I agree with the others here.

Yes, by all means experiment, adventure, and dare to go where others fear to tread. Whenever I have a student return with new ideas and tunes it gives me a new opportunity to develop their skills.

The boredom you experience is natural at an early stage while there is little variation in lesson material and much repetition. That will soon change as your ability develops. If you want, ask your teacher for more to play at the same level so that you can practice with more interest, but beware that he will likely ask you to demonstrate your ability with the piece of his choosing, so have that polished for lesson day.

I think of myself as a skills guy, and I tell every new student that that is my focus (besides the fun, the theory, and the exposure to new ideas). My intent is to instill the skills so that the student can apply them to music outside of the lesson material. They self-teach better that way. I choose lesson material, practical tunes, based on skills they can learn rather than simply providing tunes for them to regurgitate on demand without knowledge of how they work.

Don't be afraid to communicate with the teacher so that he can fully understand your needs.

Ultimately, the student doesn't need the teacher, and when that happens I've done my job.

Peace, Mooh.