What do you spend time doing at your martial arts dojo besides kata?
Kata was just one part of my students training and one of the testing requirements. Self -defense was another big training aspect and a testing requirement and that included both stand-up as well as grappling and ground fighting aspects along with some jiu-jitsu and that included some chokes as well as restraint and controlling techniques. Another aspect was falling and I favored and taught the Judo method of falling over the jiu-jitsu method. The jiu-jitsu method carries with it more risk of long term damage to your lower legs and having circulation problems down the road for those that train long-term. The basic karate skills and techniques up through intermediate and advanced skills and techniques were also taught and practiced. There was a clear cut difference then in the approach and skill an advanced student or black belt could take and execute something than what you saw with my intermediate and novice students. I have talked about that last aspect here in this forum before and is one of the ways you can tell if a school and instructor is any good in what they are teaching and the standards they have established for testing and promotion. If you see novice and intermediate students doing the same things as advance students and don't see a difference in the quality of execution of that advance group and black belts then keep looking for a place to study martial arts at. As far as competition went the only requirement for students was that they go and watch a tournament before they tested for brown belt. That way my students could see and observe something of some other styles in that environment as well as gauge their own skill, knowledge and ability and what they had been taught at my school. We did spar and I had also a full contact fighting and sparring class separate as well as a separate MMA program so some days were much more than an eight hour day for me and it was not unusual for me to be at my school till 10 PM or so after being there most or much of the day.
I attend a kwoon and practice sets, as opposed to going to a dojo and practicing kata! ;) We spar, perform drills that include rolls, chin-na, kicks, hand strikes, etc., 2-person drills, weapons practice, calisthenics, and stretching, to name a few things. EDIT: I'd like to start doing more in the way of lion dancing too.