The pilot under instruction (PUI) and certified flight instructor (CFI) were practicing slow flight at approximately 200 feet above ground level when the CFI noticed that the airplane was sinking and the airspeed was low. He instructed the PUI to add power in order to maintain altitude; the PUI did, but the airplane continued to sink. The CFI then added more power and pitched the nose up in an attempt to gain altitude and arrest the sink, but in response, the PUI pushed the nose down and the airplane made an inadvertent landing, bouncing twice and coming to rest inverted. The airplane's firewall and vertical stabilizer were substantially damaged. The CFI reported no preimpact mechanical malfunctions or failures that would have precluded normal operations.