The student pilot was practicing normal touch-and-go landings. On the third landing, the pilot did not pitch the nose up sufficiently and the airplane began to porpoise and wheelbarrow on the nose wheel. The student pilot attempted to steer the airplane back towards the centerline of the runway, but was unsuccessful and the airplane departed the left side of the runway. As the airplane left the pavement, it hit a snow berm and it nosed over onto its back. The airplane sustained substantial damage to both wings and to the vertical stabilizer. The pilot stated that there were no pre-impact mechanical malfunctions or failures with the airplane.