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Observar las transformaciones que van ocurriendo en los estudiantes es la idea principal que conduce las siguientes lineas, y es que al diseñar una clase y/o curso con base en un referente teórico surge la siguiente pregunta. ¿Cuáles son los cambios que se notan en los estudiantes en relación a las Matemáticas? Tales cambios están referidas a diversos aspectos tales como: el aprendizaje, las actitudes, las emociones, habilidades, destrezas, etc. Este tema de tesis 59 tiene por intención centrar la mirada en la forma de observar tales cambios en los estudiantes en relación a la matemática durante y/o después de haber llevado una clase diseñada con base en algún referente teórico. Veamos:
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| Tema de tesis 59: Cambios con y en Matemáticas, en estudiantes de algún nivel educativo |
En un estudio reportado por Hunter & Anthony (2011) se presentan resultados de cambios en la disposición que tienen los estudiantes hacia las matemáticas después de estar tomando clases de Matemáticas basados en el referente teórico metodológico de "Comunicación y Participación" (CPF, por sus siglas en Inglés).
A partir de entrevistas personalizadas que realizaron los autores del escrito; a lo largo de un año, observaron que: la aplicación de este enfoque propició cambios positivos en el aprendizaje por parte de los estudiantes cuando las obligaciones generales y matemáticas se ocupan del bienestar matemático, social y cultural de todos los estudiantes en el aula.
Esta perspectiva de trabajo propició además que los estudiantes tuvieran un concepto acerca de su aprendizaje de la Matemática tanto de manera individual como colectiva.
Como se observa, analizar el cambio en los estudiantes en relación a las matemáticas en una clase diseñada con algún referente teórico es de lo más interesante. Tales cambios están referidos a diversos aspectos más allá del aprendizaje mismo, impactan en la vida de los estudiantes tanto en el momento que está tomando una clase como para su vida fuera de ella y en el futuro. Continuar un trabajo de investigación bajo esta línea se nota fructífera y es que al tener varios niveles educativos, varios grupos de estudiantes y diversas perspectivas, tenemos un panorama amplio de donde elegir.
Si te interesa este tema te recomiendo lo siguiente:
1.- Elegir un nivel educativo.
2.- Elegir un curso de Matemáticas.
3.- Diseñar el curso y su aplicación en términos de un referente teórico.
4.- Observar y documentar los cambios que van surgiendo en los estudiantes en relación a aquél curso de Matemáticas.
5.- Analizar y difundir tus hallazagos.
6.- Disfrutar tu trabajo de investigar investigando.
Te recomiendo las siguientes lecturas.
Anthony, G. J., & Walshaw, M. (2007). Effective pedagogy in mathematics/Pangarau: Best evidence synthesis iteration. Wellington, New Zealand: Ministry of Education.
Bibby, T. (2009). How do pedagogic practices impact on learner identities in mathematics? In L. Black, H. Mendick, & Y. Solomon (Eds.), Mathematical relationships in education: Identities and participation (pp. 123–135). London, United Kingdom: Routledge.
Boaler, J. (2002). Experiencing school mathematics. Mahwah, NJ: Erlbaum.
Boaler, J. (2006). Promoting respectful learning. Educational Leadership, 63(5), 74–78.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110, 608–645.
Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education 40, 40–68.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.
Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 31(1), 5–8.
Esmonde, I. (2009a). Explanations in mathematics classrooms: A discourse analysis. Canadian Journal of Science, Mathematics and Technology Education, 9(2), 86–99.
Esmonde, I. (2009b). Ideas and Identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79, 1008–1043.
Forman, E., & Ansell, E. (2001). The multiple voices of a mathematics classroom community. Educational Studies in Mathematics, 46, 115–142.
Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.
Gresalfi, M., & Cobb, P. (2006). Cultivating students’ discipline-specific dispositions as a critical goal for pedagogy and equity. Pedagogies: An International Journal, 1(1), 49–57.
Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2009). Constructing competence: An analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematics, 70, 49–70.
Gutiérrez, R. (2002). Enabling the practice of mathematics teachers in context: Toward a new equity research agenda. Mathematical Thinking and Learning, 4, 145–188.
Gutiérrez, K. D., & Rogoff, B. (2003). Cultural ways of learning: Individual traits or repertoires of practice. Educational Researcher, 32(5), 19–25.
Hawk, K., Tumama Cowley, E., Hill, J., & Sutherland, S. (2005). The importance of the teacher/student relationship for Maori and Pasifika students. Set: Research information for Teachers, 3, 44–50.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.
Higgins, J., & Parsons, R. (2009). A successful professional development model in mathematics. Journal of Teacher Education, 60, 231–242.
Hunter, R. (2006). Structuring the talk towards mathematical inquiry. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities cultures and learning spaces: Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 309–318). Adelaide, Australia: Mathematics Education Research Group of Australasia.
