kenbiki,
Sounds like an OK teacher.
I have had a few teachers over the years and they're all a bit different.
Why I think your teacher is good is this:
1. He/she gives you homework. ie a goal. That means that they have a progression in mind, so that if you stick with them, in 6 months' time, you'll be able to see you've made progress.
2. He asks you to play what you learned last week. Which means he remembers what you did last week. That means you have to practice/ learn what you are given.
The "quick explanation" bit is a worry if you spend half the lesson chatting. Some teachers are chatty, others get down to business straight away (and finish just as abruptly after 1/2hr).
I'd ask just one question: "Where are you taking me with this?" It sounds like your teacher has a plan, which is a good thing.
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