INSTRUCTOR WITH STUDENT PLT TAKES EVASIVE ACTION WHEN SIGHTING ANOTHER ACFT AT CLOSE RANGE.

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I WAS GIVING A STUDENT A LESSON ON VOR ORIENTATION/NAV; SHORT FIELD TKOFS/SOFT FIELD TKOFS/LNDGS. MY STUDENT AND I JUST GOT PERMISSION TO SQUAWK VFR AFTER DEPARTING GFK CLASS D AIRSPACE. I WAS SHOWING HIM HOW TO USE THE VOR. I KNEW HE WOULD MAINLY LOOK INSIDE THE ACFT SO I MADE SURE I WAS SCANNING FOR ACFT. MY STUDENT WAS JUST FIGURING OUT HOW TO USE THE VORS TO FIND HIS POS ON THE SECTIONAL CHART WHEN I STARTED MY SCAN FROM THE R. AS I SHIFTED MY VIEW FROM 3 O'CLOCK; 2 O'CLOCK; 1 O'CLOCK; 12 O'CLOCK; 11:30 O'CLOCK; 11 O'CLOCK; I IMMEDIATELY SAW ANOTHER ACFT AHEAD HEADING A LITTLE FROM MY L TO MY R. PRETTY MUCH STRAIGHT OFF OUR NOSE TO THE L. THE ACFT SEEMED TO BE ABOUT 10-20 FT ABOVE THE ALT WE WERE FLYING. I INSTINCTIVELY PUSHED FORWARD ON THE YOKE AND TURNED TO THE L (TURNING TO THE R WOULD HAVE BEEN DEADLY). I HAVE NEVER PUSHED FORWARD ON THE YOKE THAT ABRUPTLY IN MY LIFE. EVERYTHING IN THE COCKPIT THAT WAS LOOSE SLAMMED INTO THE CEILING. A COUPLE THINGS THAT COULD HAVE CONTRIBUTED TO THE INCIDENT WAS THAT OFF IN THE DISTANCE AT OUR SAME ALT THERE WAS A HAZE LAYER; WHICH IMPAIRED OUR VISION DIRECTLY IN FRONT OF US (FOR LOOKING AT DISTANT OBJECTS). ALSO; I BELIEVE THE OTHER ACFT DID NOT HAVE RECOGNITION LIGHTS ON WHICH SHINE OUT IN FRONT OF AN ACFT (WHICH ARE NOT REGULATORY). THIS MIGHT OF HAVE HELPED US PICK OUT THE ACFT SOONER THAN WE DID. OBVIOUSLY; IF TWO ACFT ARE HEADING ON A COLLISION COURSE HEAD-ON DURING THE DAY ONE ACFT WOULD LOOK LIKE A FLAT PANCAKE TO THE OTHER WITHOUT ANY LIGHTS. I TAKE MANY TRAINING FLTS FROM GRAND FORKS EVERY WK. MAYBE A STEP TOWARD ACCIDENT PREVENTION AROUND THIS AREA WOULD BE TO DESIGNATE THE AREA AROUND GRAND FORKS AS AN ALERT AREA ON SECTIONAL CHARTS. BY DOING THIS; MORE PLTS WILL BECOME MORE PRONE (AWARE) TO COLLISION AVOIDANCE PROCS.