What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
(-23) After landing on a touch and go, the pilot (the student in the left seat) was holding back pressure on the control wheel allowing the gear to retract when he touched the gear handle while reaching for the carburetor heat. The nose landing gear began to retract, causing the prop to strike the runway. The yoke was pulled back and the gear handle was placed back in the down position, causing the nose gear to extend back down. The pilot was cleaning up the airplane for take-off during his complex aircraft check-out that that included a series of touch-and-go landings. It appears that the pilot accidentally touched the gear handle before pushing in the carb heat. The handle may not have been in the downlock detent position which would have allowed it to easily go to a partial up position.
As the FAA filed it
(-23) AFTER LANDING ON A TOUCH AND GO, THE PILOT (THE STUDENT IN THE LEFT SEAT) WAS HOLDING BACK PRESSURE ON THE CONTROL WHEEL ALLOWING THE GEAR TO RETRACT WHEN HE TOUCHED THE GEAR HANDLE WHILE REACHING FOR THE CARBURETOR HEAT. THE NOSE LANDING GEAR BEGAN TO RETRACT, CAUSING THE PROP TO STRIKE THE RUNWAY. THE YOKE WAS PULLED BACK AND THE GEAR HANDLE WAS PLACED BACK IN THE DOWN POSITION, CAUSING THE NOSE GEAR TO EXTEND BACK DOWN. THE PILOT WAS CLEANING UP THE AIRPLANE FOR TAKE-OFF DURING HIS COMPLEX AIRCRAFT CHECK-OUT THAT THAT INCLUDED A SERIES OF TOUCH-AND-GO LANDINGS. IT APPEARS THAT THE PILOT ACCIDENTALLY TOUCHED THE GEAR HANDLE BEFORE PUSHING IN THE CARB HEAT. THE HANDLE MAY NOT HAVE BEEN IN THE DOWNLOCK DETENT POSITION WHICH WOULD HAVE ALLOWED IT TO EASILY GO TO A PARTIAL UP POSITION.