Mathematics Socialization Through Games: Bilingual Third Graders After School

• In Event: After the School Bell Rings: Opening Up New Spaces for Teaching/Learning Mathematics With Latinas/os

Abstract

In this qualitative study, I examine the interactions of Spanish/English bilingual 3rd graders and adult facilitators in an after-school mathematics club as they play mathematical games. My research questions are based on a characterization of learning and cognitive development that stresses social interactions, particularly between more and less experienced participants (Vygotsky, 1987). This study is inspired by my experience with the UIC-CEMELA after-school mathematics club, Los Rayos, which brought together 3rd grade bilingual students, their parents, graduate researchers, and undergraduates. I treat each game activity as a case study situated within the larger context of the after-school club, Los Rayos, which began in January 2006 and continued until November 2009. The data corpus consists of 35 hours of game activities recorded on video between February 2006 and January 2007. I use discourse analysis with a focus on language tensions (Razfar, Sutton, & Radosavljević, 2009) to understand processes of mathematical socialization in this context.
The types of mathematical thinking norms and customs I consider in this study are characterized by activities such as exploring patterns, framing problems, conjecturing, generalizing, and justifying reasoning processes (National Research Council, 1989; Schoenfeld, 2006). Engagement with these activities is thought to be essential in cultivating a “mathematical disposition” or “mathematical point of view”. During their game activities, participants’ mathematical beliefs and values are visible through their game strategies and discourse. For example, when more experienced participants mark mathematical errors, they use a variety of communicative techniques to support and encourage children’s understanding. The facilitators use suggestions, prompts, questions, hints, directives, praise, demonstration, and modeling. Children also use these communicative devices in the course of game play. This study examines how these communication devices influence children’s understanding, motivation, and persistence as well as how their use changes over the course of game play.
The significance of this study lies mainly with how it can inform elementary mathematics teachers and teacher educators about mathematical socialization through game activities. Mathematical games are promoted as vehicles for learning in mathematics curriculums, as evidenced by NCTM standard 5.1 Communicating about Mathematics Using Games: “Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills”, (NCTM, 2000). Games in general play a prominent role in the history of human intellectual development. However, there is a need for more evidence of how interactions in game activities orient participants to mathematical thinking and learning.
Although particular game structures have embedded mathematics principles, these games alone do not transmit mathematics concepts or modes of mathematical thinking. Rather, it is the people involved in the activities who do the work of socialization (Gauvain, 2001; Gauvain & Perez, 2007). Thus, the focus of my analysis is on the interactions between individuals. These interactions, in turn, shape the way that mathematical norms and values are communicated and constructed.

Author

• Alexander Radosavljevic, University of Illinois at Chicago