A. Was it loose first?
Could she have cracked the tooth?
Did it seem like it had a cavity in it?
It isn't normal for teeth to come out in pieces like that, so you likely should see a pediatric dentist. It may just be that you are seeing her permanent tooth beginning to come through already, although it is a little early for that. The first permanent teeth usually don't come in until a child is 6 to 7 years old.
In fact, it is even a little early for her to lose her first baby tooth. The average age for shedding the first baby teeth is also 6 to 7 years old, although some kids do start losing teeth at age 5.
Another option, if she isn't due for a visit to the dentist, is to see if you can just bring the tooth by your dentist's office and have someone look at it. If they really think that it isn't a whole tooth, then schedule an appointment for your child.
Also see this article on The Tooth Fairy and Losing a First Baby Tooth for more information.
Our guide to dentistry and oral health might also be able to help you further.