TRACON Controller reported aircraft on departure turned towards area of higher terrain when assigned runway heading. The Student Air Traffic Controller vectored the aircraft away from the higher terrain resulting with the aircraft returning to their flight plan.

Narrative

Aircraft checked on with departure from tower after takeoff. The aircraft's clearance was to fly Runway heading and expect vectors to first fix. After checking in the aircraft began a left turn into higher terrain. My trainee caught the turn and issued a vector towards lower terrain. Due to other aircraft and data tag overlap the student thought the aircraft was above current MVA and believed him to be inside the DVA as well. I could not read data tags due to overlap and focal distance from where the instructor must sit. Instructors do not have a close; clear or unobstructed view from where they must sit when giving instruction at this position. I felt the student had a good and prompt catch on the pilot deviation and gave prompt instructions for recovery. After learning the aircrafts altitude during playback; we all agree a Local Airport Advisory (LAA) should have been given as well.Suggestion: We have multiple pilot deviations each year by pilots turning on course into higher terrain here. These are usually due to pilots missing the clearance to fly runway heading on initial departure on their ADC. Since this is a recurring item either the ADC system should show initial headings more prominently or we should be using a SID instead of an initial heading.