Aprender en los márgenes: posicionamiento y pensamiento algebraico de un estudiante haitiano en un aula chilena
DOI:
https://doi.org/10.4151/07189729-Vol.64-Iss.1-Art.1637Palabras clave:
Ambiente educacional enseñanza de las matemáticas educación inclusiva multilingüismo relaciones entre paresResumen
Este estudio exploró las experiencias de aprendizaje en el aula de Daniel, un estudiante haitiano de tercero básico, mientras resolvía tareas algebraicas con su grupo de pares. Desde una perspectiva no deficitaria del bilingüismo potencial, el análisis se centró en las dinámicas de posicionamiento dentro del grupo y en el pensamiento algebraico de Daniel, a partir de un enfoque de cognición corporizada. Los resultados revelan que, a pesar de las dificultades de Daniel para realizar cálculos básicos y expresar sus ideas en español, mostró un notable potencial para la generalización algebraica, evidenciado principalmente a partir del repertorio gestual. No obstante, el análisis de las interacciones con sus pares mostró que, a pesar de su capacidad sobresaliente, las ideas de Daniel fueron mayormente ignoradas o no desarrolladas por sus compañeros. Estos resultados subrayan la necesidad de abordar las dinámicas de exclusión en la enseñanza de la matemática.
Citas
Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 267-299.
Araya, P. (2024). Algebraic thinking and learners' second language: Importance of the analysis of gestures. In A. Twohill, I. Isler-Baykal, E. Knuth, A. J. Ribeiro, & J. Miller (Eds.), Proceedings from ICME 15, Topic Study Group 1.2: Teaching and learning of early algebra (15th International Congress on Mathematics Education, Sydney, Australia). https://doi.org/10.5281/zenodo.14525049
Araya, P., & Martínez, S. (2025) Does ‘any number’ exist? Development of understanding of indeterminate quantities in natural and symbolic language by third grade students. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-025-00521-8
Barwell, R. (2012). Heteroglossia in multilingual mathematics classrooms. En H. Forgasz, & F. Rivera (Eds.), Towards equity in mathematics education: gender, culture, and diversity (pp. 315-332). Springer. https://doi.org/10.1007/978-3-642-27702-3_28
Battey, D., & Franke, M. (2015). Integrating professional development on mathematics and equity: Countering deficit views of students of color. Education and Urban Society, 47(4), 433-462. https://doi.org/10.1177/0013124513497788
Bishop, A. (1994). Cultural conflicts in mathematics education: Developing a research agenda. For the Learning of Mathematics, 14(2), 15-18.
Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., & Strachota, S. (2019). Does Early Algebra Matter? The Effectiveness of an Early Algebra Intervention in Grades 3 to 5. American Educational Research Journal, 56(5), 1930-1972. https://doi.org/10.3102/0002831219832301
Brizuela, B. M., & Blanton, M. (2014). El desarrollo del pensamiento algebraico en niños de escolaridad primaria. Revista de Psicología-Segunda época, 14(1), 37-57.
Cañadas, M. C., Blanton, M., & Brizuela, B. M. (2019). Special issue on early algebraic thinking/Número especial sobre el pensamiento algebraico temprano. Infancia y Aprendizaje, 42(3), 469-478. https://doi.org/10.1080/02103702.2019.1638569
Civil, M. (2020). Immigrant students in mathematics education. En S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 359-365). Springer. https://doi.org/10.1007/978-3-030-15789-0_73
Clarkson, P. (2009). Mathematics teaching in Australian multilingual classrooms: developing an approach to the use of classroom languages. En R. Barwell (Ed.), Multilingualism in mathematics classrooms: global perspectives (pp. 145-160). Tonawanda. https://doi.org/10.21832/9781847692061-012
Contreras, F. (2009). Sin papeles y rompiendo barreras: Latino students and the challenges of persisting in college. Harvard Educational Review, 79(4), 610-632. https://doi.org/10.17763/haer.79.4.02671846902gl33w
Corvalán, J., Córdoba, C., Rojas, K., & Margarit, D. (2023). Migrant Students in Chilean Schools. En V. Dupriez, J. P. Valenzuela, M. Verhoeven, & J. Corvalán (Eds.), Educational Markets and Segregation. Evaluating Education: Normative Systems and Institutional Practices (pp. 227-243). Springer. https://doi.org/10.1007/978-3-031-36147-0_12
Davies, B., & Harré, R. (1990). Positioning: The discursive production of selves. Journal for the theory of social behavior, 20(1), 43-63. https://doi.org/10.1111/j.1468-5914.1990.tb00174.x
Domínguez, H., Takeuchi, M. A., & Civil, M. (2023). Three embodied voices speaking on/to research on language, mathematics, and the learner. ZDM–Mathematics Education, 55(6), 1037-1051. https://doi.org/10.1007/s11858-023-01525-z
Esmonde, I. (2009). Mathematics Learning in Groups: Analyzing Equity in Two Cooperative Activity Structures. Journal of the Learning Sciences, 18(2), 247-284. https://doi.org/10.1080/10508400902797958
Flores, N., Kleyn, T., & Menken, K. (2015). Looking holistically in a climate of partiality: Identities of students labeled long-term English language learners. Journal of Language, Identity & Education, 14(2), 113-132. https://doi.org/10.1080/15348458.2015.1019787
Hand, V. M., Quindel, J., & Esmonde, I. (2010). Status and competence as entry points into discussions of equity in mathematics classrooms. In Mathematics Teaching and Learning in K-12: Equity and Professional Development (pp. 151-166). Palgrave Macmillan US. https://doi.org/10.1057/9780230109889_11
