Where have you assigned the user the role of student? If you do it in users>permissions>assign system roles then the student will be able to edit the front page
. Do not assign them the role of student that way. Make a course and add them into the course admin block of that course. Also, if you check site admin>front page>front page roles and make sure your default front page role is none (not student or teacher). These are possible reasons why your student can see the front page editing button.