I'm currently an undergraduate mathematics student in my final semester. I plan to start a master's program in mathematics at the same university with an adviser that I did research with last summer.
I meet regularly with the adviser. He has stated that his goal is to help me go to a great PhD program, and the best way he sees to do that is to pump out publications, presentations, etc.
However, it seems that we are pursuing publication opportunities at the expense of understanding. He is giving me projects to work on that are frankly above my head. I spend hours and hours trying to find a bug in code that I didn't write about a subject I haven't studied. The time I spend debugging could potentially be spent more productively learning the fundamentals of our field. My approach has always been to understand a topic from the ground up, but he wants me to be able to work with PhD level code because it's the best way to get a publication.
I know that publications are essential. I want to eventually publish something, but not before I have built my own essential knowledge foundation of our field. Learning the topics thoroughly is more important to me than making a publication, and it seems to me that if one strives to truly understand and advance their field, then publications will come much more easily.
I plan on communicating this to him as clearly as possible. I have also drawn up a one-page document detailing my goals for my final semester as an undergraduate, my vision for my master's degree, and what I am looking for in the advisee-adviser relationship. I plan on delivering this document to him and using it as a guide for our discussion. Yes, I am willing to compromise on some points.
Of course, I understand that I can't just have everything my way. But I haven't started grad school yet, and now is the best time to cement the type of experience that I will have. As far as I can see, the cards are in my hands. If my adviser is adamantly against my approach, he can drop me, and I will go to grad school somewhere else.
Well, I wish I had a better question to sum all this up. What are your thoughts?
Edit: I am studying applied mathematics, computation, high performance computing in the United States.