magnetic numbers on a white board.
Pretending to move the numbers by going through the motions.
Pointing at the relevant terms and the unknown quantity.
Any guess which one won?
To my surprise it was 3. I guessed 1.
In method 3 the children were taught to spot the number that appears on both sides of the equation (9 above) and then point to the other two (4 and 5 above) while also pointing at the unknown (x).
Method 3 seems to give children a more generalised understanding of the problem whereas 1 and 2 perform quite well so long as the form of the equations doesn't change too much.