Narrativized Identity in Mathematics:
Understanding the World of Mathematics from Students' Perspectives
Perspective
Context & Method The three focal
students in this project were classmates in a 5th 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
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
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.
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.