You cannot prevent students from editing Discussion posts on a course-by-course basis, but instructors can see an edit history for discussion posts.

In the Grid View:

1. Go to Discussions.
2. Select the title of the discussion topic.
3. Select the title of the student's post.
4. Select More Actions.
5. Select History.

In the Reading View:

1. Go to Discussions.
2. Select the title of the discussion topic.
3. Select the dropdown arrow next to the title of the students' post. 
4. Select View Post History.

Please note: You can modify your Discussion display settings by selecting the Settings gear icon in the upper right corner of the Discussions area.