PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Commercial; Flight Crew Multiengine
Flight Crew Last 90 Days 130.7; Flight Crew Total 520; Flight Crew Type 130
Communication Breakdown
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Overcame Equipment Problem; Flight Crew Took Evasive Action
Human Factors
We were making right traffic for Runway XX.  We made a normal upwind; turned crosswind at 700 feet AGL.  When turning downwind; we rolled wings level and pilot flying; noticed departing traffic on our right climbing right to left on a near direct course with our aircraft.  The aircraft passed just out ahead of us (a couple to hundred feet out ahead) and just below (50-100 feet vertical separation).  I was the pilot monitoring/instructor pilot) called Tower to inform them of the near miss and we were told we could make a right 360 degree turn to rejoin the downwind which would have taken us over the runway and done nothing to help us avoid the departing eastbound traffic which was now off of our left side. No action was taken to turn the right 360 for consideration of other aircraft departing the runway and joining the downwind behind us.
PA-28 flight instructor reported an NMAC event during traffic pattern training. Reporter stated ATC's response was inadequate.