A C172 INSTRUCTOR PLT AND STUDENT MAKE A TOUCH-AND-GO ON THE WRONG RWY AT HWD; CA.

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MY STUDENT AND I WERE INBOUND FOR TOUCH-AND-GOES. MY STUDENT CONTACTED HWD TWR AND REQUESTED INBOUND INFO. THE ARPT WAS LNDG TFC RWY 28R&L. TWR SAID TO EXPECT RWY 28R. MY STUDENT THEN ASKED FOR RWY 28L FOR TOUCH-AND-GOES. TWR SAID EXPECT RWY 28L; RPT CAL STATE HAYWARD. WHEN WE ARRIVED AT CAL STATE HAYWARD; WE RPTED THE SCHOOL. TWR ASKED US TO DO R 360 DEG TURN FOR SPACING. WHEN WE CAME OUT OF 360 DEG TURN; THEY WERE VERY BUSY AND WE CONTINUED THE R 360 DEG TURN FOR SECOND TIME. WHEN THE FREQ WAS CLR; WE ASKED TWR IF THEY WANTED US TO CONTINUE THE TURN. THEY SAID YES. THEN THEY SAID CLRED R BASE RWY 28R; CLRED FOR TOUCH-AND-GO L TFC. MY STUDENT SAID (I THINK) R BASE RWY 28L L TFC CLR FOR TOUCH-AND-GO. THERE WAS A LOT OF TFC AROUND. FREQ WAS VERY BUSY. MY STUDENT WAS NOT TOTALLY AWARE OF WHAT WAS GOING ON. I WAS TRYING TO HELP HIM FLY THE PLANE. I THOUGHT RWY 28L WAS CLRED TO TOUCH-AND-GO BECAUSE THEY SAID EXPECT RWY 28L. I HEARD L TFC; AND TOUCH-AND-GOES ARE DONE ON THE L RWY. I THOUGHT THE REASON WE DID 360 DEG TURN WAS TO SEQUENCE US INTO THE L RWY. I WAS PAYING MORE ATTN TO ALT; TFC; AIRSPD AND BUSTING AIRSPACE (CLASS C OVERLAYING CLASS D). WHEN MY STUDENT LANDED ON RWY 28L; TWR ASKED WHERE WE WERE. I CAME ON THE RADIO AND SAID RWY 28L. HWD TWR ASKED IF WE WERE CLRED FOR THE R. I SAID NO; THE L. AFTER WE (MY STUDENT AND I) TAXIED BACK TO THE SCHOOL; TWR CALLED MY SCHOOL AND SAID THEY LISTENED TO THE TAPE AND WE WERE CLRED FOR THE R. I APOLOGIZED AND AGREED WE (ATC AND PLTS) SHOULD WORK AS A TEAM. I REALIZED MY MISTAKE AND EVERY TIME I OR MY STUDENT LANDS; CONFIRM L OR R AND SAY L OR R WITH EMPHASIS.