Response to a reading of Erna Yackel and Paul Cobb on Sociomathematical norms, argumentation and autonomy in Mathematics.

The normative understanding of what counts as Mathematically different, Mathematically sophisticated, Mathematically efficient and Mathematically elegant in a classroom are the socio-mathematical norm. The writer gives the difference between the socio-mathematical norm and a social norm as former to be what constitute the argument and later as the case or class discussion. What accounts as an acceptable Mathematical explanation and justifiable is the socio-mathematical norm. Class discussions are supposed to be supervised by the teacher so that it leads to proper learning and acquisition of mathematics concepts. Students given a chance for arguments may deviate and end up not having a healthy class discussion leading to achievement of the lesson objective,  professionalism should be displayed to provide direction when conducting class discussions.

The teacher is required to regulate mathematics argument so as to influence the learning opportunity. Students should be guided to argue their points at appropriate moment so that learning takes place. The writer gives a fascinating example of why students need to stick to their answers when they are sure of it or the need for learners to provide concrete answers. The student who changed the answer, but could not when asked her name remained same after asked more than once.

In my teaching experience, I could let group leaders choose members of the group alternatively, as they choose those who could help them in solving mathematics problems, give a task and then do the marking. Students from another group could name a member of a competing team, one they suspect may not handle the given task competently this will warrant named student perform the work on white board for all to witness steps involved. Each group is supposed to teach one another in how to do the task they got as a group well. Another one they would sit beside one a student choose to compete and argue how they reached to a conclusion of each mathematic problem. This method gave learners extensive experience on handling different questions.

The timed lessons may not urger well with this method since if not carefully monitored by teachers ,then students may end up discussing other experiences irrelevant to the lesson. It is demanding situation for teachers because they have to try make sense of the wide array of solutionsoffered by children [Carpenter, Ansell, Franke, Fennema, and Weisbeck 1993].This way of learning mathematics develops intellectual autonomy which is a major goal in current educational reform movement. The reform is in agrement with Piaget [1948-1973].
Question
Most teacher will agree with me that class discusion is an important laerning tool and if not supervised well may lead uneccesary argument and time consuming,  how do you captualise and give proffessional guidelines ?