Harré, R., Moghaddam, F. M., Cairnie, T. P., Rothbart, D., & Sabat, S. R. (2009). Recent advances in positioning theory. Theory & psychology, 19(1), 5-31. https://doi.org/10.1177/0959354308101417
Hwang, J., Castle, S. D., & Karunakaran, S. S. (2022). One is the Loneliest Number: Groupwork within Linguistically Diverse Classrooms. PRIMUS, 32(10), 1140-1152. https://doi.org/10.1080/10511970.2021.2019149
Kaput, J. (2008). What is algebra? What is algebraic reasoning? En J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Lawrence Erlbaum. https://doi.org/10.4324/9781315097435-2
Langer-Osuna, J. M., Moschkovich, J., Norén, E., Powell, A. B., & Vazquez, S. (2016). Student agency and counter-narratives in diverse multilingual mathematics classrooms: Challenging deficit perspectives. En R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas, M. S. Phakeng, P. Valero, & M. Villavicencio (Eds.), Mathematics education and language diversity: The 21st ICMI study (pp. 163-173). Springer. https://doi.org/10.1007/978-3-319-14511-2_9
Liu, S., & Takeuchi, M. A. (2023). Embodied mathematical pedagogy to liberate racialized and multilingual bodies. Educational Studies in Mathematics, 112(2), 267-287. https://doi.org/10.1007/s10649-022-10185-x
Lüssenhop, M., & Kaiser, G. (2024). Mathematics teaching for migrant students in German schools—How do teachers respond to their students’ diverse needs? Asian Journal for Mathematics Education, 3(1), 60-80. https://doi.org/10.1177/27527263241236813
Mayring, P. (2014). Qualitative content analysis: theoretical foundation, basic procedures and software solution. Gesis. https://doi.org/10.1007/978-94-017-9181-6_13
McEachin, A., Domina, T., & Penner, A. (2020). Heterogeneous effects of early algebra across California middle schools. Journal of Policy Analysis and Management, 39(3), 772-800. https://doi.org/10.1002/pam.22202
Mielicki, M. K., Kacinik, N. A., & Wiley, J. (2017). Bilingualism and symbolic abstraction: Implications for algebra learning. Learning and Instruction, 49, 242-250. https://doi.org/10.1016/j.learninstruc.2017.03.002
Moschkovich, J. (1999). Understanding the needs of latino students in reform-oriented mathematics classrooms. En L. Ortiz-Franco (Ed.), Changing the faces of mathematics: Perspectives on Latinos (pp. 5-12). National Council of Teachers of Mathematics.
Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Math Think Learn, 4(2-3), 189-212. https://doi.org/10.1207/S15327833MTL04023_5
Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights. Beacon Press.
Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. TIMSS and PIRLS International Study Center.
Nunes, T., Bryant, P., Evans, D., & Barros, R. (2015). Assessing quantitative reasoning in young children. Mathematical Thinking and Learning, 17(2-3), 178-196. https://doi.org/10.1080/10986065.2015.1016815
Organización para la Cooperación y el Desarrollo Económico. (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing. https://doi.org/10.1787/53f23881-en
Planas, N., & Civil, M. (2013). Language-as-resource and language-as-political: Tensions in the bilingual mathematics classroom. Mathematics Education Research Journal, 25(3), 361-378. https://doi.org/10.1007/s13394-013-0075-6
Pérez-Arredondo, C. (2024). Una aproximación interseccional y discursiva a la identidad en la educación multicultural: el caso de la comunidad haitiana en Chile. Journal of Gender Studies, 1-12.
Polkinghorne, D. E. (1995). Narrative configuration in qualitative analysis. International Journal of Qualitative Studies in Education, 8(1), 5-23. https://doi.org/10.1080/0951839950080103
Radford, L. (2003). Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students’ Types of Generalization. Mathematical Thinking and Learning, 5(1), 37-70. https://doi.org/10.1207/S15327833MTL0501_02
Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational studies in mathematics, 70, 111-126. https://doi.org/10.1007/s10649-008-9127-3
Radford, L. (2018). The Emergence of Symbolic Algebraic Thinking in Primary School. En C. Kieran (Eds.), Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. ICME-13 Monographs, Springer. https://doi.org/10.1007/978-3-319-68351-5_1
Radford, L., & Sabena, C. (2015). The Question of Method in a Vygotskian Semiotic Approach. En A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education (pp. 157-182). Springer. https://doi.org/10.1007/978-94-017-9181-6_7
Ríos, J. (2024). Positioned as a burden: Analyzing the participation of multilingual students of color in undergraduate mathematics courses that use group work. The Journal of Mathematical Behavior, 74, 101-148. https://doi.org/10.1016/j.jmathb.2024.101148
Schoenfeld, A. (1995). Report of working group 1. The algebra initiative colloquium, (2), 11-18.
Tapia, C. I., & Tour, E. (2022). Challenges for Teachers Working in Mainstream Schools with Culturally and Linguistically Diverse Students in Chile: Two Case Studies. International Journal of Multicultural Education, 24(2), 97-113. https://doi.org/10.18251/ijme.v24i2.2827
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
Yin, R. (2018). Case study research and applications: Design and methods. SAGE Publications.
Descargas
Publicado
Cómo citar
Número
Sección
Categorías
Licencia
Derechos de autor 2025 Paulina Araya Erices

Esta obra está bajo una licencia internacional Creative Commons Atribución-CompartirIgual 4.0.
El/los autores/as otorgan licencia exclusiva y sin límite de temporalidad para que el manuscrito sea publicado en la revista Perspectiva Educacional, editada por la Pontificia Universidad Católica de Valparaíso (Chile), a través de la Escuela de Pedagogía.