How do I stop pop up text message notifications

There is no option to turn this off.

What is available at Settings > Messages is it as far as the available options in regards to messages except for turning the new message alert sound on or off.

I too wish Apple would get with the program and fix this. They spend all their time talking about how "This changes everything. Again" but they can't get text messaging right. It's like they are oblivious to everything around them. No other phone I know of does this without having the ability to turn off for either privacy or just non-intrusiveness. I'm not 12 and I don't think it's cool for everyone around me to know i got a message and who it's from!!! I really wish they'd provide this option. All these new features come out with each new update and they completely neglect things that have been wished for since e beginning. This is just plain ridiculous!!

amen!!