PA-28 flight instructor with student reported a runway excursion during a takeoff roll when the trainee veered off runway by applying wrong directional input. The aircraft came to rest in the grass area adjacent to runway and ground personnel were notified.

Narrative

I was doing a TOLs flight with my student. We were on the third touch and go when the incident happened. We landed normally; then the student retracted the flaps and applied full power to takeoff again. When the power was applied; we began to veer slightly to the left; the student accidentally applied left rudder instead of right rudder; this caused us to veer hard to the left; as this was happening I immediately said 'my controls' and began applying right rudder to try to get us back towards centerline as we were quickly approaching the edge of the runway. I believe the student froze on the controls and my rudder inputs were not effective. I realized we didn't have enough time/airspeed to takeoff before going off the runway so I immediately closed the throttle and applied the brakes to try and stop before exiting the runway. We were going too fast to stop in time and we exited the runway into the grass on the left side. I continued to apply the brakes and steer clear of the runway lights and signs before coming to a stop before the intersecting Runway XXL. I notified tower of what happened and they instructed me to contact ground. I called ground and told them we would be shutting down to which they notified us that fire rescue was on the way.