A TRNEE PLT IN A TWIN SMA HIT HIS L PROP ON THE RWY ON TKOF.

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LNDG GEAR RETRACTED ON TKOF. HIT L PROP TIP. RETURNED TO ARPT. SUPPLEMENTAL INFORMATION FROM ACN 252412: WE COMPLETED THE BEFORE TKOF CHKLIST AND TAXIED ONTO THE RWY. AS THE STUDENT BROUGHT THE THROTTLES FORWARD FOR THE TKOF; I WAS CALLING OFF SOME OF THE NUMBERS HE HAD NOT COMMITTED TO MEMORY YET. JUST AS WE REACHED ROTATION SPD; HE RAISED THE NOSE AND FOR NO EXPLAINABLE REASON; HE REACHED DOWN AND RAISED THE GEAR AT THE SAME TIME. THE L PROP HIT THE RWY AND AS THE AIRPLANE STARTED TO YAW AND ROLL L; HE YANKED BACK ON THE YOKE TO TRY AND CLB. I TOOK CTL OF THE AIRPLANE TO STRAIGHTEN IT OUT AND WHILE I'M DOING IT; THE STUDENT REDUCED BOTH THROTTLES TO IDLE IN AN ATTEMPT TO ABORT. I MADE THE DECISION THAT ABORTING IN THIS PARTICULAR SIT WAS NOT THE BEST CHOICE; SO I REAPPLIED FULL PWR AND LOWERED THE NOSE TO NORMAL CLB ATTITUDE. MY DECISION NOT TO ABORT WAS BASED ON SEVERAL FACTORS. ONE WAS THE RATHER RADICAL ATTITUDE OF THE AIRPLANE. ANOTHER WAS THE POS OF THE AIRPLANE RELATIVE TO THE ARPT. THE OTHER 2 WERE THE AIRSPD WHICH WAS AT SINGLE ENG SAFE SPD AND THE PWR INDICATIONS WHICH WERE ALL NORMAL. AT THIS POINT THE AIRPLANE WAS HANDLING OK SO MY NEXT DECISION WAS TO FEATHER OR NOT FEATHER THE L ENG. I DECIDED NOT TO FEATHER BASED ON THE HANDLING CHARACTERISTICS. I WAS ABLE TO CLB; BRING THE AIRPLANE BACK AROUND FOR LNDG ON THE RWY. THE ONLY DAMAGE FOUND WAS TO THE L PROP. ALL 3 BLADES WERE BENT APPROX 90 DEGS AT A POINT ABOUT 25 PERCENT INBOARD FROM THE TIP. IT IS BECAUSE OF INCIDENTS EXACTLY LIKE THIS ONE THAT I DO NOT DO TOUCH-AND-GO LNDGS. IN DISCUSSING THIS WITH THE PLT; AFTER THE FACT; HE WAS AT A TOTAL LOSS AS TO WHY HE DID WHAT HE DID.