The Other Noticing and Noticing the Other: How Teachers and Bilingual Latina/o Students Investigate Mathematics Concepts Through Reciprocal Noticing

• In Event: Noticing Practices of Teachers and Students in Equitable Mathematics Classrooms

Abstract

Reciprocal noticing is an interpersonal, other-oriented, resource-building process in which teachers and students notice each other’s mathematical ideas. The construct is particularly but not exclusively relevant in bilingual Latino classrooms, where it has been investigated (Dominguez, 2013; 2012). Its importance in these contexts is that it brings teachers closer to students’ voices and perspectives (Confrey, 1998); it transforms teachers’ ideas of students from receivers of information to students as researchers (Kincheloe & Steinberg, 1998); and it promotes a classroom culture based on hermeneutical noticing (Davis, 1996; Crespo, 2000).

Teachers of Latino/a students (and students of color in general) are predominantly White with personal histories that have little in common with those of their students (Hollins & Guzman, 2005; Gay, 1993). This lack of shared experience extends to teaching and learning resources, as teachers of Latinos/as tend to notice what Latino/a students cannot do and link these perceived limitations to other deficit perspectives. Teachers’ failure to notice students’ ideas leads to students’ disinterest to notice as well, and eventually escalates to students’ withdrawal from participation. The nonreciprocal nature of these relationships shortchanges teachers and students, and opportunities to create common resources for teaching and learning mathematics are lost.

The research activities discussed in this presentation involved teachers and students in three analytical categories: togethering (Radford & Roth, 2012), mathematical caring relationships (Hackenberg, 2010), and exploratory talk (Mercer, et al, 1999). The study is guided by the interpretivist methodology, and also by critical theory, by focusing on how reciprocal noticing can transform classroom interactions with Latino/a students. Drawing from a conjecture-driven perspective (Confrey & Lachance, 2000), participating teachers developed conjectures based on what they noticed and their interviews with students about what they were noticing. These conjectures began by noticing something uncommon between the teacher’s understanding and the students’ understanding of a particular topic (e.g., estimation). Teachers continuously refined their conjectures until both teachers and students came to a common understanding of a math topic. Ongoing and reflective analyses of interactions supporting the development of teacher conjectures were used.

To capture this process, video data were collected during mathematics instruction in the participating teachers’ elementary classrooms (two classrooms in two different states). Transcripts and summaries were prepared of selected videos, particularly those lessons in which conjectures were beginning to form and then tested. Additional data sources—used to triangulate evidence—included the researcher’s field notes, analytic memos, teacher-researcher e-mail messages, videotaped teacher-researcher planning sessions, student work, and teacher and student interviews.

The study suggests that noticing the other—bilingual Latino/a students in this case—is a different experience for different teachers. While some teachers experienced great challenges learning how to elicit and include student noticing, other teachers appropriated reciprocal noticing to the point that each year that they welcomed a new group of students, they renewed and refined the conjectures previously investigated with other groups of students. In this presentation I illustrate both types and how the three analytical categories have contributed to teachers learning to notice mathematical ideas together with their students.

Author

• Higinio Dominguez, Michigan State University