Cessna 172 Flight Instructor reported a trailing edge flap failure resulting in a flap asymmetry condition during stall recovery training. The Instructor immediately assumed control and returned to the departure airport.

Narrative

I was instructing my student on slow flight and stall recovery which involves operating the aircraft with flaps deployed and within the white airspeed arc of the flap operating range. My student retracted the flaps when we heard a loud bang off the left side of the aircraft and shortly thereafter the aircraft began rolling to the right. I took over the controls which required full left aileron control yoke input as well as moderate right rudder inputs to remain at level flight; as well as near full power to maintain altitude. I turned direct to ZZZ at this point.After stabilizing the aircraft I looked outside and saw the left flap was fully deployed and the right flap was fully retracted at this point I determined the airplane had an asymmetrical flap failure. I tried retracting the flaps again; I could hear the flap motor engaging but the left flap remained down. I then attempted to put the flaps down and the right flap then deployed; bringing the flaps back into a symmetrical position however the aircraft remained without the capability to symmetrically retract flaps. I was over ZZZ at this point and continued to ZZZ1 which was our point of origin. The rest of the flight was uneventful and I made a normal landing at ZZZ1 with no aircraft damage or injury to aircraft occupants.