NMAC WHEN 1 OF 2 C172'S FAIL TO EXERCISE THE SEE AND AVOID CONCEPT NEAR PIE; FL.

Narrative

AFTER 35 MINS INTO THE LESSON; STUDENT PLT AND CFI WERE RETURNING FROM TRAINING AREA ON A HDG OF 180 DEGS AT 3200 FT; 1.5 MI W OF THE SHORE OF ANCOLTE KEYS. CFI SPOTTED TFC AT 12 O'CLOCK POS; SAME ALT; APPROX 4 MI AWAY. STUDENT ENSURED THAT ALL THE LIGHTS WERE TURNED ON; WHICH WAS FOLLOWED BY THE OTHER TFC TURNING ITS LNDG LIGHTS ON. CFI ORDERED THE STUDENT TO TURN R 45 DEGS IN ACCORDANCE TO 14 CFR PART 91.113(E) TO AVOID TFC HEAD-ON. PROMPT RESPONSE OF THE STUDENT WAS OBSERVED. HDG WAS KEPT IN 230 DEGS AND VIGILANCE TO AVOID TFC WAS KEPT BY THE CFI AND STUDENT. WHEN THE OTHER ACFT WAS AT OUR 10 O'CLOCK POS; HDG (ESTIMATED) 360 DEGS; AT LEAST 1 MI AWAY; IT ROLLED INTO A STEEP TURN TO THE L (NEGLECTING AIM SECTION 4-4-14 PARAGRAPH ITEM 4 AND NOT OBSERVING 14 CFR 91.111(A)). I; THE CFI; TOOK EVASIVE ACTION; CLBING TO AVOID THE COLLISION. AS A CONTRIBUTING FACTOR; THE LACK OF EFFICIENT CLRING PROC PRIOR TO THE MANEUVER SHOULD BE CITED. THE FACT THAT I KEPT THE TFC IN SIGHT THE WHOLE TIME WAS FUNDAMENTAL TO MY SURVIVAL.