I did a BA in Political Science in the States, and every single teacher was very concerned about cheating... at the same time they were giving out multiple choice tests/quizzes and assigning small paper assignments which were similar for everyone.
I then did a study abroad program in Holland, where nobody was truly concerned about cheating. Grades were based on group presentation of literature in class, class discussion, an a big final paper who's topic you developed with the teacher (and then presented). Final exams, if they even existed for the course, were long-essay format.
You can't do that with every subject, but there's no reason why your students should be able to text quiz answers to each other or re-use another students paper... there shouldn't be any multi-choice quizzes and papers should be individually developed by students with the teacher.
Needless to say I went back to NL for my next degree.