Instructor pilot reported having a near mid air collision with another aircraft that turned towards them during landing. The instructor took control of the aircraft and took evasive action to avoid a collision.

Narrative

Myself and student flying Aircraft X practicing instrument approach procedures. Upon vectoring my student 2 miles before the final approach fix; we proceeded inboound once established and began making CTAF calls around 8nm from GVL. I had heard Aircraft Y make a call regarding their location and intention to enter downwind. Myself and student made calls every 2 miles to CTAF frequency. There was 2 other planes in the pattern at this time. We were descending on glideslope as published and Aircraft Y turned towards us on a left base. The distance quickly closed as Aircraft Y is much faster. We initiated a full power climb in Aircraft X and proceeded to add flaps to 20; then 30 to slow the plane down and create distance between us and Aircraft Y. I took controls from my student and avoiding the collision. I simultaneously made calls that I was climbing and remaining behind Aircraft Y on final approach for runway 05. After other planes had seen this occur; a instructor from a Flight School was in the pattern and called over CTAF; 'Aircraft Y how do you hear this transmission?'. Aircraft Y replied 'Aircraft Y; I hear you loud and clear.' The instructor asked this to confirm that Aircraft Y had indeed been hearing our distance calls over CTAF. We landed uneventfully after the plane had cleared the runway. NMAC was imminent had action not been properly input.