This powerpoint was used in my presentation during the PME-NA 2013 conference in Chicago in which I shared my dissertation research.

1. Dismantling the
Birdcage
Relational Problem-Based Learning: Adolescent Girls’
Experiences with an Inclusive Pedagogy for Mathematics
Carmel Schettino, Ph.D. - November 2013

2. If you look very closely at just one wire in the
cage, you cannot see the other wires…You could
look one wire up and down the length of it, and be
unable to see why a bird would not just fly around
the wire any time it wanted go somewhere…There
is no physical property of any one wire…that will
reveal how a bird could be inhibited or harmed by
it except in the most accidental way. It is only
when you step back, stop looking at the wires one
by one and take a macroscopic view of the whole
cage, that you can see why the bird does not go
anywhere; and then you will see it in a moment. It
is perfectly obvious that the bird is surrounded by a
network of systematically related barriers, no one
of which would be the least hindrance to its flight
but which by their relations to each other, are as
confining as the solid walls of a dungeon. (p.5)
-Marilyn Frye, Oppression, in The Politics of Reality
(1983)

3. 
Call for change – movement in math education
(Boaler, 1994; Fennema, 1985; Freire, 1970).

New forms of instruction- support equity and
inclusiveness of underrepresented groups- including
girls and women (Mau & Leitze, 2001; Meece &
Jones, 1996; Solar, 1995).

discussion and more relationally-based teaching
methods researched and recommended (Boaler,
2008; Lubienski, 2007)

Although achievement gap is closing, “interest gap” is
not (higher grades, fewer majors) (Hill, Corbett, & St.
Rose, 2010) and continuing dichotomous cultural view
of mathematical identity (Mendick, 2008, RiegleCrumb et al, 2012)
Education Research Statement

4. An approach to curriculum and pedagogy
where student learning and content
material are (co)-constructed by students
and teachers through mostly contextuallybased problems in a discussion-based
classroom where student voice,
experience, and prior knowledge are
valued in a non-hierarchical environment
utilizing a relational pedagogy.
Relational Problem-Based Learning

6. What is the nature of the relationship between
girls’ attitudes towards mathematics and their
learning of mathematics during and after
experiencing it in an RPBL environment? How do
they describe their experiences?
Enjoyment
Self-confidence
Value
Empowerment
Agency
Research Question

7. A Pedagogy
of Feminist
Relation
Feminist
Mathematics
Pedagogy
Inclusion/No
Hierarchy
Active
Participation
Voice &
Agency
Connection
Relational
Pedagogy
Relational
Equity &
Authority
Relational
Trust
Solar (1995), Anderson (2005),
Boaler (2008), Rodgers &
Raider-Roth (2006), Bingham
(2004), Biesta (2004)
Theoretical Framework

8. Student
Interviews
•Approximately 5 participants, 2 interviews each
•Determine Students’ perceptions of their learning
experience in RPBL
Classroom
Observations
•2-3 Class Observations per Participant
•Determine students' externally observed learning
experience and extent to which RPBL is used by
teachers
Teacher
Interviews
Student
Journals
•2-3 Individual Teachers, 1 interview each
•Determine teachers’ descriptions of students’ learning
experiences
•One Journal per Participant
•Read for additional information about student’s
description of their learning experience
Research Design

9. Name
Leona
Isabelle
Kacey
Sarah
Alanna
Grade
10
9
10
9
9
Teacher
Schettino
Johnson
Schettino
Brown
Schettino
Race
White
Mixed
White
White
AfricanAmerican
SES
Upper
Middle
Middle
Upper
Middle
Lower
Ability
Low
Middle
Low
Middle
High
Interest
Low
Medium
High
Low
Low
Boarder/Day
Boarder
Boarder
Boarder
Day
Day
Student Participants

10. 
Comparison with Teacher Interview, Journal
and class observation Codes

The Listening Guide, VoiceCentered,Narrative Analysis, Gilligan & Brown
(1991)

Coding Maps creating and overlapping
themes vetted (MaxQDA)

Analyzed each girl on Continuum of Girls’
Learning in RPBL based on Brew, et al (2001)
Data Analysis

