Positioning and Latinas/os: A Study of Small-Group Interactions in Mathematics

Current approaches in mathematics education emphasize collaborative learning and problem solving (Baumeister & De Walle, 2005; NCTM, 2000). Although social interactions are relevant to these processes, the quality of interactions may not always guarantee the equitable distribution of opportunities for learning among participants (Moll, 2001; Zevenbergen, 2001). Some approaches have suggested interactional structures to promote equalized participation. Nevertheless, this study further explores spontaneous processes of how social interactions mediate student positioning as they problem solved in small groups. This interest emerged through direct observations and reviews of theoretical stances developed by the author in relation to the phenomenon of positioning as it was empirically detected through the work of students and facilitators in a mathematics afterschool program (Khisty, 2004). Using sociocultural (Lave & Wenger, 1991; Martin, 2006; Vygotsky, 1978) and Positioning Theory perspectives (Harré & Van Langenhove, 1999), this qualitative, longitudinal, ethnographic, and multiple-case study with instrumental purposes (Stake, 1995) explores the social interactions of four Latina/o bilingual students who attended the program for over three years (3rd-6th grades). These four represent contrasting cases of positioning regarding social status, school grades, and language fluency (Spanish and English). The comparative analysis (Miles & Huberman, 1994) of videotaped interactions, facilitators’ field notes, and student-developed artifacts focused on face-to-face interactions, language usage, and positioning patterns over time. These analyses identified three factors mediating the co-construction of various positions: attention, alignment, and ability. Positioning was found to be flexible and recurrent, and linked to language codeswitching practices and power dynamics. Positioning afforded students differentiated quality of both opportunities to understand and use mathematical concepts during problem solving as well as the social support in the group. This demonstrates that all students can have access to productive positions during social interactions, but also that interaction trends may reify specific kinds of positions in a group for particular students. Thus habitual trends of interaction create separate pipelines of student performance by supporting those with already high levels of mathematical understanding and limiting those struggling with mathematical concepts or practices. Issues of language use in positioning and implications for teaching and research are elaborated on and discussed.