The flight instructor and the student pilot were practicing short field landings. Following an uneventful first landing, the airplane approached the runway for a second. While on the short final leg of the approach to the runway, the airplane began sinking rapidly. The flight instructor responded by advising the student, "full power." The student pilot thought the flight instructor had said, "pull power," and subsequently reduced engine power to idle. The airplane impacted the runway and bounced back into the air. The flight instructor then took control of the airplane and aborted the landing. Subsequent inspection of the airplane by maintenance personnel revealed that the nose landing gear and engine firewall had been substantially damaged during the landing. Following the accident, the operator reemphasized to their flight instructors the importance of utilizing standard phraseology during training flights, including use of the phrase "go around" to indicate the necessity to abort a landing.