1. Dismantling the Birdcage Adolescent Girls’ Attitudes towards Learning Mathematics with a Relational Pedagogy in a Problem-Based Environment

2. -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)

3. 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 (Boaler, 2008; Lubienski, 2007) Although achievement gap is closing, “interest gap” is not (higher grades, fewer majors) (Hill, Corbett, & St. Rose, 2010)

4. 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)

5. 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.

6. 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

7. Research Design Approximately 5 participants 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 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

8. Teacher Participants Teacher # of sections Education Years of teaching experience Years of Teaching RPBL Ms. Brown1 B.A., Math M.A.T, Education 133 Ms. Johnson2 B.S. Physics M.S., Physics and Engineering 83 Ms. Schettino2 B.A. Math M.A. Math 1915

9. Student Participants NameLeonaIsabelleKaceySarahAlanna Grade109 99 TeacherSchettinoJohnsonSchettinoBrownSchettino RaceWhiteMixedWhite African- American SESUpperMiddle Upper Middle Lower AbilityLowMiddleLowMiddleHigh InterestLowMediumHighLow Boarder/DayBoarder Day

10. Data Analysis The Listening Guide – narrative, voice- centered, relational approach “often coded, indirect language of girls and women” (Beauboef, 2007). ListeningPurpose FirstPlot, Story, What is being told, Reader Response SecondI statements coded, I-Poems formed, stories told by them Third/FourthContrapuntal Voices listened for, stories/voices in opposition to other voices heard?

11. Further Analysis Comparison with Teacher Interview, Journal and class observation Codes Coding Maps creating and overlapping themes vetted (MaxQDA) Analyzed each girl on Continuum of Girls’ Learning in RPBL based on Brew, et al (2001)

12. Sample Overlap Diagram

13. 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 )

14. Sarah 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

15. Leona 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

16. Isabelle 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”

17. Alanna Self-ConfidenceSelf-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

18. Kacey 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

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

20. RPBL Framework

21. Conclusions –Dismantle the Birdcage For years, researchers looked “one wire up and down” trying to explain the reasons behind why girls were not achieving in mathematics – there was a gender gap, they said. Once that was dispelled, they moved onto other wires of the cage of oppression in the mathematics classroom – standardized testing bias, test anxiety, self-efficacy issues – the list goes on. Unfortunately, there is no “physical property” on any one wire that will explain for us all what the reasoning is. It is different for many girls and women, people of color or students with learning differences. What seems to be the case is that there is a “network of systematic barriers” in place and sadly it is the traditional, dichotomous, gendered and authoritarian method in which mathematics is viewed and taught in our society. It is this very system that serves as the “walls of the dungeon” for underrepresented students in mathematics and what hinders them from fully experiencing mathematics as it should be – a sharing of ideas and discovering of patterns in open creativity with intellectual peers.