hi
im going to college for trombone performance/music ed
and they have a private lesson program at my school
so my question is
should i go along with the teachers practice, whatever they give me right of the bat?
or should i tell them what ive been working on over the summer (tenor/treble clef/ the song Doolallynastics as a college project)?
because i dont want it to be like when i had to find a new guitar teacher, where they all treated me like i was a brand new player.
and i dont want to feel like im ages ahead of what they are trying to teach me.

because ive heard some of the other trombone players that are going to my college, and i know that i can do some things better than some of them.

this is all assuming that the teacher is giving actual personal lessons, not general long tone exercises.

also one more thing
polytoning
i can do it on certain notes, but higher notes start to wave and bubble
its also hard to change the pitch of my hum
tips?

You did have to audition right? I suspect the teacher has already heard you play and has an idea of what they're going to be working on. If not, they will most likely do some sort of diagnostic playing test to see where you're at and take it form there.
Listen to your teacher right off the bat. It's disrespectful to do otherwise. Besides, remember that if they are having you do stuff you don't find so interesting, it may be because you're not playing as well as you think you are and you may have to go back to work on some fundamentals. Just go in with and open mind, ready to learn. Check your ego at the door.

I agree with Steve 99.9%.

If this is a good college and a reputable teacher then yes, you should do as the professor instructs. If you disagree with something for some reason you can certainly enter into a dialogue about the subject. But be respectful when discussing things, use facts and demonstrations. You are there to learn from them, so do that, learn from them.

You are entering a new world of musicianship and somethings may not make sense to you at first.

I like that you already know you do some things better than others (and perhaps others do some things better than you). Remember this and don't try and place yourself or rate yourself to the others. Don't get into personality clashes - it can ruin you.

Short story:
I sent to a college and insited I was better than this other guy (who happened to be the son of the director of music). I insisted that I play first and he insisted that he play first. His father, band director, orchestra director, and private teacher would not make a decision. They got together and decided to let us work things out. We hated each other. We were mean to each other. We sabotaged music, we would physically move the others instrument while playing a concert to make him make a mistake. The whole first year of college went this way - we should have been kicked out of school. We were bad people.

Now, we are best freinds. And the most ridiculous part is I'm a low horn specialist, always have been. So why did I care so much to be playing first? That's not what I was going to do professionally.

See where you fit in. Enjoy the experience and learn from everyone there.