My niece was having trouble with math (she was in 3rd grade, now 4th), and her mother asked me to help out. One "problem" was that she still used her fingers for math problems. Her mother wasn't too pleased when I encouraged her to continue with this - use the tools you've got at hand, so to speak... Anyway, the trick was, as I saw it, to let her use her fingers, just make the problems more difficult, so you've got to be creative.
To put this in perspective, I have a doctorate in physics, but I still use my fingers regularly when solving cross products, just to see the right-hand rule. I almost always wrap my fingers around when doing E&M problems to figure out how the magnetic field will affect things, etc. This is common in physics, we see it all the time. I see no reason a grade school student can't use the same tools.
Anyway, now she's in 4th grade, and we play a game called Nemo. Here's how it goes: Take toothpicks, as many as you want. Make an arbitrary number of piles of toothpicks, with as many as you'd like in each pile (hopefully none more than 31, or you'll need both hands for the solution). On your turn, you may remove as many toothpicks as you would like, but only from a single pile. The winner is the person to pick up the last toothpick.
Now, if you're good enough at math, adding and multiplying by 2, you can solve the problem right from the beginning, ang guarantee a win. Here's how: For each pile, figure out how many toothpicks are in the pile, and break it down into powers of 2. For instance, a pile with 19 toothpicks would be 16 + 2 + 1, or 2^4 + 2^1 + 2^0. Now, let each finger on your hand represent one of the powers of two - we usually let the thumb be 0, and the pinky 4. Put down each finger represented in that sum. Now move to the next pile, and do the same thing. Only, this time, when you're moving your fingers, put it down if it was up, and up if it was down. For instance, say our second pile has 7 toothpicks, or 4 + 2 + 1, or 2^2 + 2^1 + 2^0. Then, our thumb and index finger, which were down, go back up, and our middle finger, which was up, goes down. Continue this until you have "done" every pile this way.
If all your fingers are up, and it is your turn, you will lose unless your opponent makes a mistake. Period. If you have any fingers down, you will be able to win. To figure out your move, do the calculation again, excluding the largest group. See which fingers you have down, and use the sum above. That's how many you want to leave in the largest group. So, using the above examples, where we had 19 and 7, we would just do the 7 - leaving out first 3 fingers down. Adding them up leaves 7 (this is a simple example, we usually play with 5-20 piles), so that's how many we want to leave. We remove 12 from the larger pile, leaving 7, and will win the game. In future turns, you always want to leave your opponent with the symmetric solution (all fingers up.) At some point, he will have to leave you with all the toothpicks in 1 pile, which you then pick up and claim victory.
This makes heavy use of your fingers for doing the math, but you can't just count. My niece plays quite well, and she's also doing great in math now, since she gets so much practice. So don't knock using your fingers...
Drew Garrett