C172 student with instructor was turning final for the right runway and experiences a NMAC with a PA28 on the ILS for the left runway. The instructor takes evasive action and the PA28 goes around.

Narrative

Instructor pilot was demonstrating a soft-field landing to the student (me). We were cleared for touch and goes on the right runway and we were on a right downwind. After turning right base the Instructor announced that he saw traffic for the left runway (the Cherokee; however we did not know aircraft type). After completing roll out onto final; Instructor and student noticed the traffic for the left was rapidly drifting toward us. Instructor turned right and descended rapidly. When I looked back at the other aircraft it was where we would have been if the Instructor had not taken evasive action. Aircraft Y started a gradual climbing left turn. Instructor then called Tower and asked; 'Were we supposed to follow another aircraft or were we cleared for touch and goes?' Tower replied; 'You are number one and cleared for touch and goes.' Instructor stated; 'Another aircraft just flew past us and we almost had a mid air.' Tower replied; 'Was the aircraft a low wing?' Instructor replied; 'Yes.' Tower responded; 'The aircraft was a Piper Cherokee and he was on the ILS for the left runway; he just reported going missed.'