The certificated flight instructor (CFI) stated that he and the student pilot were returning to the airport at the conclusion of a local flight. The student conducted the landing approach, and the airplane touched down "hard" on the runway, resulting in a bounced landing. The CFI directed the student to apply full engine power and initiate a go-around. After increasing engine power, the student continued to pull back on the control yoke and the airplane subsequently stalled at an altitude about 50 feet above the ground. The CFI responded by applying forward elevator and right rudder, but the airplane impacted the runway, resulting in substantial damage to the left wing and engine firewall. The CFI stated that there were no mechanical malfunctions or anomalies with the airplane.