PROPS DAMAGED DURING TRAINING WHEN TOUCH-AND-GO WAS MADE WITH LNDG GEAR UP.

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AN INADVERTENT PROP STRIKE WHILE I WAS CONDUCTING A MULTI-ENG TRAINING FLT. THE STUDENT; TRAINING FOR A MULTI-ENG LAND RATING; AND I WERE PRACTICING ENG FAILURE EMER PROCS AND SINGLE ENG APCHS AT A LCL NON TWR ARPT. MY NORMAL PROC FOR FLYING AND INSTRUCTING IN THESE TYPES OF SITS IS TO DO A COMPLETE 'BEFORE LNDG CHKLIST' PROC ABEAM THE TOUCHDOWN POINT. THE REASON FOR THIS IS I WANT THE STUDENT TO PUT THE LNDG GEAR IN THE DOWN POS AT THE NORMAL POINT IN THE APCH; REGARDLESS OF WHETHER IT IS A 1 ENG OUT EMER OR A NORMAL 2 ENG APCH. THIS IS WHAT I HAD INSTRUCTED THE STUDENT TO DO DURING GND INSTRUCTION AND DURING PRIOR FLT INSTRUCTION. ON THIS PARTICULAR CIRCUIT; THE STUDENT HAD HESITATED DURING HIS ENG FAILURE CHKLIST AND WAS HAVING TROUBLE MAINTAINING HIS ALT AND AIRSPD. HE WAS OVERLOADING HIMSELF AND BECOMING FRUSTRATED. BECAUSE OF THIS; HE FORGOT TO DO HIS CHKLIST PROCS (BEFORE LNDG); AND HE FORGOT TO PUT HIS LNDG GEAR DOWN ABEAM THE LNDG POINT. THIS IS A NORMAL OCCURRENCE IN NEW MULTI-ENG STUDENTS AND HAD OCCURRED ON PRIOR FLTS WITH THIS STUDENT. UNTIL THIS POINT I HAD PROMPTED THE STUDENT TO GO THROUGH HIS BEFORE LNDG CHKLIST AT THE NORMAL TIME -- BEFORE OR ABEAM THE LNDG POINT. THE NORMAL REPLY TO MY PROMPTING IS USUALLY ALONG THE LINES OF 'I WAS JUST GETTING READY TO' OR 'I WAS WAITING UNTIL I WAS LINED UP ON FINAL.' THE PROB WITH THESE REPLIES ARE: 1) I DON'T KNOW FOR SURE IF THEY WERE ACTUALLY 'JUST GETTING READY TO;' OR HAD FORGOTTEN THE CHKLIST; AND 2) IF THEY WERE WAITING UNTIL FINAL TO DO THE CHKLIST; I WANT THEM TO UNDERSTAND WHY THAT IS NOT A GOOD IDEA. IN THIS PARTICULAR PATTERN; THE STUDENT FORGOT TO PUT THE LNDG GEAR DOWN. I DECIDED TO LET HIM CONTINUE. AS WE TURNED FINAL; THE STUDENT OVERSHOT SLIGHTLY AND WAS HAVING DIFFICULTIES WITH OVERCTLING AND AIRSPD STABILIZATION. THE STUDENT HAD BEEN HAVING DIFFICULTIES WITH THIS BEFORE; AND I BEGAN COACHING HIM ON STABILIZING HIS CTL AND AIRSPD. BY THE TIME WE CROSSED THE THRESHOLD THE AIRPLANE WAS STABILIZED AND THE STUDENT BEGAN A VERY HIGH FLARE. THE AIRSPD BEGAN TO DECREASE AND AT THIS TIME I TOOK CTL OF THE ACFT AND BEGAN TO INITIATE THE GAR. THE AIRPLANE BEGAN TO SINK AS I ADDED FULL PWR. A THUD WAS HEARD AND THE AIRPLANE BEGAN A NORMAL CLBOUT. I FLEW A NORMAL PATTERN AND LANDED WITHOUT FURTHER INCIDENT. UPON ENG SHUTDOWN IT WAS APPARENT THAT A DUAL PROP STRIKE HAD TAKEN PLACE. I BELIEVE THE CONTRIBUTING FACTORS WHICH LED TO THIS SIT WERE: 1) THE HIGH FLARE; 2) THE HIGH DENSITY ALT WHICH RESULTED IN A DELAYED RESPONSE OF ENG PWR; AND FINALLY AND MOST IMPORTANTLY; 3) MY FAILURE TO INITIATE THE GAR IN A TIMELY MANNER. I BELIEVE THAT IF I HAD INITIATED THE GAR A LITTLE SOONER; THIS SIT WOULD HAVE BEEN AVOIDABLE. I ALSO SHOULD HAVE ANTICIPATED THE STUDENT'S HIGH FLARE AND REACTED TO IT SOONER. FINALLY; THE DENSITY ALT SHOULD HAVE BEEN BETTER TAKEN INTO ACCOUNT AND FURTHER MOVED MY POSITIVE CTL AND GAR. THE STUDENT LEARNED A VALUABLE LESSON; AS DID I. WHAT I HAVE LEARNED FROM THIS; AND MY ADVICE TO OTHER INSTRUCTORS; IS TO NOT ALLOW A SIMULATED EMER TO TURN INTO A REAL ONE. STAY AHEAD OF THE AIRPLANE. TRY TO ANTICIPATE THE STUDENT'S ACTIONS; AND ALWAYS LEAVE YOURSELF AN OUT.