Interestingly enough, they use Toulmin‘s model of argumentation as a part of the theoretical framework for their analyses. The research that they report and discuss in this article occurred in the context of a research project called “Informal Mathematics Learning”, which is a project supported by the NSF.
In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants, they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion analyzed in this paper to occur.
Keith Weber, Carolyn Maher, Arthur Powell and Hollylynne Stohl Lee has written an article called “Learning opportunities from group discussions: warrants become the objects of debate” that has recently been published online by Educational Studies in Mathematics. The article deals with the interesting issues concerning discourse and learning opportunities in group discussions. Here is the abstract of the article: