HDG TRACK DEV ON TKOF DEP PROC DURING AN M20C TRAINING FLT AT CMH; OH.

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I WAS INSTRUCTING A STUDENT PLT/OWNER IN AN M20C. WE WERE INSTRUCTED TO DEPART RWY 27R AND ENTER A L TFC PATTERN FOR RWY 27R TO PRACTICE TOUCH-AND-GOES. WE DEPARTED AND BEGAN OUR CLB TO PATTERN ALT. AT 400 FT AGL; WE INADVERTENTLY BEGAN A R TURN TOWARDS RWY 27R. I WAS MOMENTARILY CONFUSED AS TO HOW TO ENTER THE PROPER PATTERN FOR L-HAND TURNS FOR RWY 27R. I THEN DECIDED THAT THE PROPER WAY WAS TO FLY A L XWIND FOR RWY 27L; L DOWNWIND ON RWY 27L AND WAIT FOR CLRNC TO BEGIN AN EXTENDED L BASE FOR RWY 27L. I QUICKLY BEGAN AN IMMEDIATE L TURN TO HDG OF 180 DEGS TO ENTER THE L XWIND; AS ORIGINALLY INSTRUCTED. I DID NOT PROPERLY BRIEF OR FLY (AS A CFI) THE GIVEN ATC INSTRUCTION. THIS TYPE OF ATC CLRNC IS TO BE FULLY UNDERSTOOD BEFORE ACCEPTANCE AND IF MISUNDERSTOOD; THE BEST OPTION IS NOT TO DEPART OR IF AIRBORNE; TO CONTINUE A STRAIGHT-OUT DEP ON RWY HDG. AS A CFI AT A CLASS D ARPT WITH PARALLEL RWYS; I SHOULD INSTRUCT MY STUDENTS ON THESE ATC CLRNCS AS PART OF MY INSTRUCTION GIVEN ON ARPT OPS. I DEBRIEFED THE STUDENT UPON COMPLETION OF OUR LESSON AND USED IT AS A LEARNING EXAMPLE ON FOLLOWING AND UNDERSTANDING ATC CLRNCS. I AM EMBARRASSED BY SETTING A POOR EXAMPLE AS A CFI AND HAVE COMPLETED A PERSONAL SELF REVIEW IN THE AIM ON SUCH TOPICS TO ENSURE IT DOES NOT OCCUR AGAIN.