On August 20, 2005, about 1010 central daylight time, a Cessna 177B, N34329, registered to and operated by a private individual, experienced a hard landing during arrival at Olive Branch Airport, Olive Branch, MS, Visual meteorological conditions prevailed at the time and no flight plan was filed for the 14 CFR Part 91 instructional flight from Tupelo Regional Airport, Tupelo, MS. The airplane was substantially damaged and the student pilot was not injured. The flight originated about 0805 from Olive Branch Airport. The pilot stated that on the last leg of the three leg cross country flight he received a weather advisory from the automated weather observation station at Olive Branch Airport and a traffic advisory over the Unicom frequency. He also stated he experienced thermals during descent to runway 18. As he flared the airplane, a thermal lifted the nose causing the airplane to bounce upon touchdown. The wind then pushed the nose to the left and he applied full power to recover. The aircraft then departed the side of the runway and the nose strut impacted a runway light causing the strut to collapse and the propeller to impact the ground. The pilot secured the electrical system then exited the airplane.