Skylane 182/RG Turbo Skylane/RG
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 6
Situational Awareness
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Became Reoriented
Airspace Structure; Human Factors; Procedure
Aircraft X was released local IFR to ZZZ on the SID. They wanted to go direct to the Initial Approach Fix; but with their rate of climb I told them I would have to vector them onto the approach; as they would be past the fix before at an appropriate altitude. Once they reached the Minimum Vectoring Altitude I gave them a vector to join the approach and an altitude of 5;000 feet. This was a Student Pilot and in order to not overwhelm them; I asked them to join the approach and report established. Aircraft X flew through final and into a 6000 foot Minimum Vectoring Altitude that was less than a mile from the final approach course. I issued them a low altitude alert; a higher altitude and a turn. They were very slow to respond and I knew it was a student with an instructor; so I then asked of they could maintain their own terrain and obstruction clearance through 6000 feet feet. They said they could; then very shortly after cancelled IFR and continued the rest of their flight training under VFR conditions.The only recommendation I can imagine would be to have instructors in this flight school take over and join the approach. I assume the instructor didn't realize letting the student mess up the approach would put them in a higher Minimum Vectoring Altitude.
A TRACON Controller reported a student pilot flew through the final approach course and below the Minimum Vectoring Altitude.