If unhook the starter and remove it. Then using a test light or meter, verify the starter gets power when cranking but not run. Then hook up the starter, with it off the motor and see if it keeps going after you crank...
Or take it out and have autozone or O'Reilly test it and see if it repeats the behavior on their bench. Less hassle that way, maybe. Plus you can teach those kids a thing or two ;)
