C172SP Flight Instructor reported taking evasive action to avoid traffic pattern traffic resulted in a NMAC event.

Narrative

I was with a student on an IFR Flight Plan to ZZZ. We were cleared for the RNAV XX by ZZZ Approach Control. We were on a 3.5 mi final for the RNAV Approach in VMC. Aircraft Y was on a 3 mi extended left downwind for Runway XX at ZZZ. Aircraft Y asked us over CTAF saying 'Aircraft on final for XX say position' to which I responded 'We are on a 3.5 mile final for the RNAV XX approach.' The response from Aircraft Y was 'Okay; we're turning left base runway XX.' Thankfully; I had identified the aircraft on the left downwind as we were approaching the runway and was able to keep an eye on them the whole time. Their distance from the airport and altitude led us to be on a collision course after they had turned the left base. I took the flight controls from my student and made an evasive diving maneuver; creating around 300-400 ft of vertical separation between our aircraft and Aircraft Y. Aircraft Y passed directly over us on the final approach course roughly 200 ft below traffic pattern altitude and made a left-hand circle back towards the left downwind and landed after us. The evasive diving maneuver that I was forced to make was the key factor in the avoidance of the collision. The decision of Aircraft Y to turn a left base directly at us seemed like the result of a lack of situational awareness in a busy pattern and a lapse in Aeronautical Decision Making judgement. I think that a continuing focus on ADM and situational awareness in initial and re-currency training could help prevent this situation in the future.