11. Sample Overlap Diagram

12. Based on Brew (2001), Belenky (1986), Perry (1970), Baxter Magolda (1992)
Absolute Dualism
Transitional Multiplicity
•No voice
•Absolute orientation
towards knowledge
and truth
•Each piece of
knowledge is
discrete
•Listening to others’
voices/Receptive
•Emerging
acceptance of
multiple
perspectives in
areas where
knowledge is
considered uncertain
•directed awaresness
of connected
knowledge
Independent
Relativism
•Listening to the
voice of reason
•Rejection of
absolute truth where
context plays an
important part is
assessing knowledge
•independent
awaresness of
Connected vs.
Separate knowledge
Contextual
Commitment
•Integration of the
two procedural
voices
•Perception that
meaning-making
once expected to
come from outside
themselves, from
authority, emanates
from within
•ability to perceive
the complexities of
interconnectedness
of knolwedge
Voice Awareness in Learning
Dichotomous Truth in Learning
Connected vs. Separate Knowledge
Continuum of Girls’ Learning

13. The Listening Guide – narrative, voicecentered, relational approach
 “often coded, indirect language of girls
and women” (Beauboef, 2007).

Listening
Purpose
First
Plot, Story, What is being told,
Reader Response
Second
I statements coded, I-Poems
formed, stories told by them
Third/Fourth
Contrapuntal Voices listened for,
stories/voices in opposition to
other voices heard?
Narrative Analysis

14. I
You
We
we’d fill in notes
we’d do homework
we still go over the homework
you can really
If you don’t understand
you can definitely ask
I think
in my old class
I was so afraid to ask
all be judging you
Sarah – Passivity to Agency

15. I
You
As you grow
When you turn 18
You have the power
You get to express yourself
No matter what side you’re on
We
I feel like
I could be on
I like to solve it this way
We both get to express
One of us is wrong
If one of us is right
Or even if both of us is right
Changed my identity
Given me a voice
I didn’t really have one before
Leona – Finding Your Voice

16. I
You
You’re more in control
You can
You have to participate
You don’t have to
You choose to participate
You want to help
You want to understand
I didn’t understand
I would go up
I could understand
I expected everybody
I have a question
I ask it
I know
You should not do it
You find out the reason why
Then you’re like “OK”
Isabelle – Transparency

17. Self-Confidence
I can get it
Alanna
C
o
n
t
r
a
p
u
n
t
a
l
V
o
i
c
e
s
Self-Doubt
I wouldn’t comprehend it
I probably would
I want algebra to die
I don’t…
I don’t know
I don’t remember
I would have to do
I could really do
I can’t do those
I can draw
I wouldn’t know
I have those
I wouldn’t know
I just combine
I think
I know the way
I just had to plug
I’ve had practice
I was taught that
I got it
I know the formula
I just put it together
I try not to get confused
I wouldn’t really know

18. I
You
We
I feel like once
you understand the connection
you actually become smarter
you can make connections
I think that’s the beauty
we learned
I love the problems
we do
you can have one problem
we learned
Kacey - Empowerment

19. ABSOLUTE
DUALISM
TRANSITIONAL
MULTIPLICTY
Sarah
INDEPENDENT
RELATIVISM
CONTEXTUAL
COMMITMENT
Sarah
Leona
Leona
Isabelle
Isabelle
Alanna
Alanna
Kacey
Relative Growth on Learning
Continuum
Kacey

20. Encouragement of individual and
group ownership
-journals
-student presentation,
-revoicing and other deliberate
discourse moves
Ownership
of
Knowledge
Dissolution of authoritarian
hierarchy
-discourse moves to
improve equity
-send message of valuing
risk-taking and all ideas
Connected
Curriculum
RPBL
Framework
Shared
Authority
RPBL Framework
-scaffolded problems
-decompartmentalized topics -the
connected nature of mathematics
Justification
not
prescription
-Focus on the “why” in
solutions
- foster inquiry with
multiple perspectives -value
curiosity & assess creativity

21. 
Mathematics education research - Looking “one wire up
and down”

Common wires - standardized testing bias, test anxiety,
self-efficacy issues

no “physical property” cultural, implicit, relational - girls
and women, people of color or students with learning
differences

“network of systematic barriers” - the traditional,
dichotomous, gendered and authoritarian mathematics
pedagogy

RPBL gave a different experience
Conclusions –Dismantle the Birdcage