Aprender es participar: el caso de la demostración en geometría euclidiana
Tipo de documento
Autores
Lista de autores
Camargo-Uribe, Leonor
Resumen
Expongo una conceptualización de aprendizaje desde la teoría de la práctica social que se concreta en una propuesta sobre cómo ver el aprendizaje de la demostración en geometría euclidiana plana. Las ideas se ilustran con fragmentos de la actividad académica realizada por estudiantes de segundo semestre de Licenciatura en Matemáticas. La conferencia está dirigida a futuros profesores, profesores de matemáticas de secundaria y formadores de docentes.
Fecha
2012
Tipo de fecha
Estado publicación
Términos clave
Geometría | Procesos de justificación | Razonamiento | Unidimensional
Enfoque
Idioma
Revisado por pares
Formato del archivo
Título libro actas
Memorias del 13er Encuentro Colombiano de Matemática Educativa
Editores (actas)
Lista de editores (actas)
Obando, Gilberto
Editorial (actas)
Lugar (actas)
Rango páginas (actas)
719-745
ISBN (actas)
Referencias
Adler, J. (1998).Lights and limits: recontextualising Lave and Wenger to theorise knowledge of teaching and learning school mathematics. En A. Watson (Ed.),Situated cognition and the learning of mathematics (pp. 161 - 177). Oxford: Centre for Mathematics Education Research. University of Oxford. Department of Educational Studies. Anderson, R. (2007). Being a mathematical learner: four faces of identity. The mathematics Educator, 17(1), 7 - 14. Arsac, G. (2007). Origin of Mathematical Proof. History and Epistemology. En P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 27 - 42). Rotterdam: Sense Publishers. Blanton, M.L., & Stylianou, D.A. (2003). The nature of scaffolding in undergraduate students’ transition to mathematical proof. Proceedings of the 27th PME International Conference, 2, 113 – 120. Boylan, M. (2005). School classrooms: communities of practice or ecologies of practice? http://org.man.ac.uk/projects/include/experiment/mark_boylan.pdf-. Camargo, L. (2010). Descripción y análisis de un caso de enseñanza y aprendizaje de la demostración en una comunidad de práctica de futuros profesores de matemáticas de educación secundaria. Tesis doctoral, Departamento de Didáctica de las Matemáticas, Universidad de Valencia – España. Clark, P. (2005). The emergence of a classroom community of practice in a mathematical structures course. Doctoral Dissertation. Department of Philosophy, Arizona State University. Cobb, P., McClain, K., de Silva Lamberg, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and school district. Educational Researcher, 32 (6), 13-24. De Villiers, M. (1986). The role of axiomatization in mathematics and mathematics teaching. http://mzone.mweb.co.za/residents/profmd/axiom.pdf. Fernández, E. (2008). Rethinking success and failure in mathematics learning: the rol of participation. Proceedings of the Fifth International Mathematics Education al Society Conference, 1 - 11. Forman, E.A. (1996). Learning mathematics as participation in classroom practice: implications of sociocultural theory for educational reform. En L, Steffe; P, Nesher; P, Coob; G, Goldin; B, Greer (Eds.), Theories of Mathematical Learning(pp. 115 - 130). New Jersey: Lawrence Erlbaum Associates. Gómez, P. (2007). Desarrollo del conocimiento didáctico en un plan de formación inicial de profesores de matemáticas de secundaria. Disertación doctoral. Departamento de Didáctica de la Matemática. Universidad de Granada. Goos, M. (2004). Learning mathematics in a Classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258 - 291. Graven, M., & Lerman, S. (2003). Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Journal of Mathematics Teacher Education, 6, 185 - 194. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6 - 13. Herbst, P.G. (2002). Establishing a custom of proving in American school geometry: evolution of the two - column proof in the early twentieth century. Educational Studies in Mathematics, 49, 283 - 312. Krainer, K. (2003). Teams, communities & networks. Journal of Mathematics Teacher Education, 6, 93 - 105. Lave, J., & Wenger, E. (1991). Situated learning. Legitimate peripheral participation. Cambridge: University Press. Lerman, S. (2001). A review of research perspectives on mathematics teacher education. En F.L. Lin, T. Cooney (Eds.), Making sense of mathematics teacher education: Past, present and future (pp. 33-52). Dordrecht: Kluwer Academic Publishers. Mariotti, M. A. (2000). Introduction to proof: the mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25 - 53. Mariotti, A., Bartolini Bussi, M.G., Boero, P., Ferri, F., & Garuti, R. (1997). Approaching geometry theorems in contexts: from history and epistemology to cognition. Proceedings of the 21th PME International Conference, 1, 180-195. Martin, T. S., Soucy McCrone, S. M., Wallace, M. L., & Dindyal, J. (2005). The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in Mathematics, 60, 95-124. Richards, J. (1996). Negotiating the negotiation of meaning: Comments on Voigt(1992) and Saxe & Bermudez (1992). En Steffe, L., Nesher, P., Cobb, P., Goldin, G., & Greer, B. (Eds.), Theories of Mathematical Learning (pp. 69-75). New Jersey: Lawrence Erlbaum Associates. Rogoff, B. (1997). Los tres planos de la actividad sociocultural: apropiación participativa, participación guiada y aprendizaje. En Wertsch, J.V., del Río, P. & Álvarez, A. (Eds), La mente sociocultural. Aproximaciones teóricas y aplicadas (pp. 111–128). Madrid: Fundación Infancia y Aprendizaje. Smith, T. (2006). Becoming a teacher of mathematics: Wenger’ social theory oflearning perspective. Proceedings of MERGA International Congress. www.merga.net.au. /documents/symp32006.pdf. Stylianides, A.J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321. Vygotsky, L.S. (1978). Mind in society. Harvard University Press, Cambridge, M.A. Wenger, E. (1998). Comminities of practice. Learning, meaming and identity. Cambridge, Cambridge University. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.