We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they should.

In response to this, faculty I know do everything from constructing elaborate daily homework exercises graded with various degrees of rigor, to simply giving students weekly quizzes and midterm exams...since if the students aren't going to take responsibility for the feedback given to them, there really is no point in sinking many, many extra hours grading homework. In fact, many mathematics faculty report very little gain from grading homework, which may be related to the sort of damping phenomenon found in certain answers to this helpful question on grading homework.

Of course, depending on the type of institution, the answers to my following question will differ. That said, there must be some research to help us guide our efforts to build a sense of responsibility and autonomy of study in our undergraduate students.

Question: What is an appropriate amount of responsibility for an undergraduate student in mathematics courses, roughly classified by student year (Freshman, Sophomore, Junior and Senior). Please discuss in particular Freshman service courses like Calculus and Finite Mathematics. What I mean by responsibility is, essentially, how much and what sort of professor feedback foster optimal student performance? What, according to mathematics education research, is an appropriate amount of responsibility to put on undergraduate students in mathematics courses?

The purpose of this question is, roughly, to address the difficulty that comes from giving either too much or too little feedback to one's students. Qualitatively, colleagues have noticed that when faculty over-organize student work, students continue to expect this and don't take on adequate responsibility for their mastery in later coursework, whereas too little guidance in early courses simply leads to disastrous outcomes since students seem to leave high school with very little sense of how to appropriately study.

The purpose of this question is to provide some sort of standard guidelines for determining when it is best to "remove training wheels" etc. for undergraduate students.

I personally try to use in Inquiry Based Learning approach as early on as possible that puts a great deal of responsibility on the students, but this may not be best, scientifically. EDIT: I should flesh this out a bit. Students seem to come to college without the idea that they both need to teach themselves AND we need to teach them. The IBL approach puts a ton of responsibility on students to create knowledge for themselves, but requires a lot of energy from the instructor to guide that knowledge creation. The general idea is that student homework is the content that drives an IBL course, and the professor evaluates this content production. This, in contrast to an instructor meticulously grading homework and passing it back in order for it to be glanced at and filed away or thrown in the bin. IBL puts enormous responsibility on the student, and a lot of work on the professor. I'm wondering how much of such responsibility is best, according to research.