Dismantling the Birdcage

Relational Problem-Based Learning: Adolescent Girls’ Experiences with an Inclusive Pedagogy for Mathematics

Carmel Schettino, Ph.D. - November 2013

-Marilyn Frye, Oppression, in The Politics of Reality (1983)

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)

Education Research Statement

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, Riegle-Crumb et al, 2012)

Relational Problem-Based Learning

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

Research Question

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

Theoretical Framework

A Pedagogy of Feminist

Relation

Feminist Mathematics

Pedagogy

Inclusion/No Hierarchy

Voice & Agency

Active Participation

Connection

Relational Pedagogy

Relational Equity & Authority

Relational Trust

Solar (1995), Anderson (2005), Boaler (2008), Rodgers & Raider-Roth (2006), Bingham (2004), Biesta (2004)

Research Design

•Approximately 5 participants, 2 interviews each

•Determine Students’ perceptions of their learning experience in RPBL

Student Interviews

•2-3 Class Observations per Participant

•Determine students' externally observed learning experience and extent to which RPBL is used by teachers

Classroom Observations

•2-3 Individual Teachers, 1 interview each

•Determine teachers’ descriptions of students’ learning experiences

Teacher Interviews

•One Journal per Participant

•Read for additional information about student’s description of their learning experience

Student Journals

Student Participants

Name Leona Isabelle Kacey Sarah Alanna

Grade 10 9 10 9 9

Teacher Schettino Johnson Schettino Brown Schettino

Race White Mixed White White African-

American

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

Data Analysis

Comparison with Teacher Interview, Journal and class observation Codes

The Listening Guide, Voice-Centered,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)

Sample Overlap Diagram

Continuum of Girls’ Learning

Absolute Dualism

•No voice

•Absolute orientation towards knowledge and truth

•Each piece of knowledge is discrete

Transitional Multiplicity

•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

Based on Brew (2001), Belenky (1986), Perry (1970), Baxter Magolda (1992)

Voice Awareness in Learning

Dichotomous Truth in Learning

Connected vs. Separate Knowledge

Narrative Analysis

The Listening Guide – narrative, voice-centered, 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?

Sarah – Passivity to Agency

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

Leona – Finding Your Voice

I You We

As you grow

When you turn 18

You have the power

You get to express yourself

No matter what side you’re on

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

Isabelle – Transparency

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”

Alanna

Self-Confidence Self-Doubt

I can get it

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

C

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a

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V

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Kacey - Empowerment

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

Relative Growth on Learning Continuum

Sarah Sarah

Leona Leona

Isabelle Isabelle

Alanna Alanna

Kacey Kacey

ABSOLUTE DUALISM

TRANSITIONAL MULTIPLICTY

INDEPENDENT RELATIVISM

CONTEXTUAL COMMITMENT

RPBL Framework

RPBL Framework

Connected Curriculum

Justification not

prescription

Shared Authority

Ownership of

Knowledge

-scaffolded problems -decompartmentalized topics -the connected nature of mathematics

-Focus on the “why” in solutions - foster inquiry with multiple perspectives -value curiosity & assess creativity

Encouragement of individual and group ownership -journals -student presentation, -revoicing and other deliberate discourse moves

Dissolution of authoritarian hierarchy -discourse moves to improve equity -send message of valuing risk-taking and all ideas

Conclusions –Dismantle the Birdcage

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