A C172 Flight Instructor on a left base for the right runway experiences a NMAC with another flight school C172 on a right base for the left runway. The instructor in a third aircraft detects the conflict and goes around.

Narrative

Approaching from the east; Aircraft X was following another C-172 (Aircraft Y); who Tower claimed to have called up '30 seconds' prior at the same point. Tower directed Aircraft X to follow that traffic and report a two mile left base for the left runway. As Aircraft X continued to the airport Aircraft Z; who had been on the right runway practicing touch-and-goes; requested a transition to the left runway for landing. Aircraft Z was cleared to make the transition to the left runway by entering a right base for the right runway. Right before reporting the two mile right base for Aircraft X; Aircraft Y was on final and cleared to land; Aircraft Z was told they were number two for landing. When Aircraft X reported the left base; Tower told the pilots they were number two for landing. Aircraft X assumed they were number two behind Aircraft X; who was now on short final; not Aircraft Z (on the right base). Both Aircraft X and Aircraft Z started to turn final at the same time; luckily Aircraft Z saw what was happening and alerted the Tower. Aircraft X was cleared to land on the left runway; while Aircraft Z went around. The confusion between the landing order of aircraft was a major contributor to this event. Also; the position of the two converging aircraft was in question.