Does this happen only with group texts or all texts? Is it a pop-up window that is displayed or does the text message, when received, automatically take you into the messaging app?
In most cases, you'll see a notification with a preview of the text message. Pull down on the message (in the notification shade) and it will display the whole message, but in the notification shade not open the app unless you click it.
Provide us with a little more detail (stock messaging app?) and we'll try and help problem solve.