Flight Instructor providing instruction in a light fixed gear aircraft reported the student temporarily lost control while practicing landings resulting in a tail strike and damaged tailwheel.

Narrative

The student and myself took the plane to ZZZ to work on tailwheel landing. After doing 7 or 8 landing with a couple go-around due to rough landings; we came in for another wheel landing; the mains hit the ground harder then normal. Maybe due to a higher power setting or by forcing the airplane to the ground. We bounced into the air and as we were coming back to the runway I called for a go around because the landing could not be saved; it would be better to come back around and try again. The student pushed power full and pulled back on the stick. I then notice that he was pulling back too far so I tried to push the stick forward to avoid the tail from hitting and to reduce the angle of attack. That is when the tailwheel hit the ground as we were climbing out. I heard a noise and as we climbed I looked at our shadow to see if the tailwheel was still attached. I then pushed on the rudders and they seemed to move freely. I thought that everything was fine and in working condition because it was flying normally and everything looked fine. We then came back to ZZZ1 and landed and taxied back to the hangar. Everything still seemed to be working fine. We shut down the plane and that is when I looked at the tailwheel and noticed the damage.