First, thank you all for the interesting and helpful comments! I was a little nervous to post at first.
My experience is that few graduate students really get training in this...many a masters or doctoral project is based on a pre-existing research question determined by the advisor.
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Ideally we'd all come out of grad school prepared to crank out ingenious and creative grant proposals. In reality many of us need additional training and experience before we can really consider ourselves researchers.
Bingo. My MS project, which I really did enjoy, was an idea that had been floating around in my advisor's head for some time. I'm encouraged to know that although this maybe isn't ideal, it's not uncommon to feel a little unprepared even after an MS.
... Finding a good mentor who is both intellectually compatible and encouraging, but who will also prod one along, is really, really important.
And I believe there's really no way to know ahead of time how much or how little one will enjoy the research process. It's filled with uncertainty and ambiguity, which some people find very difficult to tolerate, and demands a lot of perseverance even when things just aren't going well--another difficult skill. Were there parts of the process of doing research that you really loved and/or really hated? (And it's always pretty hideous the first time!)
I'm loath to lay too much blame on my advisor but looking back now, I can see ways that I could have been a much better grad student and he could have probably been a better mentor. I was his first grad student so we both had a lot to learn.
I'm glad to hear that a hideous first experience is not abnormal. As for what parts I loved and hated, I loved the literature searching. It was so interesting to go into depth and to really understand what had been looked at in my little subfield. I love library research and I think that's one area I did very well in and did persevere when it felt like just going down blind alleys.
I don't think I specifically hated any part of the research. What I hated was just not knowing how to really think about problems in my field. I felt like I would dig in to something and then just hit a wall and I could scratch at the wall but not get through it. One of the members of my committee was just an amazing scientist - he just understands the Earth's processes so deeply and I am just in awe. I want to get to that level.
All of the parts of research that truly are skills can be taught if you are willing to learn, try new things, and can find someone whose methods of giving criticism and feedback match well enough with your methods of learning.
I think this is a good mission statement for me, moving forward. I'm not sure I was as willing to learn back then. In the time since my MS, I think I've gotten better at knowing that I need to ask questions sometimes, find the answers on my own other times, and overall, be more receptive to feedback and criticism. At times, it's been rather painful to realize how little I knew back then and how much more I could have learned.
I truly appreciate all of your comments and insights. It's given me a lot to think about and consider.