NMAC BTWN 2 SMA ACFT. 1 CRUISING JUST ABOVE TFC PATTERN ON DOWNWIND LEG NEAR AN ARPT AND THE OTHER DSNDING TO LAND.

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WE WERE IN A CESSNA 152 ENRTE ON A VFR XCOUNTRY FLT FROM SGJ TO SFB. FLT FOLLOWING WAS RECEIVED FROM DAB APCH CTL. CONVECTIVE ACTIVITY EXISTED JUST W OF DAB AND WE WERE VECTORED E OF DAYTONA DOWN THE SHORELINE AT 1100 FT MSL. 5 MI TO THE SE OF DAB WE WERE TOLD BY APCH TO PROCEED ON COURSE TO SFB. VISIBILITY WAS APPROX 3-5 MI WITH HAZE AND LIGHT RAIN. WE THEN TURNED TO A HDG OF 210 DEGS AT 1100 FT MSL. THIS TOOK US SLIGHTLY TO THE S OF SPRUCE CREEK ARPT. WITHIN A FEW MINS; APCH ADVISED US THAT TFC HAD '...JUST POPPED UP AT 1100 FT...;' TO OUR R BUT GAVE NO TA OR DISTANCE INFO. MY STUDENT WAS FLYING THE AIRPLANE AND I BEGAN LOOKING OFF THE R WING FOR THE TFC. JUST THEN THE STUDENT BANKED SHARPLY L AND THE TFC; A LOW WING SINGLE; PASSED SLIGHTLY BELOW AND TO OUR R IN THE DIRECT OPPOSITE DIRECTION. I ESTIMATE THE DISTANCE AT 100-200 FT; CLOSE ENOUGH TO HEAR THE OTHER ACFT'S ENG AS HE PASSED. I BELIEVE HE WAS DSNDING TO LAND AT SPRUCE CREEK ARPT; WHICH FORTUNATELY BROUGHT HIM BELOW OUR ALT.