Let's say you want to assign independent research in your science class. What a laudable goal -- whether you're doing laboratory or library work, the opportunity for a student to carry through his own project to completion can be a meaningful and memorable experience. If it's done right. If it's not done right, the project can be either a frustrating turn-off to your course, or an object lesson in bull%#$@.
Successful research, of any type and at any level, starts with a well defined and appropriately scoped problem or question. The most critical part of mentoring student research is crafting that problem or question for the student.
Yes, I know that we want the students to be invested in a problem, we want to allow them to pursue topics of interest to them. Thing is, high school students do not generally have the experience or background to know what types of problems are interesting or doable. If you ask them what they want to do, they'll say something like "build a small scale nuclear reactor" or "find a way to power a car with saltwater."*
* Or, likely, "um, well, I don't know, can we blow something up?"
It's the teacher's job to make that critical decision of what to investigate. Well-chosen problems can set everyone in the class up for success, including both those who are perfectly motivated self-starters and those who need a prod to get things done. You must supervise these projects, after all, and you'll be stuck doing the prodding where necessary. It's probably a good idea to make sure there's some hay in the direction you're prodding, right?
Now, there's nothing wrong with presenting students with a menu of possible investigations, allowing them some choice. I've done this with my "pseudoscience" investigations: I hand the class a list of about twenty statements, such as "aliens built the pyramids" or "vaccines cause autism." Each student is asked to pick one of the statements to investigate. My colleague who teaches sophomores runs a "mythbusters" project; he provides a wide choice of topics like "a piece of food picked up from a dirty floor within five seconds is still safe to eat."* Sure, students can propose something new, but Jason makes the final decision based on what he thinks can be successfully accomplished.
*Myth status: irrelevant. Boys and dogs will eat off of the floor regardless.
Point is, if you assign topics or give limited choices, the students will in no way be upset; they will just dive in to the assignment. But if you allow them to waffle for a week about what they're gonna do, you've lost that week of work, and you've created ill will when their choice turns out to be unworkable.