Hi Eileen,
I believe you would have to control that through security groups. I'm not seeing an "edit contact fields" permission under Action Permissions, but you can restrict their ability to access Fields and Views from Setup as well as accessing individual contact records through Interface Access. That isn't that great, though, as I understand you would ideally like for them to be able to view, not edit. I'll be interested to see if someone else comes up with a better answer!
Hope this at least gets the wheels turning.