Cessna instructor pilot reported becoming confused while conducting an instrument approach.

Narrative:

I was conducting an IFR training flight with my foreign student under IFR. When we briefed the flight we agreed on flying to kcrq (VOR-a approach) and then back to [the origin airport]. We requested VOR - a to kcrq but were given ILS 24; first approach went very good with a few mistakes made by the student not staying on course which I corrected right away. When we were flying missed I had to take over to make sure we were flying to oceanside VOR. While I was flying the student was talking to ATC. We got cleared to oceanside VOR and cleared for VOR a approach. At this point in my mind I am expecting a VOR-a to palomar just as we planned on the ground. The student was in communication with ATC. I was flying the airplane when the student received the clearance for VOR-a to oceanside airport. That is when I missed vital info. I've heard that we are cleared for VOR-a but it wasn't to palomar; it was to oceanside airport. That is the part that I missed while I was flying in IMC.we loaded the approach into our GPS and flown it. During the approach the student was using VOR-a plate for the oceanside; I was using VOR-a to palomar; also the approach loaded to GPS was also to palomar. The student spoke up after crossing ocn VOR that our course should be 096 and I pointed to the GPS and onto my approach plate that it should be 119. The student agreed and we kept on flying. Once we got out of IMC and started looking for the airport; the student exclaimed: we gotta go missed! And that's when I looked at the approach plate that he had pulled up and I asked him: which approach you got on there? VOR-a to kokb. I told him go missed and call approach. When we called approach that's when a terrifying realization came in that we flown an approach which we were not cleared for.this incident could have been prevented in many ways. To prevent this situation from happening in the future; I will always file a flight plan; that way it will be clear between me and ATC what the plan is. Second is I should be in charge of communications; I let my confidence in the student go too far. He is a good pilot but I shouldn't have treated him with less caution. Third is that when he was briefing the approach I didn't understand much of what he said due to his accent. And I was flying in IMC which had most of my attention. Fourth is that when we were given a frequency change I could have kept monitoring approach frequency on comm 2 just in case.

Original NASA ASRS Text

Title: Cessna instructor pilot reported becoming confused while conducting an instrument approach.

Narrative: I was conducting an IFR training flight with my foreign student under IFR. When we briefed the flight we agreed on flying to KCRQ (VOR-A approach) and then back to [the origin airport]. We requested VOR - A to KCRQ but were given ILS 24; first approach went very good with a few mistakes made by the student not staying on course which I corrected right away. When we were flying missed I had to take over to make sure we were flying to Oceanside VOR. While I was flying the student was talking to ATC. We got cleared to Oceanside VOR and cleared for VOR A approach. At this point in my mind I am expecting a VOR-A to Palomar just as we planned on the ground. The student was in communication with ATC. I was flying the airplane when the student received the clearance For VOR-A to Oceanside airport. That is when I missed vital info. I've heard that we are cleared for VOR-A but it wasn't to Palomar; it was to Oceanside airport. That is the part that I missed while I was flying in IMC.We loaded the approach into our GPS and Flown it. During the approach the student was using VOR-A plate for the Oceanside; I was using VOR-A to Palomar; also the approach loaded to GPS was also to Palomar. The student spoke up after crossing OCN VOR that our course should be 096 and I pointed to the GPS and onto my approach plate that it should be 119. The student agreed and we kept on flying. Once we got out of IMC and started looking for the airport; the student exclaimed: we gotta go missed! And that's when I looked at the approach plate that he had pulled up and I asked him: which approach you got on there? VOR-A to KOKB. I told him Go missed and call approach. When we called Approach that's when a terrifying realization came in that we flown an approach which we were not cleared for.This incident could have been prevented in many ways. To prevent this situation from happening in the future; I will always file a flight plan; that way it will be clear between me and ATC what the plan is. Second is I should be in charge of communications; I let my confidence in the student go too far. He is a good pilot but I shouldn't have treated him with less caution. Third is that when he was briefing the approach I didn't understand much of what he said due to his accent. And I was flying in IMC which had most of my attention. Fourth is that when we were given a frequency change I could have kept monitoring approach frequency on comm 2 just in case.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1574606
Time
Date	201809
Local Time Of Day	1801-2400
Place
Locale Reference	SCT.TRACON
State Reference	CA
Environment
Flight Conditions	IMC
Light	Daylight
Aircraft 1
Make Model Name	Cessna Aircraft Undifferentiated or Other Model
Operating Under FAR Part	Part 91
Flight Phase	Initial Approach
Route In Use	Other Cleared for VOR-A
Flight Plan	IFR
Person 1
Function	Instructor Pilot Flying
Qualification	Flight Crew Commercial Flight Crew Flight Instructor Flight Crew Instrument
Experience	Flight Crew Last 90 Days 182 Flight Crew Total 1007 Flight Crew Type 554
Events
Anomaly	Deviation - Procedural Clearance Deviation - Procedural Published Material / Policy