Yes, but only with parental consent.
Kids and teens can set up their own log-in credentials (separate from the adult’s) so they can see how their stocks are doing anytime they want, without bugging mom or dad. They can also place stock trades with the adult’s consent.
For example, if a teen wants to buy $20 of Facebook stock, he sets up the transaction, which is routed by email to mom for approval. If mom approves, the trade goes to market and executes. Otherwise (you guessed it), it doesn't.