I believe children should be involved when they understand the concept of adding, subtracting, and saving. However, there is a point where a parent can stress a child’s emotional state; causing the child or teenager to resist asking for anything needed and may result in an ulcer. This may also cause the child to feel like they have to take on the adult responsibility of helping with the finances.
I don’t think there is anything wrong with having the child help subtract their parent’s checking withdraws and adding the deposits in the register. They may not understand the concept of not having the money to spend on something they want if the parent(s) still have money in the account after balancing the checkbook. This is where trying to explain the difference between wants, needs and goals for saving for something in the future comes in. Just because there is money in the account doesn't mean the money is available to spend.
If the child has their own savings account, this helps. An allowance helps the young realize, once they spend their money, it’s gone until the next allowance time.
Starting out small with the younger and then when they are a teenager bringing them into the family finances without emphasizing that they are responsible for more than they should be. Teenagers have enough stressful situations to deal with in their everyday events. It is the parents’ responsibility to get them ready for being able to take care of themselves; finances plays a huge part in their future and parents are their first and over all biggest remodel.