Although constructivist discussions in the classroom are often treated as if they were all of the same kind, in this paper I argue that there are subtle but important distinctions that need to be made. An analysis of these distinctions shows that there is a continuum of different constructivist discussions. At one extreme are teacher-directed discussions where students are led to construct the "correct" understanding of a pre-decided conclusion; at the other extreme are unstructured discussions where students are free to construct any understanding. While there are many positions on the continuum, the middle ground is occupied by discussions that find a balance between teacher-control and student-independence, and between having set-answers and a free-for-all. I argue that the Community of Inquiry is a useful conception of constructivist discussions in this middle ground.