Hunter, R. (2007). Teachers developing communities of mathematical inquiry (Unpublished doctoral dissertation). Massey University, Palmerston North, New Zealand.
Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions: Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 31–39). Brisbane, Australia: Mathematics Education Research Group of Australasia.
Jones, A. (1991). At school I’ve got a chance. Culture/privilege: Pacific Island and Pakeha girls at school. Palmerston North: Dunmore.
Kazemi, E., & Franke, M. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203–235.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, United Kingdom: Cambridge University Press.
Lerman, S. (2009). Pedagogy, discourse, and identity. In L. Black, H. Mendick, & Y. Solomon (Eds.), Mathematical relationships in education: Identities and participation (pp. 147–155). New York: Routledge.
MacFarlane, A. (2004). Kia hiwa ra! Listen to culture. Wellington, New Zealand: New Zealand Council for Educational Research.
Planas, N., & Gorgorió, N . (2004). Are different students expected to learn norms differently in mathematics classroom? Mathematics Education Research Journal, 16, 19–40.
RAND Mathematics Study Panel. (2003). Mathematical proficiency for all students: Towards a strategic research and development program in mathematics education. Santa Monica, CA: RAND
Sekiguchi, Y. (2006). Mathematical norms in Japanese mathematics lessons. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insiders’perspective (pp. 289–306). Rotterdam, The Netherlands: Sense.
Sherin, M., Linsenmeier, K., & van Es, E. (2009). Selecting video clips to promote mathematics teachers’ discussion of student thinking. Journal of Teacher Education, 60, 213–230.
Staples, M. (2008). Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom. Journal of Mathematics Teacher Education, 11, 349–371.
Staples, M., & Truxaw, M. P. (2010). The mathematics learning discourse project: Fostering higher order thinking ad academic language in urban mathematics classrooms. Journal of Urban Mathematics Education, 3(1), 27–56. Retrieved from http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/74/49.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking & Learning, 10, 313–340.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. London, United Kingdom: Sage.
Walshaw, M. (2007). An archaeology of learning, In Working with Foucault in education (pp. 27–37). Rotterdam, The Netherlands: Sense.
Walshaw, M., & Anthony, G. (2008). The role of pedagogy in classroom discourse: A review of recent research into mathematics. Review of Educational Research, 78, 516–551.
Wood, T., & McNeal, B. (2003). Complexity in teaching and children’s mathematical thinking. In N. L. Pateman, B. J. Dougherty, & J. Zilliox (Eds.). Proceedings of the 27th annual conference of the International group for the Psychology of Mathematics Education (Vol. 4, pp. 435–443). Honolulu, HI: Psychology of Mathematics Education.
Wood, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37, 222–255.
A partir de entrevistas personalizadas que realizaron los autores del escrito; a lo largo de un año, observaron que: la aplicación de este enfoque propició cambios positivos en el aprendizaje por parte de los estudiantes cuando las obligaciones generales y matemáticas se ocupan del bienestar matemático, social y cultural de todos los estudiantes en el aula.
Esta perspectiva de trabajo propició además que los estudiantes tuvieran un concepto acerca de su aprendizaje de la Matemática tanto de manera individual como colectiva.
Como se observa, analizar el cambio en los estudiantes en relación a las matemáticas en una clase diseñada con algún referente teórico es de lo más interesante. Tales cambios están referidos a diversos aspectos más allá del aprendizaje mismo, impactan en la vida de los estudiantes tanto en el momento que está tomando una clase como para su vida fuera de ella y en el futuro. Continuar un trabajo de investigación bajo esta línea se nota fructífera y es que al tener varios niveles educativos, varios grupos de estudiantes y diversas perspectivas, tenemos un panorama amplio de donde elegir.
Para concretar esta idea es recomendable tomar en cuenta diversos aspectos, tanto personales como profesionales, para que de allí se concrete en un protocolo de tesis y/o en un anteproyecto y, finalmente terminar tu trabajo de tesis. Es importante que recibas un acompañamiento certero para que tu proceso de investigación por tesis sea lo mejor de lo mejor y yo, Xaab Nop Vargas Vásquez, editor de 1000 Ideas de tesis, puedo ser tu mentor y guía, te invito a revisar mi lista de servicios personalizados, estoy seguro que en mi persona encontrarás las herramientas necesarias y suficientes para que la tesis no sea un dolor de cabeza para ti. Atrévete a encaminar tu trabajo de investigación hacia la originalidad y alto impacto.
1.- Elegir un nivel educativo.
2.- Elegir un curso de Matemáticas.
3.- Diseñar el curso y su aplicación en términos de un referente teórico.
4.- Observar y documentar los cambios que van surgiendo en los estudiantes en relación a aquél curso de Matemáticas.
5.- Analizar y difundir tus hallazagos.
6.- Disfrutar tu trabajo de investigar investigando.
Te recomiendo las siguientes lecturas.
