My problem is that my sensei talks and talks and talks, forever. He spends a good 5-10 minutes explaining something, we then practice what he explained for a about 2 minutes, then he starts talking again. During a typical one hour class, he often spends a good 30 to 45 minutes talking. He can't even stay quiet long enough to finish a count. Say we are doing a combination 5 times, he goes: 1, 2... and when you think he is going to say "3", he starts talking again. It's like you better not react too quickly. You have to wait before you move, to see if he is gonna say 3" or maybe he just wants to make some additional comments. I used to think I needed to adjust my attitude and listen with respect. But this is getting to be too much. Many times, I just feel frustrated and disgusted and it takes a lot of discipline not to walk out of there. That's too bad, because I love doing Karate, the few minutes I actually get to do something, during his classes.
Reading it charitable, he's a perfectionist, just @Sardathrion wrote. I sometimes catch myself talking too much in class and it's been brought forward. Especially when teaching adults this can become a common theme, but I, personally, was thankful for pointing that out, as I want to be the best teacher I possibly can be. So in the end, both sides got positive outcomes from that.
With more than 16 years of teaching MAs, I came to the conclusion that interaction is the most central thing in good teaching. This has two dimensions:
Personal level of interaction
While this is probably the less important one, it is quite important for retaining your participants. But I consider interaction on a personal level to be quite important as you
want to get to know the person you are teaching techniques that potentially harm both participants of your group and others
you can adjust methods and how to engage the person so that there is trust and development that would not be possible in a one fits all method
you bond with and bind people (which is important imho)
Interaction on a professional level
Here's the core of the problem as you describe it: holding a monologue may help to understand something, but MA is about being able to do something.
You need both practice (like, a lot) and constant feedback in order to become better. You have to have more repetitions in order to correctly learn a technique you did wrong than you had for learning the wrong technique.
This necessary level of personal feedback is impossible to provide with short, non-interactive practicing periods. And by this, I mean on a 1-on-1 basis, not correcting mistakes in front of the whole group (except it's a very common mistake, which you then point out explicitly).
There are two steps: First, speak to him heads up. I've been told long talks make it so that most people forgot what I told at the beginning before I finished. I adapted and had positive feedback. If a teacher cannot cope with constructive feedback, he is both a bad martial artist in terms of personality and in terms of instruction. So if he is unwilling or unable to work on that, he is the wrong person to teach you (and, imho, anyone).
I am afraid you need both and a third one.
First, you need to pay attention to what sensei says and steal as much of his knowledge as possible. To me, he sounds like a perfectionist wanting all his students to learn as if they were tenth dan. This is a curse and a blessing at the same time.
Second, you need the space and time to actually practice what he says. This is hard to do in class but finding some time is a good idea.
Thirdly, do talk to him like two adults in the room: no recriminations, no fake modesty, and no blame. Bring solutions to the problem. For example, you could say something like:
I want to steal as much of your knowledge as you can share. However, I am finding it a little of an information overload. Can you help with that? I thought that maybe a one to three ratio of talking to training would be good? What do you think?
I'd say don't be scared to change. The personal relationship with a coach is of utmost importance for any athletes.
Is this the national training center of your country ? if not you can probably safely go an choose another dojo...
BUT you are still a student and I think you own your coach a little respect in this case, this would mean to talk to him and explain frankly (as other have said) that you are just seeking a different, more combat-oriented approach in your training. Just steer away from personal remark and it will be fine.
I was told there are two ways to teach (in judo) the European and the Japanese way. The European include a lot of direct interaction from the coaching. Japanese is a lot more of a personal learning through observation during a practice. (Our coach would just make us fight for 2 hours, sitting in a corner and observing, and would call errors when he saw something he didn't like)
Some people just love hearing themselves talk. Although he may have to take up some time giving guidance and input on techniques and applications, using half or even more of a class doing nothing but talking does seem unreasonable. Honestly, your attitude sounds amazing. In your shoes I would have walked out the door after a few classes, you clearly have dedication and patience. Changing dojos is bound to be a difficult decision, but... If your instructor is doing anything that you feel seriously degrades the quality of the class, or that you wholeheartedly disagree with, you should probably consider a different school.
For me, digging into the theory and nuance of a technique is never sinks in until I've drilled it into muscle memory and used it in sparring. If that's your preferred learning style too, it may be worth looking at other dojos or gyms, or at least bringing it up with your instructor.
Learning every detail of the theory behind a technique is a good idea, but not at the expense of actually learning to use the technique. Throwing that combo should require absolutely no thought, it should be on deck, ready to go whenever you need it. It takes practice to get there, not TED Talks!
Is the stuff your teacher says relevant to what you're doing? Does he tell stories that are not lessons and seem like bragging? Rambling?
It's hard to answer that because my teacher talked (I don't want to say "a lot"). He was a former Bruce Lee student, so class had a lot of mental stuff as well as the obvious physical elements. He told stories about Lee, but the stories were always relevant to class. In my case, his talking was equally important (plus it was cool to hear stories from a person that knew The Man and not simply repeating quotes he read or saw in an interview).