Our family does not pay our children to do things that we feel are part of being family. Chores and helping are what makes our home run smoothly, these tasks are expected. We feel paying them for these tasks is teaching them to always be looking for what they can get out of doing something.
An allowance is giving them a set amount of money each week sometimes based on something, sometimes not. We do not feel our children need an allowance, neither free money or as a way to learn to manage money.
As our children get old enough to earn money (babysitting, helping neighbors, a job, or even gifts) then we teach them how to manage that money. Our family has set up a 10% goes to tithe while the rest is divided 50% to savings and 50% to spending money. Although our children then have "spending money" we still talk through their spending with them and try to get them to think before spending.
Again I want to point out that this is not a right/wrong, should/shouldn't matter. The Bible says we are to train our children in the way they should go, so this is a matter of us as a family deciding how we can best train our children in the matter of money management.