INSTRUCTOR RPT REGARDING SPI WHO HAS RWY EXCURSION ON FIRST SOLO.

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MY STUDENT AND I WENT TO THE PRACTICE AREA AND REVIEWED STALLS AND RETURNED TO REVIEW TFC PATTERN OPS; GAR PROCS; XWIND LNDG TECHNIQUES AND EMER PROCS. AFTER COMPLETING ALL OBJECTIVES AND THE STUDENT CONSISTENTLY MAKING SAFE LNDGS; I MADE HIM DO A FULL STOP AND DROP ME OFF TO COMPLETE HIS FIRST SOLO FLT IN THE PATTERN. I BRIEFED HIM TO DO 3 FULL STOP LNDGS AND TAXI BACK. I REMINDED HIM OF AIRSPD CTL; EMER PROCS AND USING JUDGEMENT ON GAR PROCS IF THE NEED ARISES. I THEN CALLED THE TWR AND ADVISED THEM THAT THIS WAS THE STUDENT'S FIRST SOLO FLT AND GAVE THEM THE NUMBER I COULD BE REACHED AS THE TWR WAS QUITE A DISTANCE AWAY AND UNACCESSIBLE. THE STUDENT THEN PROCEEDED TO COMPLETE HIS SOLO FLT. HIS FIRST LNDG WAS UNEVENTFUL AND HE HAD BACK TAXIED AND TOOK OFF FOR HIS NEXT LNDG. THE LNDG APPEARED TO BE NORMAL; BUT UPON AND SHORTLY AFTER LNDG ON HIS LNDG ROLL; THE PLANE SUDDENLY VEERED OFF TO THE L AND OFF THE RWY BTWN THE PARALLEL TXWY AND RWY 30R. THE STUDENT WAS UNHARMED AND THE ACFT RECEIVED MINOR DAMAGE. THE STUDENT HAD APPROX 24 HRS IN THAT ACFT. WHEN I BRIEFED THE STUDENT ON WHAT HAPPENED; HE DID NOT KNOW. I ASSUME HE HAD INADVERTENTLY HAD HIS FOOT ON THE L BRAKE AND UPON LNDG; VEERED OFF THE RWY. I HAD REPEATEDLY FROM DAY ONE; TAUGHT THE STUDENT TO MAKE SURE HIS HEELS WERE ON THE FLOOR WHEN LNDG. I WILL PUT EVEN MORE EMPHASIS ON STUDENTS TO MAKE SURE THEY CHK TO MAKE SURE THEIR FEET ARE NOT ON THE BRAKES.