STUDENT PLT DURING TOUCH AND GO LNDG LOST CTL OF ACFT. LEFT RWY AND BROKE NOSE GEAR.

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I TOOK OFF FINE AND CLBED OUT AT ABOUT 70 KTS. AS I WAS CLBING OUT I HEARD AN ACFT CALL OUT HIS POS AS BEING ON R BASE FOR RWY 18. I THOUGHT THIS WAS ODD SINCE IT WAS SUPPOSED TO BE A L HAND TFC PATTERN. SINCE I WAS ON THE XWIND LEG AT THE TIME I KNEW THE GUY WOULD BE CLR OF THE RWY BY THE TIME I GOT AROUND TO LNDG. I CLBED UP TO ABOUT 1200 FT AND TURNED BY L DOWNWIND LEG. I BEGAN A SLOW; DSNDING APCH TO LAND. I TURNED BASE AT ABOUT 1000 FT AND 65-70 KTS. I WENT TO 20 DEGS OF FLAPS AND RADIOED MY POS. I TURNED ABOUT A 2 MI FINAL APCH AT ABOUT 900 FT AND 65- 70 KTS. I CHKED MY INSTRUMENTS AND EVERYTHING LOOKED GOOD. I CHKED THE VASI LIGHTS AND NOTICED THAT I WAS A LITTLE HIGH (WHITE OVER WHITE); SO I DECREASED THE THROTTLE BACK TO ABOUT 1500 RPM; WENT TO 30 DEGS OF FLAPS AND LOWERED THE NOSE TO KEEP MY SPD AT ABOUT 65 KTS. I KEPT ON COMING DOWN AND INTERCEPTED THE GLIDE SLOPE ABOUT 300 YARDS FROM THE FENCE. AS I CONTINUED DOWN I NOTICED THAT MY NOSE WAS NOT DIRECTLY IN THE CTR OF THE RWY; SO I ADDED SOME MORE R RUDDER TO STRAIGHTEN THE NOSE. I WAS RIGHT DOWN THE CTR OF THE RWY AT ABOUT 60 KTS AS I CAME OVER THE FENCE. I KEPT COMING DOWN; FLARED; AND LANDED ABOUT 30 YARDS PAST THE NUMBERS. SINCE THIS WAS GOING TO BE A TOUCH AND GO LNDG; I IMMEDIATELY CLEANED UP THE CTLS (CARB HEAT COLD; FLAPS UP); POSITIONED THE AILERONS FOR A XWIND TKOF; AND ADDED FULL PWR. THE NEXT THING I KNOW; THE PLANE VEERED TO THE L. I TRIED TO GET THE ACFT BACK ON THE RWY BUT I WAS GOING TOO FAST; BTWN 45-50 KTS. I WENT OFF THE RWY INTO THE GRASS. WHEN I HIT THE GRASS I PULLED THE THROTTLE BACK AND BEGAN TO APPLY THE BRAKES. IT FELT LIKE I WAS SKIDDING ACROSS THE WET GRASS. I KEPT ROLLING AND HIT A TROUGH IN THE GND; WHICH CAUSED THE PLANE TO BOUNCE. WHEN I BOUNCED I FELT THE FRONT LNDG GEAR GO DOWN AND THAT'S WHEN THE PLANE WENT NOSE FIRST INTO THE GND. AFTER I GATHERED MY SENSES I CUT OFF ALL ELECTRICAL EQUIP AND GOT OUT OF THE ACFT. I AM STILL NOT SURE WHAT THE CAUSE OF THIS INCIDENT WAS.