Random thoughts of an ed admin lifer

With the ease of cutting and pasting material from the internet, we are continuously dealing with incidents of plagiarism.  Sometimes it is so blatant that it can be proven by  simply entering the suspected phrase into a search engine.  The more difficult to deal with scenario is that which cannot be proven.  We have built processes into the writing/research process aimed at educating students about the issue and proper citation methods.  We have even gone so far as creating steps that make it difficult for students to cut and paste info (including jot notes, first drafts etc.) and pass it off as their own.  In spite of these efforts, some students still insist on plagiarizing.  A couple of questions come to mind . . . 1.  What more can we do to curtail this sort of behaviour? & 2.  If this truly is a behaviour issue, is it appropriate to grade a plagiarized paper with a mark of 0?  Thoughts???