A C172 Flight Instructor reported a flap malfunction in the pattern while practicing touch and goes.

Narrative

Student was conducting touch and goes on RWY XXR. On 6th takeoff; at approximately 6100 MSL noticed plane was not climbing properly and airspeed was very low. Initially thought it was student technique and gave corrections to lower the nose. Plane did not accelerate appropriately and was barely holding altitude. I noticed the flaps handle was set to zero but the flap indicator was at 20 degrees. I confirmed flaps were not retracted visually while taking the controls from the student. I was able to start a slow climb at about 100 fpm. Airspeed was fluctuatiing between 50 and 60 knots. I notified Tower I had a flap malfunction and needed an immediate return. Tower asked if I needed further assistance. I requested priority handling and advised that I was going to start a gradual turn back to Runway XYR. At this time I was approximately 6300 MSL. Checked the fuse for flaps and it was not out. I was able to complete the turn and successfully land on XYR. Taxied to parking without incident. Upon inspection on the ground; discovered that the flap switch worked to extend the flaps but not retract the flaps. I notified our maintenance staff and downed the aircraft.The problem was caused by some type of mechanical failure of flap system causing the flaps to only retract to 20 degrees. Contributing factors include low level up and down drafts caused by turbulence and a density altitude that limited the aircraft's ability to climb. In the future; I will ensure my students verify flap position by both the switch position and indicator position. I will also add a visual scan of the flaps before starting the departure roll on touch and goes.