Saving is important - but saving without purpose is just a notch better than spending without thinking.
Talk with your kids about how you are planning to spend your savings. It could be for their tuition fees, their new dress, next summer's vacation, or whichever ways you prepare for the money you are keeping.
Then ask them how they look forward to using their own savings and what their time table is. If their plan is unrealistic, try to explain to them that their money will not be enough for their goal so they either set aside more from their allowance or they save for a longer period of time.
If ever you think that their target is unimportant, suggest to them other essential and interesting things on which they can spend their money. With regard to spending decisions, you still know better than them.