Monitoring as in tracking your child or monitoring as in seeing everything they do on the phone itself? There are apps you can use to track your child's iPhone (yours too, if it's lost or stolen) that can show you where they're at (provided they're carrying their phone in the first place).
There aren't any app store apps that will give you the functionality to see what your child does on the iPhone itself -- those apps are invasive to the OS and Apple does not approve apps like that.
If you jailbreak, however, there is probably a tweak you can buy or download to monitor what they're actually doing on the phone.
yes, I mean if I jailbreak is there a program you guys would recommend? We are just getting the iphone for her and are concerned about a boy that has been harrassing her and she won't tell us most of the time so we would like to monitor it for a while to be sure it has stopped!
TightVNC and RealVNC wouldn't let you read her texts, unless she had her messages app open while you were remotely spying on her phone, which isn't likely, especially if you're trying to spy on her texts with one specific person.
Rather than spying on her, you should just talk to your child to make sure she's okay, or you could report the kid who's bothering her to her school's guidance counselor.