How Do I Wean A Zebra Finch?

I have two adult zebra finches, the female laid a clutch of eggs. They hatched at around February 19th. Everything was going well, they came out of the nest at normal times and such. I have, what I think is a problem. The mother has laid a new clutch of eggs and stopped feeding the other birds. The birds are a little over a month old and I read that they begin to eat solid food around then. The babies will ask for food from the mom or dad and the parents will fly away and the babies would go and eat some solid food. But now when the parents wont give them food, one of their brothers or sisters will feed them. I didn't know fledglings could feed other fledglings. Is this normal? Should I be concerned? What should I do if there is a problem.