Learning opportunities from group discussions: warrants become the objects of debate

Abstract

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.

Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms

“…The role of student group discussions in mathematics education has attracted much attention in mathematics education research (e.g., Cobb, 1999 Lee, 2008). Research has produced both several diverse ways of conceptualizing interactions (e.g., Radford, 2011;Schwarz, Dreyfus, & Hershkowitz, 2009) and diverse results in terms of the benefits of group discussions.…”

“…That is, while some researchers conceptualize interactions as, for instance, empowering acts in which citizenship, agency, power and political matters are constituted (cf. Radford, 2011;Valero & Stentoft, 2010), others examine how learning opportunities of content are established in interactions (e.g., Kieran, 2001; Nilsson & Ryve, 2010;Weber et al, 2008). Furthermore, several studies show positive effects of mathematical group work (e.g., Amigues, 1988;Coleman, 1998;Prusak, Hershkowitz, & Schwarz, 2012) while others find that students have substantial difficulties establishing productive group discussions (e.g., Barron, 2003McCrone, 2005Ryve, 2006;Sfard, 2001).…”

Expanding participation in problem solving in a diverse middle school mathematics classroom

“…First, the norms of this study were stable and continued throughout our interactions with the students. An illustration of how some of these norms provided the students with opportunities to engage in sophisticated mathematics is discussed in Weber et al (2008). Second, after observing our lessons, teachers in the school district in which our study was couched were able to successfully create a problem-solving environment that was similar to what was reported here with another group of students.…”

“…We believe these episodes each constitute specific instances where increased participation had specific cognitive benefits for individual children. In Weber, Maher, Powell, and Lee (2008), we discuss the relationship between students' interaction patterns and learning opportunities in more detail.…”

Building a constructivist social learning environment through talk in the mathematics classroom

“…The limited exchange of information and explanation provide the students in collaborative seatwork for just routine learning, but if it is purposed structured conceptual learning with group tasks and ill-structured problems more open exchange and elaborated discussion are necessary (Cohen (1994). According to Weber, Maher, Powell and Lee (2008), learning can be facilitated by group discussion having new claims about the ways and about the standards used in deciding whether an argument is acceptable.…”