By Bronwyn Bevan - March 2011
Esmonde, I. (2009). Mathematics learning in groups: Analyzing equity in two cooperative activity structures. Journal of the Learning Sciences, 18(2), 247–284.
This article discusses the design and conditions of high school mathematics activities that aim to distribute opportunities to learn to all students. Of particular interest to ISE educators is the analysis of how some ostensibly equitable group activities—where in theory all children have the opportunity to discuss and develop understanding—may be implemented in ways that may shut down equal participation. Also of interest is the theoretical discussion of the relationship between opportunities to productively participate in mathematical activities and the development of positive mathematical learning identities.
The author conceptualizes learning as encompassing opportunities to be socialized into particular mathematical practices and also opportunities for students to position themselves as knowers and doers of mathematics; i.e., opportunities to develop knowledge, skills, practices, understandings, and identities. Esmonde conceptualizes identity not as an individual trait that one carries from place to place in one's life, but rather as the way in which a person positions him/herself at particular moments in his/her life.
This article is concerned with how learning activities are structured and enacted to provide studentsaccess to identities, that is, "opportunities to develop positive positional identities that place them as authoritative and competent members of the classroom community" (p. 251). The relationship between opportunities to access positive identities and the longer term development of an identity trajectory has been noted to be complex (Nasir & Saxe, 2003) and is beyond the scope of this article. ISE educators, who frequently have limited temporal access to learners (e.g., one summer, or one set of Saturdays), may be especially interested in how they can design rich experiences that provide opportunities for learners to access positive identities during the programs, and that potentially contribute to the life-long trajectory of identity development for participants.
The article describes two activity structures: (1) a group quiz, where students work in teams to answer math questions in the quickest and most correct manner; and (2) a group presentation activity where students solve problems and then one of the members presents it to the class. The researcher examined the ways these activities were structured to allow students to discuss, share, explain, and develop their understanding of mathematics. Her findings challenge some assumptions about the a priori value of providing students opportunities to talk to one another in class.
Visibly the groups appeared to be highly collaborative, with talking, sharing, and pointing to each other's worksheets. However, a closer examination found that, frequently, the emphasis on getting the right answer positioned the student already identified as being strong in math as the group expert. As such, and contrary to assumptions about the benefits of providing students opportunities to talk and interact, the underlying activity structures actually shut down talk by students who were not already perceived by themselves or their peers as strong in math. Instead, the less strong students deferred to the answers provided by the "group expert" student, and the group expert provided "answers" without "explanations" to the rest of the team.
The quiz activity in particular led to superficial mathematical discussions, oriented on answers and not reasoning. In the group presentation activity, the researcher found that, while there was a broader array of ways to participate, students did not always opt to collaborate and participate. Thus while the opportunities may have been present, students did not always seize them.
This study suggest that ISE educators—who frequently design activities to be social, collaborative, and ostensibly inclusive—must take care to distinguish between activities where all students have opportunities to share and develop their knowledge—and thus access increasingly positive identities with respect to their ability to do and know math—versus those that enable students already strong in the subject matter to dominate the process.
For further reading, see Nasir, N., & Saxe, G. (2003). Ethnic and academic identities: A cultural practice perspective on emerging tensions and their management in the lives of minority students. Educational Researcher, 32(5), 14–18.