The goal of constructivist learning is to produce students who self-regulate. Self-regulation moves students from dependence on the teacher for feedback and direction to self-reliance. This is "taught" by modeling the thought processes for solving problems--either by the teacher or peers. Once students get used to "thinking about how they think," they become more adept at seeing logical steps in their own problem solving.
In my classes, I allow for a lot of group discussion. I think it is very important for students to hear the opinions of their fellow students, and smaller groups allow students that are not normally outspoken in whole-group discussion to be more vocal. History is sometimes easier to understand when students can discuss events with their peers. Discovering patterns in historical events is also easier to do when students are able to talk about these events. Group projects are the closest thing to discovery learning that I have used in my classroom. I give each group a different topic to research and teach to the rest of the class. Usually, however, I have already given preliminary information on the topic, so I am not sure if that can qualify as true discovery learning.
It was interesting to read what some of my classmates wrote on the topic of student-centered learning this week. I remember one post in particular where a teacher was reluctant to give up control over her classroom in order to allow for group activities. I replied that you can still have control over your class while they work cooperatively. As long as you have set behavior guidelines, and have been firm and fair in dealing with problems, your class is still well under your control when they work in groups. I think it's very important for students to take more responsibility for their learning, and if that means less "stage time" for me, then that is how I need to teach!