Traditional models focus on teachers as being the sole providers of instruction. The CLM argues that the aquistion of knowledge requires active participation. Students should observe and question topics that are of interest to them and then investigate those topics to construct their own understanding. By working in small groups, students share, critique, and defend their understandings.
Constructivism is a great idea and it's a great way to teach.
However, I too do not feel that a completely constructivist class is very practical. Not that it would not be worth it professionally and for the students, but that it is a lot to do, specially for a new teacher.