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Abstract and Figures

Despite significant gains in K-12 mathematics achievement, females(1) in the United States are still underrepresented in STEM careers. While many researchers have focused on individual traits of women and girls that might contribute to promoting persistence in these areas, others have taken a broader approach to look at the social practices that routinely exclude women from masculinized spaces. We follow this perspective, and use an interactionist view of identification to shed light on this mechanism. To accomplish this, we take as a starting point the practices of textile crafts, which themselves involve mathematics, but which have traditionally been understood as feminized. In this analysis, we compare six women’s experiences in math classrooms to their experiences in crafting communities with an eye to what differences in these identification processes might contribute to broader sex-linked differences in participation.
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Room for Everyone?
Identification Processes in Crafting
Katherine Chapman, Melissa Gresalfi, Amanda Bell
Vanderbilt University
Email: k.chapman@vanderbilt.edu; melissa.gresalfi@vanderbilt.edu; amanda.m.bell@vanderbilt.edu
Weaving identification from available
engagement practices in CRAFT and in MATH
(* + in math class )
Participant
Lucinda
Olympia
Caroline
2
Mica
Marlo
Paula
Craft
Knitting
Knitting
Crochet
Crochet
Knitting
Knitting
Liked math
Yes
Yes
Yes
No
No
No
Career
Accountant
Librarian
Forms
Specialist
Intermediate
Math Teacher
Student
Services
Administrator
Scientist
Math norms
logical, pattern
-
driven, sense of
a single right answer
concept
-driven, sense of
mathematics as a constellation
of connected topics
sensemaking, particularly to
overcome dyscalculia
as a student
rote, repetitive; as
a teacher
problem-solving,
multiple pathways
solitary, black and white,
confusing, anxiety
-provoking
speed, natural ability, no clear
path
Identification
full identification
full identification, though makes
separate claims about
professional mathematicians
rejected some aspects but
strongly identifies with the
discipline
ambivalent
full rejection
rejected math, though identified
with math
-in-science
Crafting norms
seeing things fall into place;
putting in the time; using
judgment
process
-focus; skilled iteration;
flexibility
balance; flexibility; fuzziness;
fluidity
goal
-oriented; crafter as final
authority; expertise takes time
many ways to engage; fluid
movement between practices;
mistakes are inevitable and
people will help you
process
-oriented; lots of
resources; expertise shows in
product
The goal of this project is to explore how identities develop through
relationships with practices and narratives, connecting with the
significant literature from the Learning Sciences that explores the
situated nature of identity. Specifically, this analysis contrasts identities as
they develop in two distinct domains: school mathematics and craft.
Although there are many differences between school math and craft, we
chose these contexts because they are both spaces where mathematical
thinking and reasoning could occur. However, whereas school math is
often seen as alienating, boring, and accessible only to the privileged few,
crafting is demonstrably a life-long practice that invites broad
participation. We wondered why mathematics is positioned so differently
in these two domains, and whether and how such different positioning
might result in the development of different relationships.
overview
We take a view of identification as an interactional achievement (Cobb,
Gresalfi, & Hodge, 2009; Gresalfi & Cobb, 2011), looking at how personal
identities—the extent to which a person identifies, complies, or resists—
develop in relation to prevailing normative identities in a given social
context (Cobb, Gresalfi, & Hodge, 2011)
theoretical framework
Semi-structured interviews were conducted by one of the first two
authors over the phone, audio recorded, and later transcribed by a third
party. Transcripts were reviewed by all three authors in four distinct
phases of inductive coding.
methods
Remarkable within-person consistency across the contexts of mathematics and crafting.
It is not the case, for example, that each woman was performing in one way in math class and in a completely different way in her crafting community. Rather, in each case, the rationale that the women described for their
identification, compliance, or rejection of the normative identity was consistent, whether for math or for craft. Participants brought something they felt personally committed to—be it a focus on process, a love of logic, or a deep
need for deliberate sense-makingand that was in a sense measured against the local normative identity.
Differences in identification with school math that were not always perfectly aligned with liking math or not.
In three of the cases women rejected the local normative identity of mathematics, resulting in disidentification with mathematics as a discipline. In two cases, individuals identified with the practices of the class, perhaps because
they felt they were recognized and valued in math class. In a final case, one woman was able to carve out her own space in which to identify with mathematics, despite embodying certain conflicts with the local normative identity.
Crafting is a space where everyone can carve out their own way of being.
In this space, multiple identities were recognized and valued, and many women even moved fluidly between those practices, while still maintaining a commitment to a dominant preference. Thus we find, in crafting there is
remarkable consistency across the normative identities available precisely because those identities are themselves heterogeneous, allowing for the legitimate participation of many different kinds of crafters. As a follow on to the
recognition of this consistency, next steps include a potential “lines of practice” reading of engagement in both domains, as suggested by the graphic below.
discussion
We acknowledge that this is a preliminary sketch. Future work will
compare these findings to the larger corpus in an effort to explore any
patterns that emerge, both in other knitters and crocheters, and in
comparison with sewers and weavers. More work is needed to
investigate and document how these identification processes intersect
with the social construction of gender and other identities, both within
and across these different settings.
Furthermore, we seek to further articulate these lines of engagement in
robust problem-solving activities across math and craft. In this figure (at
left) we trace the problem solving and sensemaking activities
described by each participant in the two domains. In all cases
participants described rich engagement in craft that were often absent
in math, or at least absent in math class, further emphasizing how
identification is influenced not merely by personal interest, preferences,
or inclination toward a particular kind of task, but by the opportunities
to engage afforded students in different domains.
limitations and next steps
This work is part of the Re-Crafting Mathematics study, a partnership between Indiana
University and Vanderbilt University, funded by the National Science Foundation
acknowledgements
flexibly using resources
experiencing /pursuing self-sufficiency &
personal judgment
enjoying the feel/process
finding new challenges
problem solving / sensemaking
pursuing beauty
accessing and applying
epistemic authority
pursuing a sense of completion / skill building Caroline
Olympia *
Lucinda *
Mica
Paula Paula *
Marlo
Olympia
Lucinda
key:
Liked math in school:
Caroline
Olympia
Lucinda
Mica
Marlo
Paula
Didn’t like math in school:
in CRAFT only
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The Mathematics of Quilting: A Quilter's Tacit Knowledge of Symmetry, Tiling and Group Theory
  • K Hebb
Hebb, K. (2003). The Mathematics of Quilting: A Quilter's Tacit Knowledge of Symmetry, Tiling and Group Theory. In Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings (pp. 511-520). University of Granada.