Narrativized Identity in Mathematics: 

Understanding the World of Mathematics from Students' Perspectives

Perspective

One perspective forwarded to support students become successful in the domain of school mathematics has been to attend to how students identify with the world of classroom mathematics.  Boaler & Greeno (2000) apply the framework of "figured worlds" (Holland et al., 1998) to compare students participating in two different AP calculus classrooms:  didactic and discussion based. In the didactic classroom, students identified with mathematics as a subject that did not require any thought (Boaler & Greeno, 2000).  In discussion-based classrooms, students identified with mathematics as a subject open to discussion and exploration.    This paper is part of a larger qualitative project aimed at understanding students' identities in elementary school (Author, 2008).  In this paper, I focus on "narrativized identities" (Holland et al, 1998, p. 127).  "Narrativized identities" are situational – the concept is similar to what Vygotsky has referred to as the "subjects individual history" or ontogeny in which individual development and cultural development co-occur (Scribner, 1985).  I argue that attending to students' narrativized identity is critical for designing learning environment that will help students develop expanded mathematical visions (Gutierrez, Sengupta-Irving, & Dieckmann, 2010)

Context & Method

The three focal students in this project were classmates in a 5^th grade classroom and also participated in an after-school math club I facilitated. The after-school club spanned 3 months where students were involved in the Geo-City Project (NCTM, 2001).  To understand student's narrativized identities I pursued the following question: How did different members of the same fifth grade classrooms talk about themselves as math students and their experiences with doing math in their classroom? I collected (a) semi-structured student surveys and (b) pre-project video interviews.  I used a qualitative methodology and used grounded theory (Strauss & Corbin, 1990) to categorize the information in themes.  

Data Sources

Surveys

The survey was designed to understand students' view of themselves and their perception of how others- teacher and peers - viewed them.  To develop themes, I started with the three focal students in this study.   To examine the extent to which the focal students' identities were generalizable to other fifth grade students at the school, I compared their responses to the written responses of thirty-three other students. 

Group Interviews:

The purpose of the group interview was to understand the "normative identity" (Cobb et al., 2005) of students' classroom culture.  Normative identity refers to the norms students would have to affiliate with in order to become "mathematical persons" (Boaler & Greeno, 2000).  In math classrooms, two types of norms have been identified: social and socio-mathematical (Yackel & Cobb, 1996).  Social norms are general norms of participation that may apply to any subject matter and are not unique to mathematics.  In contrast, sociomathematical norms pertain to norms around mathematical discussions and what counts as an acceptable mathematical explanation or justification.  The group interviews were conducted with four students from the same classroom and all three focal students were part of the same group interview.   The development of these themes was informed by the literature in field of math education that examines the relationship between classroom math practices and students math identities (Boaler & Greeno, 2000; Cobb et al, 2005)

Results & Conclusions

Surveys

Figure 1 provides a visual model of the different themes; students' self awareness relative to mathematics, awareness of others (teacher and classroom peers), their individual effort, performance in mathematics, and their history with doing mathematics.         

Figure 1.  Model of student identity in mathematics based on semi-structured surveys

            Analysis of students' surveys (focal and larger group) indicates a range of issue such as self-awareness of "what kind of math it is", how they felt when doing math, what grade they got in class, and whether or not they were in the position to help their peers with doing math.  Though the survey responses were based on students' individual perspectives, they revealed the influence of social aspects on identity development.

Group Interviews:

Figure 2 below is a visual representation of the aspects of students' normative identity. 

Figure 2.  Model of student normative identity in mathematics based on group interview

Analysis of the group interviews revealed that the "normative" identity of who was considered a good math student was formed in relation to the social norms of their classroom and broader institutional practices.  In the classroom, the students were considered a good math student if they aligned themselves with the social norms of the classroom which involved: 1) copying teacher's notes; 2) exactly following the teacher's steps for sample problems; 3) working individually; 4) being categorized based on performance in assessments as well as institutional programs.  As Figure 2 indicates that the normative identity did not involve alignment with any socio-mathematical norms (Yackel & Cobb, 1996) – norms where students were accountable to engage in discussions about mathematics or justify their thinking.  Survey analysis indicated that students (focal and larger group) had narrow views of what is meant to be a good math student.  Conversations from the group interviews indicated that the students had narrow views of what it meant to do mathematics.   Overall, the experiences of the focal students and the larger group appeared to be similar to students in didactic classrooms (Boaler & Greeno, 2000).

Significance:

The results of this study, taken in conjunction with the Boaler and Greeno (2000) study indicates that the practices of didactic classrooms can be a constrain on students developing a "mathematical vision" (Gutierrez, Sengupta-Irving, & Dieckmann, 2010) in both elementary and high schools.  Developing a mathematical vision entails "a socially organized way of seeing, understanding, envisioning and doing mathematics that are accountable to the distinct norms of the mathematical community" (p. 30).  Every classroom that our students enter will mediate students' mathematical visions. To ensure that our students develop expanded visions, I argue that soliciting students' perspectives about their present vision about mathematics – through surveys and interviews -- is a key first step in gathering information to make the necessary adjustments in the learning environment.

References

Author (2008):  "Gimme that calculator" vs. "use your noggin": the development of standard and non-standard positional identities.  Unpublished doctoral dissertation, University of California Los Angeles, Los Angeles, CA. (OCLC No. 287137776) Retrieved July 21 from Worldcat)

Cobb, P., Hodge, L., & Gresalfi, M. (2005). An Interpretive Scheme for Analyzing the Identities that Students Develop in Mathematics Classrooms. In preparation.

Boaler, J., & Greeno, J. (2000). Identity, Agency and Knowing in Mathematical Worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 171-200). Westport, CT: Ablex.

GutiŽrrez, K., Sengupta-Irving, T., & Dieckmann, J. (2010). Developing a Mathematical

Vision: Mathematics as a Discursive and Embodied Practice. In J. Moschkovich, (Ed.) Language and mathematics education: Multiple perspectives and directions for research, a volume in the series Research in Mathematics Education, Barbara J. Dougherty (Ed.), Greenwich, CT: Information Age Publishing, Inc.

Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumenntation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.