C172 INSTRUCTOR AND STUDENT HAVE AN NMAC IN THE PATTERN AT SBP.

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STUDENT FLEW A NON STABILIZED APCH; RESULTING IN A CONSIDERABLE BOUNCE ON TOUCHDOWN. I INDICATED THE NEED FOR A GAR AND THE STUDENT INITIATED A GAR. DURING THE GAR; THE STUDENT PLACED THE AIRPLANE IN A NOSE-HIGH; LOW AIRSPD SITUATION; WHICH WAS MY PRIMARY CONCERN FOR A MOMENT. DURING THIS TIME; THE STUDENT RADIOED THE TWR INDICATING OUR GAR. THE TWR CTLR'S RESPONSE WAS '(ACFT 1 CALL SIGN); (UNINTELLIGIBLE).' THE UNINTELLIGIBLE PORTION OF THE CALL WAS MAYBE 2 WORDS AT MOST; SO I ASSUME IT WAS SIMPLY ACKNOWLEDGMENT. AS THE STUDENT CLBED THROUGH 800 FT MSL (600 FT AGL); HE TURNED XWIND AS IS THE STANDARD PROC I TEACH. ESTABLISHED ON XWIND AND LEVELING AT 1200 FT; TWR RADIOED OUR FLT; ASKING 'IF WE HAD THE TFC TURING DOWNWIND IN SIGHT.' PRIOR TO THIS; I DID NOT KNOW I WAS SUPPOSED TO BE LOOKING FOR TFC. I RESPONDED (TAKING OVER RADIO RESPONSIBILITIES) THAT THE TFC WAS NOT IN SIGHT. IMMEDIATELY THEREAFTER; I LOCATED THE ACFT; A PIPER ARROW WITH GEAR DOWN; AT MY 1 O'CLOCK POS AND SAME ALT; HEADED NEARLY HEAD-ON; WITH LITTLE RELATIVE MOTION. AT TIME OF LOCATION THERE WAS PROBABLY 500 FT SEPARATION. IMMEDIATELY UPON LOCATION; I ASSUMED CTL OF THE AIRPLANE AND ENTERED A HARD L BANK TO AVOID THE TFC. PLT OF OPPOSING TFC MADE VISUAL CONTACT AT APPROX THE SAME TIME AND ENTERED A HARD L BANK AS WELL. BOTH THE ACFT #2 PLT AND MYSELF RPTED TFC IN SIGHT AND CONTINUED TO MANEUVER TO REMAIN CLR. AS A RESULT OF MANEUVERING; ACFT 32 WAS ON A CLOSE-IN LOW L DOWNWIND; SLIGHTLY BEHIND OUR ACFT; AND WE WERE ON A WIDE DOWNWIND AT PATTERN ALT. AT THIS POINT; TWR ADVISED US (IN REPRIMAND) THAT WE WERE NOT SUPPOSED TO TURN XWIND UNTIL WE HAD THE TFC IN SIGHT. I COULD NOT RECALL RECEIVING THIS INSTRUCTION OR THE STUDENT READING BACK ANY SUCH INSTRUCTION; UNTIL WE HAD ALREADY TURNED XWIND. CONFUSION CONTINUED; BECAUSE AS I UNDERSTOOD IT; (ACFT #2) WAS INSTRUCTED TO FOLLOW US TO LNDG. ACFT #2 RESPONDED SOMETHING TO THE EFFECT OF 'I THINK ACFT #1 IS OUT OF OUR PATH NOW.' THIS DID NOT MAKE SENSE TO ME BECAUSE ACFT #2 WAS IN A BETTER POS FOR LNDG. OUR FLT DID NOT RECEIVE ANY FURTHER INSTRUCTIONS FROM TWR AS I CAN RECALL; AND SOON I WATCHED AS ACFT 32 TURNED BASE. AS SUCH; I EXTENDED DOWNWIND UNTIL I COULD GET A CALL INTO TWR TO VERIFY OUR LNDG SEQUENCE. I QUERIED THE TWR; 'LOOKS LIKE ACFT #2 IS GOING TO BE LNDG AHEAD OF US.' THE TWR RESPONDED; 'AFFIRMATIVE ACFT #1; YOU ARE #2; FOLLOWING ACFT #2; CLRED TOUCH-AND-GO.'