Exploring the Mathematics Re-socialization Processes of 3 Latino Students

Transcription

1 CEMELA Exploring the Mathematics Re-socialization Processes of 3 Latino Students Carlos A. López Leiva, Zayoni Torres, & Gabriel Viego The University of Illinois at Chicago

2 Overview Background Theoretical Framework Research Questions Methods Findings Continued Discussion The data used in this presentation were originally collected in an after-school research project conducted by Dr. Lena Licón Khisty, Principal Investigator, University of Illinois Chicago (UIC) as part of the Center for the Mathematics Education of Latinos (CEMELA), University of Arizona. CEMELA is supported by the National Science Foundation under grant ESI The views expressed here are those of the author(s) and do not necessarily reflect the views of the funding agency.

3 Background: Los Rayos CEMELA-UIC partners with a Chicago public elementary duallanguage school for an after school mathematics club. Student population nearly 100% Latina/o Low-income large urban neighborhood Design alike La Clase Mágica (Vásquez, 2003) & The 5 th Dimension (Cole, 2006) Non-remedial Curriculum (probability, algebraic thinking, proportional reasoning, geometry) Bilingualism and dialogue fostered among participants Sessions twice a week for 90 minutes each Participants: self-selected students, pre-service teachers, mothers, fellows Student Name Race/Ethnicity Grade Level Rolando Latino 3 rd -6 th Graciela Latina 3 rd -6 th Candy Latina 3 rd -6 th

4 Theoretical Framework Inter-subjectivity, sense making in joint activity with others Funds of knowledge transformed into meaningful activity Equalized social interaction, equal validation Sociocultural perspective (Vygotsky, 1978) Zone of Mathematical Practice (Gonzalez, Andrade, Civil, & Moll, 2001, p ) Mathematics socialization (Martin 2006, p. 150) Experiences of individuals in contexts that legitimize or inhibit meaningful participation in mathematics Playful, accessible, natural kind of mathematics School Practices

5 Research Questions How did the afterschool program mediate the emergence of a zone of mathematical practice among its participants? How did participating within ZMP overtime mediate the appropriation of new mathematical practices and strategies for Latina/o learners? What were the processes involved in re-socializing the way that Latina/o learners engaged in mathematics within ZMP?

6 Methods Qualitative methods & Discourse analysis Data Sources: Primary Sources Secondary Sources Video Tapes Interviews Student Work Facilitators Field Notes Data analyzed across sessions mapping: development of particular mathematical ideas changes in a participant s thinking and/or discursive encounters dialogue examined in light of study s questions Results emerged in set of themes related to the ZMP: Re-socialized processes: social networks, use of tools, Mathematical Discourse, & play. Excerpts in this presentation portray main features of this re-socialization process but in only one of our student cases.

7 Findings: Candy s Pre-re-socialized Math Practices Eddie compró 23 manzanas. Le dio 12 a su hermana. Cuánto quedó en total? Eddie bought 23 apples. She gave 12 to her sister. How many does she have in total? 1) 2) 3) 4) 5) 1. Los números que me ayudan/ The numbers that help me 2. La operación numérica/ Numerical operation 3. Escribe una oración/write a sentence 4. Sumaste o multiplicaste, restaste, o división/ Did you add, mutiply, subtract, or divide? 5. Por qué hiciste lo que hiciste?/ Why did you do what you did?

8 Findings continued: Candy s Pre-re-socialized Math Practices Si Candy tenía 100,000 primos y encontró 10,000. Cuántos tiene ahora? If Candy had 100,000 cousins and she got 10,000, how many would she have now? a) Inter-subjectivity, joint-sensemaking activity b) Equalized social interaction c) Playful, natural math d) FOK meaningful activity *Use of L1 *Agency/ownership X 1/2? 1/2

9 Findings: Candy s Re-socialized Math Practices 1. If I have 24 people and 56 hearts, how many will each people will they get?

10 Findings: Candy s Re-socialized Math Practices

11 If I have 24 people and 56 hearts, How many hearts will each people will they get? - Our initial expectation: - What Yessenia & Candy did: a. 1 heart for e/o 2 hearts for e/o c. e/heart into thirds b. d. 8 hearts left for everyone

12 Findings: Candy s Re-socialized Math Practices 2. Aquí te mando un problema, cuántas veces más necesitas repetir o multiplicar esta línea de caritas para tener más de 100 caritas? I m sending a problem, how many more times do you need to repeat or multiply this line with happy faces to have more than 100 happy faces? 3. I have 144 horses. I have 6 friends. How many horses will my friends get? Yo tengo 144 caballos. Yo tengo 6 amigos. Hay para cada uno de mis compañeras?

13 Summary: Candy s Re-socialized Math Practices X 1/2? 1/2 ZMP a) Inter-subjectivity, joint-sensemaking activity b) Equalized social interaction c) Playful, natural math d) FOK meaningful activity *Use of L1 *Agency/ownership Pre-Re- Re- 1/2

14 Zone of Mathematical Practice (Gonzalez, Andrade, Civil, & Moll, 2001, p ) School Practices Mathematics socialization (Martin 2006, p. 150) Re-socialized processes: Social networks Use of tools Mathematical Discourse Play Experiences of individuals in contexts that legitimize or inhibit meaningful participation in mathematics

15 Contact Information Carlos A. López Leiva Zayoni Torres Gabriel Viego

16 References Cole, M. & The Distributed Literacy Consortium. (2006). The Fifth dimension: An after-school program built on diversity. New York, NY: Russell Sage Foundation. Gonzalez, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics. Journal of Education for Students Placed at Risk, 6(1&2), Martin, D. (2006). Mathematics learning and particiption as racialized forms of experience: African American parents speak on the struggle for mathematics literacy. Mathematical Thinking and Learning, 8(3), Vásquez, O. A. (2003). La Clase Mágica: Imagining optimal possibilities in bilingual community of learners. Mahawah, NJ: Lawrence Erlbaum Associates. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.