Ritual as Lens: The Cultural Nature of Teaching Fraction Operations in a Fifth-Grade Classroom

• In Event: Roundtable Session 10
  In Roundtable Session: Teachers and Teaching: Why the Distinction Is Important and What It Might Mean for Mathematics Education Research

Abstract

This paper reports on a study concerning the persistence of some teaching practices in elementary mathematics classrooms in the United States. Beginning with the premise that mathematics teaching is a cultural activity (Gill & Boote, 2012), a definition for the analytic lens of ritual (Quantz, 2011) was proposed: that aspect of action that is formalized, traditionalized, symbolic performance. This lens was used to gain insight into the causes and effects of some common mathematics teaching practices from a 5th grade classroom that was studied by a three-member research team for four months. The data presented here comes from a three-week long instructional unit in April 2013, in which Paige, the student teacher, taught the 25 students about multiplication and division of fractions with support from Henna, her mentor teacher, and Wanda, her supervisor. During the unit we observed a range of classroom practices, some of which supported students’ developing mathematical understanding and some of which may have limited the possibilities for student learning. Ethnographic methods (Eisenhart, 1998; Spradley, 1979; Wolcott, 1994) were used to guide all fieldwork, namely classroom observations and interviews with teachers. Fieldnotes taken during the 13 lesson observations recorded statements and behaviors of students and teachers, and interview protocols were developed to prompt the three teachers’ perspectives on teaching practices we had noted to be suggestive of aspects of ritual. The interview transcripts formed the major source of data for this study. Rather than accounting for the range of teaching practices using descriptions and analyses of Paige’s personal characteristics—such as her beliefs about teaching or her “limiting” mathematical or pedagogical knowledge—we instead sought to foreground the cultural nature of teaching and learning-to-teach mathematics by asking What were the aspects of ritual in this unit and what insights do they provide as we seek to understand Paige’s mathematics teaching? We found that Paige’s teaching practices seemed to show evidence of being formalized in that she seemed to value the role of “story problems” when posing problems; traditionalized in that “outside” influences such as students’ parents and siblings made their way into classroom discussions; symbolic to the extent we can make informed inferences about the messages students may have been receiving through instruction; and a performance, in that we identified ways that Paige was aware of and responsive to multiple audiences. Each one of these results can be considered significant, but taken together, these results help paint a picture of the mechanisms by which Paige’s mathematics teaching was influenced by culture. Stigler and Hiebert (2009) write that “what teachers do in the classroom, the methods they use to interact with the students about the content, are not determined as much by their qualifications as by the culture in which they teach” (p. xii). Ritual is not the only way, but it is a particularly promising way that practitioners and researchers in mathematics education can continue to acknowledge and address the complexity of this work.

Authors

• Andrea McCloskey, The Pennsylvania State University

• Gwendolyn Lloyd, The Pennsylvania State University

• Courtney Lynch, The Pennsylvania State University