C172 Flight Instructor reported a NMAC at a towered airport with a low wing DA-20 aircraft that resulted in a go around.

Narrative

On a training flight my student and I were on final for Runway XXL. The other aircraft was directed by ATC to follow us in line for the approach. The other aircraft (DA20) turned base inside of our final and executed a descending turn in front of our aircraft while intercepting final. By the time we made visual contact; the other aircraft was approx 100-200 ft away from our aircraft. After making visual contact the instructor pilot (myself) took control of the aircraft and executed a go around. After advising Tower we were instructed to sidestep left of the runway and we complied. After Tower asked the other aircraft if he had saw our aircraft the other pilot replied that he thought we were for the parallel runway. I want to point out this is the classic case of a high wing aircraft (ours) and a low wing aircraft (the DA20) converging on one another. I think this can be corrected by having set ground references where aircraft must be past before turning inside the pattern. This will prevent other aircraft 'doglegging' the pattern and creating conflict situations.