A DA42 experienced a NMAC with a C-172 while shooting a practice approach to PVU.

Narrative

My student and I were flying a practice VFR approach into Provo UT. We made contact with Salt Lake Approach when we were about six miles east of the Fairfield VOR. We were given no radar or separation service and were allowed to vector ourselves on to the final approach course. We intercepted the localizer and maintained 8000 FT until intercepting the glide slope; then we flew the glide slope. During the time with Salt Lake Approach we became aware of another aircraft ahead of us on an approach into Provo; and I started scanning for him. Salt Lake approach told us to contact Provo Tower when we were on the localizer over LEHI. Upon switching to Provo Tower's frequency we heard a Cessna talking about being 10 out for a straight in. We then made contact with Provo Tower and were told we would be behind Aircraft X; also that a Cessna reported 10 miles to the North. I then started looking for both the Cessna and Aircraft X. Just before reaching WAVIT the Cessna appeared about fifty feet below our aircraft. I took the controls; added power and started a climb as we passed over him. We tried to report what had happened but the Cessna started reporting he was doing a 360 for spacing. After over flying him we maintained altitude and continued to fly towards the runway with my student watching him. I feel that part the problem was the Cessna pilot's lack familiarity with operations for the Provo area. He was not talking to Salt Lake Approach prior to making a straight in approach. Blind spots were also to blame. He was below us and we were a low wing and we were above him and he was a high wing. Also lack of radar help contributed to this occurrence. Had radar been in place both of the aircraft could have known where the other was. This would also give Air Traffic Control a better idea were all the aircraft were.