General aviation aircraft training in the pattern at DTO experienced conflict when turning base; following traffic as instructed; ATC commenting that a landing clearance was required before turning base.

Narrative

The flight was a local instructional flight from our home airport; to DTO to practice tower controlled procedures. After a full stop landing and taxi back to the end of the runway; we were cleared for takeoff on Runway 35 and to perform a left closed pattern after takeoff. On the upwind leg the Controller asked if we saw an aircraft on downwind at 11 o'clock and a mile from us. We replied that we did and were then instructed to follow that aircraft. At that time I started instructing my student as to the proper spacing to follow the other traffic. Apparently at this time the Controller was instructing another aircraft on a straight in to be #2 behind the traffic we were following. Nothing was said to us. I thought that we were still #2 behind the traffic we were originally following. When we started turning base leg is when I spotted the aircraft on final; so I assumed control of the aircraft and turned behind the aircraft on final. At this time the Controller asked us our tail number and informed me that we aren't to turn base until cleared to land. I elected to turn out of the pattern for our home field. I still don't know if he was correct and think that he should have instructed us to extend our downwind; but from now on I will be querying the Controller for landing clearance prior to turning base.