Anthony, G. J., & Walshaw, M. (2007). Effective pedagogy in mathematics/Pangarau: Best evidence synthesis iteration. Wellington, New Zealand: Ministry of Education.
Bibby, T. (2009). How do pedagogic practices impact on learner identities in mathematics? In L. Black, H. Mendick, & Y. Solomon (Eds.), Mathematical relationships in education: Identities and participation (pp. 123–135). London, United Kingdom: Routledge.
Boaler, J. (2002). Experiencing school mathematics. Mahwah, NJ: Erlbaum.
Boaler, J. (2006). Promoting respectful learning. Educational Leadership, 63(5), 74–78.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110, 608–645.
Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education 40, 40–68.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.
Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 31(1), 5–8.
Esmonde, I. (2009a). Explanations in mathematics classrooms: A discourse analysis. Canadian Journal of Science, Mathematics and Technology Education, 9(2), 86–99.
Esmonde, I. (2009b). Ideas and Identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79, 1008–1043.
Forman, E., & Ansell, E. (2001). The multiple voices of a mathematics classroom community. Educational Studies in Mathematics, 46, 115–142.
Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.
Gresalfi, M., & Cobb, P. (2006). Cultivating students’ discipline-specific dispositions as a critical goal for pedagogy and equity. Pedagogies: An International Journal, 1(1), 49–57.
Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2009). Constructing competence: An analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematics, 70, 49–70.
Gutiérrez, R. (2002). Enabling the practice of mathematics teachers in context: Toward a new equity research agenda. Mathematical Thinking and Learning, 4, 145–188.
Gutiérrez, K. D., & Rogoff, B. (2003). Cultural ways of learning: Individual traits or repertoires of practice. Educational Researcher, 32(5), 19–25.
Hawk, K., Tumama Cowley, E., Hill, J., & Sutherland, S. (2005). The importance of the teacher/student relationship for Maori and Pasifika students. Set: Research information for Teachers, 3, 44–50.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.
Higgins, J., & Parsons, R. (2009). A successful professional development model in mathematics. Journal of Teacher Education, 60, 231–242.
Hunter, R. (2006). Structuring the talk towards mathematical inquiry. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities cultures and learning spaces: Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 309–318). Adelaide, Australia: Mathematics Education Research Group of Australasia.
Hunter, R. (2007). Teachers developing communities of mathematical inquiry (Unpublished doctoral dissertation). Massey University, Palmerston North, New Zealand.
Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions: Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 31–39). Brisbane, Australia: Mathematics Education Research Group of Australasia.
Jones, A. (1991). At school I’ve got a chance. Culture/privilege: Pacific Island and Pakeha girls at school. Palmerston North: Dunmore.
Kazemi, E., & Franke, M. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203–235.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, United Kingdom: Cambridge University Press.
Lerman, S. (2009). Pedagogy, discourse, and identity. In L. Black, H. Mendick, & Y. Solomon (Eds.), Mathematical relationships in education: Identities and participation (pp. 147–155). New York: Routledge.
MacFarlane, A. (2004). Kia hiwa ra! Listen to culture. Wellington, New Zealand: New Zealand Council for Educational Research.
Planas, N., & Gorgorió, N . (2004). Are different students expected to learn norms differently in mathematics classroom? Mathematics Education Research Journal, 16, 19–40.
RAND Mathematics Study Panel. (2003). Mathematical proficiency for all students: Towards a strategic research and development program in mathematics education. Santa Monica, CA: RAND
Sekiguchi, Y. (2006). Mathematical norms in Japanese mathematics lessons. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insiders’perspective (pp. 289–306). Rotterdam, The Netherlands: Sense.
Sherin, M., Linsenmeier, K., & van Es, E. (2009). Selecting video clips to promote mathematics teachers’ discussion of student thinking. Journal of Teacher Education, 60, 213–230.
Staples, M. (2008). Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom. Journal of Mathematics Teacher Education, 11, 349–371.
Staples, M., & Truxaw, M. P. (2010). The mathematics learning discourse project: Fostering higher order thinking ad academic language in urban mathematics classrooms. Journal of Urban Mathematics Education, 3(1), 27–56. Retrieved from http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/74/49.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking & Learning, 10, 313–340.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. London, United Kingdom: Sage.
Walshaw, M. (2007). An archaeology of learning, In Working with Foucault in education (pp. 27–37). Rotterdam, The Netherlands: Sense.
Walshaw, M., & Anthony, G. (2008). The role of pedagogy in classroom discourse: A review of recent research into mathematics. Review of Educational Research, 78, 516–551.
Wood, T., & McNeal, B. (2003). Complexity in teaching and children’s mathematical thinking. In N. L. Pateman, B. J. Dougherty, & J. Zilliox (Eds.). Proceedings of the 27th annual conference of the International group for the Psychology of Mathematics Education (Vol. 4, pp. 435–443). Honolulu, HI: Psychology of Mathematics Education.
Wood, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37, 222–255.
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