PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 750; Flight Crew Type 450
Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors
We were extended upwind after a touch and go on Runway XX; we proceeded to turn crosswind at traffic pattern altitude then we made the turn to downwind. After making our turn on the downwind Aircraft Y was wings level in crosswind within 30 ft after being instructed to fly west bound after departing Runway XX behind us. I had to make an evasive correction and descended immediately to avoid the Cessna flying toward us at the same altitude. I believe that this occurred due to either a lack of understanding of the instruction given to the pilot of the Cessna or a failure to maintain situational awareness by ignoring radio calls from tower. The pilot of the Cessna responded to tower after about 3 or 4 calls.
GA flight instructor reported a near-mid-air-collision in the pattern when another pilot did not follow tower instructions.