PA-12 Instructor pilot reported an engine failure when the training pilot misidentified the mixture control and unintentionally shut down the engine on base leg. The Instructor took control and landed safely; then was able to restart the engine and taxied to the hangar.

Narrative

I was acting as an instructor for a pilot seeking to re-establish landing currency after he had not flown for several months. Our intention was to complete numerous stop-and-go landings while remaining in the traffic pattern. While descending through approximately 500' AGL on base leg on our first approach; the pilot; who was occupying the front control seat; informed me that he had no throttle response. I immediately instructed him to turn directly toward the runway and he requested that I take the controls. I assumed control of the airplane and informed ATC we had lost power and might not be able to clear the runway after landing. Due to the very low altitude I elected to proceed directly to the runway and land rather than to attempt to troubleshoot the loss of power. We landed and rolled out without further incident; I rolled the airplane out to the runway edge to facilitate moving it out of the runway safety area in the event we couldn't taxi on our own power. The pilot informed me that he had pulled the mixture control in error when he intended to pull the carburetor heat resulting in an unintentional engine shutdown. From my position in the back seat; I was not able to see either the mixture or carburetor heat controls and while communicating about control positions and engine indications; the pilot in the front seat continued the mis-identification of the mixture and carburetor heat controls resulting in my inability to detect and correct the error. We successfully restarted the engine and taxiied clear of the runway and returned to the hangar but while accomplishing the engine restart another aircraft had to go around because we had not yet cleared the runway. We accomplished an engine test run-up upon clearing the runway; engine operation was smooth and normal; and a post flight visual inspection of the engine and fuel system did not reveal any abnormalities supporting our suspicion that the cause of the event was entirely pilot error resulting in an inadvertent engine shut-down.