Flight Instructor reported a NMAC during a training flight in the traffic pattern with their student. Another aircraft entered the pattern; continued directly on top of the instructor's aircraft and did not respond to requests to create spacing.

Narrative

My student and I announced our takeoff; crosswind; and our downwind for the runway at an uncontrolled field. There was one plane short final for the runway. A Luscombe announced one mile out crossing midfield. I then asked if they were planning on going behind us as we were already on downwind. They said traffic no factor; possibly confusing us with the aircraft landing. I then told them they were headed right at us as they were crossing mid field. They then said they do not have us in sight. We were right in front of them and lower than them as they approached the traffic pattern almost t-boning us. I asked him if he was planning on slowing down and getting space between us as we were ahead and lower than him. He still said he did not have us in sight. He continued to fly right on top and slightly behind us even as I told him we were turning base and he should extend downwind to create that spacing. He was careless; not paying attention to radio calls; and very complacent with not searching for traffic even though we were right in front of him if he would've just looked. After looking up the pilot on the FAA website; his last medical was [many years ago] and does not have basic med.