I think a teacher in a constructivist math classroom is the driver of the learning process. He /she is there in the classroom to facilitate the learning of mathematics through learner self discovery.
I suppose, in a constructivist math classroom the learning is learner-centred. Further, learners get to the solution of the problem for themselves through the guidance or probing questions from the teacher. That means in the learning process, learners are getting to the solution of the problem by constructing their thoughts using their existing knowledge before the problem was presented , then by giving it more thoughts and new knowledge discovering the problem solution is acquired.
In a constructivist class the teaching and learning should be guided by the theory of constructivism, as opposite to the traditional theory in teaching,which is characterised by the use of textbook and most of the talking is from the teacher. Whereby learners are getting knowledge from textbooks with the help of some few examples from the teacher.