I agree with iowajes, but maybe you are talking about different things.
I refer, and did with my kids, the process defined in a book "First National Bank of Dad". Pennies are too small. We gave them $5 per week and paid them 5% interest PER MONTH (yes a 60% annual rate). All money was theirs, sat down with them each month and showed them what they had and what their interest was. The book very clearly says you need to make it meaningful to the child and teach them spending not just compunding. They can buy whatever they want except for things you deem dangerous and unacceptable (read weapons and drugs). Other than that when they want to buy something you shut your parental mouth about if it is worth it and only ask "Do you have enough money in your bank account?" If they do you buy it. If it breaks 5 seconds later they start to learn. It was amazingly effective. You only convert them to stocks at about age 12 (not 7 or 4) when they can wrap their head around it and you still do not invest in anything real, you take whatever they want to buy, divide by 100, and track in a spreadsheet or something. You use the real prices etc. and they learn that side, but again you give them meaningful amounts that they can appreciate.
I've had kids who accumulated $1,000 over a few years that way and that I was paying $50 in monthly interest to, and I had others who were spendypants for a long time and barely got any, but it worked very well. Started them all at age 3 (basically when they start asking "Can I have?" it's time to start) and now at ages 19,16 and 14 they all have a solid grasp on money, much more so than their peers who think its magically printed by fairies under their bed. My 16 year old who has only been working at McDonald's since August, already has $4,000 saved from that. I'm happy with the results (though I agree we converted our son to stocks at age 10 instead of 12, becuase he was milking the interest and $50-$75 in interest a month was getting really hard on dear old Dad.