The flight departed Fort Lauderdale Executive Airport, and proceeded to the Immokalee Regional Airport where the student pilot demonstrated to the on-board certified flight instructor (CFI) three successful touch-and-go (T&G) landings to runway 27. Following the 3rd T&G landing, the CFI deplaned, and the student pilot departed from the same runway and remained in the traffic pattern performing 8 additional T&G landings on the same runway. During final approach for the 9th T&G landing, the student pilot reported hearing the pilot of a helicopter announce the intention to fly over runway 27. The student pilot reported he announced on the common traffic advisory frequency that he had the helicopter in sight, and his intention to perform a T&G landing on runway 27. The student pilot landed, and after touchdown during the landing roll, he applied full throttle before retracting the flaps. The airplane started to drift to the left and the right wing raised. The student pilot reduced the power to idle and applied aft control yoke then waited for the airplane to come to rest. The CFI reported seeing the helicopter flying in a southerly direction, and the helicopter flew directly overhead the airplane while it was on the runway during the landing roll. The CFI noted the student pilot did not retract the flaps and the airplane veered sharply to the left, then cart wheeled coming to rest upright. The operator reported there was no evidence of preimpact failure or malfunction of the airplane. Postaccident inspection of the airplane revealed damage to the firewall.