Latina/o Students’ Beliefs about Mathematics, Learning Mathematics, and their Sense of Agency

1. Latina/o Students’ Beliefs about Mathematics, Learning Mathematics, and their Sense of Agency Rodrigo Gutiérrez, Tal Sutton, Erin Turner, Maura Varley University of Arizona CEMELA is a Center for Learning and Teaching supported by the National Science Foundation, grant number ESI-0424983.

2. Aim of the Study • To explore the nature of Latino/a students’ beliefs related to mathematics, mathematical identity, and sense of agency, through analysis of interview data with math club participants. • Part of a larger study focusing more broadly on Latino/a students’ experiences and participation in after-school mathematics clubs. • Cross-site analysis with UIC planned for this Spring- AERA symposium.

3. Theoretical Tools • Learning as Participation (Boaler & Greeno; Nasir) • Positioning and being positioned, taking on roles • Identity and Agency (Holland; Greeno & Gresalfi; Pruyn; Sfard) • Mathematical Identities; Identity as Learners; Identity as Agents of Change • Mathematical Struggle (Middleton & Spanias; Meyer et al.) • Willingness to persist with challenging tasks, linked to mathematical identity

4. Relevant Research Questions

5. Research Context and Participants • Elementary and middle school after-school Math Club (8 elementary and 25 middle school participants) • non-traditional, problem-solving • community-based • critical mathematics • Interview Participants: 5th-8th grade; 11 female, 9 male • Students attended majority-Latino/a schools in Arizona

6. Sources of Data • 2-3 individual interviews conducted with each participant (Early Fall and Late Spring) • Total Interviews: 42 (20 participants) • Focus of Interviews: • Language Use • Beliefs about: • Discipline of math • Self as math learner • Math learning • Beliefs about self as agent of change

7. Sample Interview Questions

8. Data Analysis • Coding: • Group process of review of transcripts, generating codes based on theoretical constructs and the data, defining and refining codes. • Hyperresearch used for organization, coding and analysis • Reliability Coding • Subset of interview transcripts coded by two researchers, discrepancies documented and resolved, and code list refined. • Analysis within and across two sets of data (Elementary and Middle School)

9. Initial Findings: What is Math? • Overwhelmingly numbers and operations • Ex: “I think of numbers, like 2 times 20 or 2 times 100…. When I think of math I just see a whole bunch of numbers and problems go around me and I get dizzy and then I fall because it’s so much work.” Maria, 5th grade • Variety of real world applications (many consumer-related) • Ex: “I think of math as a way that helps your life, like in the store if you want to buy something and if you want to buy two of them then you got to know your math.” Alegria, 5th grade

10. Initial Findings: What it means to be “good at math” • Students see being good at math as measured by external evaluation (grades and test scores). Often, these tests measure one’s calculation speed and/or memorization skills. • “Good math students” engage in behaviors such as doing homework, practicing, paying attention, showing up on time for class. • VERY isolated mention of understanding or the ability to solve challenging problems as indicators of being “good at math.”

11. Initial Findings: Self as Math Learner • Disconnect between how students see themselves as mathematical learners and how they frame being “good at math.” Students see themselves as problem solvers, and describe their problem-solving strategies, while being good at math is primarily attributed to external measures and rote learning-related behaviors. • Ex: Problem solver vs. test scores • Students see themselves as having the capacity to be good at math (i.e., get a better grade). Improving in math is linked to effort/practice and “getting it”. Success in math is not static.

12. Initial Findings: Beliefs about Agency • Dance between Structure and Agency (Pickering) • Students aware that power structures can impede their individual/collective agency (sometimes this goes as far as seeing change as impossible), and structures can be leveraged to support their agency (i.e., gaining the support of people in power). • Power as embodied/operationalized in different ways (people in power, time, money, resources, power of adults over children, resistance to change, etc.). • Collective action (particularly collective action on the part of youth) is critical to effecting change (especially given the constraints to agency).

13. Initial Findings: Beliefs about Agency • Example: • “We’re gonna show [the survey results] to the parents and then show it to the principals and teachers so they can help us make change to the school safety.” Juliana, 7th grade

14. Initial Findings: Beliefs about Agency • Feel they can make change if they “have extra people” or “if the whole community comes together and talks about it.” Maggie and Veronica, 5th graders • “We’re little kids and we want the school to not close and when we showed our video I think the board members really got an idea of how we felt.” Veronica, 5th grade

15. Implications • Have explicit conversations with students about what it means to be good at math, value multiple kinds of mathematical “smartness”* in order to expand notions of what it means to be good at math beyond grades and test scores. *Dr. Marcy Wood’s term • Classroom structures should support students’ agentive beliefs about doing math (involves problem-solving and effort).

16. Implications • A aBroadened notion of mathematics as critical and community-based could lead to stronger sense of critical mathematical agency. • Students’ experiences with critical mathematics has the potential to broaden their notion of what it means to do math and their sense of agency.