Ir al menú de navegación principal Ir al contenido principal Ir al pie de página del sitio
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 25 Núm. 3 (2022): Noviembre

ANTICIPACIÓN DE ESTRATEGIAS DE RESOLUCIÓN DE PROBLEMAS DE DIVISIÓN-MEDIDA CON FRACCIONES MEDIANTE UNA PROGRESIÓN DE APRENDIZAJE

DOI
https://doi.org/10.12802/relime.22.2532
Enviado
junio 20, 2023
Publicado
2023-06-21

Resumen

El objetivo de esta investigación es caracterizar cómo los estudiantes para maestro, un año  después de un experimento de enseñanza, reconocen diferentes etapas de progresión al anticipar estrategias de estudiantes de educación primaria al resolver problemas de división - medida con fracciones. Los 41 participantes cursaban el séptimo semestre del Grado en Maestro en Educación Primaria durante el curso 2018-2019. En el análisis se tuvo en cuenta el tipo de estrategias utilizadas y si estas evidenciaban la idea de progresión. Los resultados muestran tres categorías en el uso de la idea de progresión al anticipar respuestas a problemas de división-medida: (a) No usan la idea de progresión; (b) usan parcialmente la idea de progresión; (c) usan la idea de progresión. Pese a su dificultad, es posible comenzar a desarrollar la idea de progresión al anticipar estrategias en la formación de futuros maestros

Citas

  1. Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144. https://doi.org/10.5951/jresematheduc.21.2.0132
  2. Ball, D. L., Thames, M. H. y Phelps, G. (2008). Content Knowledge for Teaching: what makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  3. Bandura, A. (1977). Self-efficacy: Toward a Unifying Theory of Behavioral Change. Psycological Review, 84(2), 191. https://doi.org/10.1037/0033-295x.84.2.191
  4. Clements, D. H. y Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89. https://doi.org/10.1207/s15327833mtl0602_1
  5. Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. y Van Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary teachers. Teaching and Teacher Education, 47, 82-92. https://doi.org/10.1016/j.tate.2014.12.009
  6. Duncan, R. G. y Hmelo-Silver, C. E. (2009). Learning progressions: Aligning curriculum, instruction, and assessment. Journal of Research in Science Teaching, 46(6), 606-609. https://doi.org/10.1002/tea.20316
  7. Duschl, R., Maeng, S. y Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123­182. https://doi.org/10.1080/03057267.2011.604476
  8. Edgington, C. (2014). Teachers’ uses of a learning trajectory as a tool for mathematics lesson planning. En J. J. Lo, K. Leatham y L. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 261-284). Springer. https://doi.org/10.1007/978-3-319-02562-9_14
  9. Edgington, C., Wilson, P. H., Sztajn, P. y Webb, J. (2016). Translating learning trajectories into useable tools for teachers. Mathematics Teacher Educator, 5(1), 65-80. https://doi.org/10.5951/mathteaceduc.5.1.0065
  10. Empson, S. B. (2011). On the idea of learning trajectories: Promises and pitfalls. The Mathematics Enthusiast, 8(3), 571-598. https://doi.org/10.54870/1551-3440.1229
  11. Empson, S. B. y Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Heinemann.
  12. Entwistle, N. (2000). Promoting deep learning through teaching and assessment. En 1st Annual Conference ESRC Teaching and Learning Research Programme (pp. 9-20). University of Leicester. http://www.etl.tla.ed.ac.uk/docs/entwistle2000.pdf
  13. Fernández, C., Llinares, S. y Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM, 44(6), 747-759. https://doi.org/10.1007/s11858-012-0425-y
  14. Fernández, C., Sánchez-Matamoros, G., Moreno, M. y Callejo, M.L. (2018). La coordinación de las aproximaciones en la comprensión del concepto de límite cuando los estudiantes para profesor anticipan respuestas de estudiantes. Enseñanza de las ciencias, 36(1), 143-162. https://doi.org/10.5565/rev/ensciencias.2291
  15. Fischbein, E., Deri, M., Nello, M. S. y Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for research in mathematics education, 16(1), 3-17. https://doi.org/10.2307/748969
  16. Gordon, C. y Debus, R. (2002). Developing deep learning approaches and personal teaching efficacy within a preservice teacher education context. British Journal of Educational Psychology, 72(4), 483-511. https://doi.org/10.1348/00070990260377488
  17. Gotwals, A. W. (2018). Where are we now? Learning progressions and formative assessment. Applied Measurement in Education, 31(2), 157-164. https://doi.org/10.1080/08957347.2017.1408626
  18. Graeber, A., Tirosh, D. y Glover, R. (1986). Preservice teachers' beliefs and performance on measurement and partitive division problems. En G. Lappan y R. Even (Eds.), Proceedings of the Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 262-267). Michigan State University, East Lansing y MI.
  19. Herbst, P., Chazan, D., Chen, C. L., Chieu, V. M. y Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM, 43(1), 91-103. https://doi.org/10.1007/s11858-010-0290-5
  20. Higgs, J. (2012). Practice-Based Education Pedagogy. Situated capability-development, relationship practice(s). En J. Higgs, R. Barnett, S. Billett, M. Hutchings y F. Trede (Eds.), Practice-Based Education. Perspective and Strategies (pp. 71-80). Sense Publishers. https://doi.org/10.1007/978-94-6209-128-3_6
  21. Ivars, P., Fernández, C. y Llinares, S. (2020). A learning Trajectory as a scaffold for pre-service Teachers’ Noticing of Students’ Mathematical Understanding. International Journal of Science and mathematics Education, 18(3), 529-548. https://doi.org/10.1007/s10763-019-09973-4
  22. Jacobs, V., Lamb, L. y Philipp, R. (2010). Professional Noticing of Children's Mathematical Thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://www.jstor.org/stable/20720130
  23. Jansen, A. y Hohensee, Ch. (2016). Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions. Journal of Mathematics Teacher Education, 19, 503-522. https://doi.org/10.1007/s10857-015-9312-0
  24. Li, Y. y Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM, 40(5), 833-843. https://doi.org/10.1007/s11858-008-0148-2
  25. Llinares, S. (2013). El desarrollo de la competencia docente “mirar profesionalmente” la enseñanza-aprendizaje de las matemáticas. Educar em Revista, 50, 117-133. https://doi.org/10.1590/S0104-40602013000400009
  26. Llinares, S., Fernández, C. y Sánchez-Matamoros, G. (2016). Changes in how prospective teachers anticipate secondary students’ answers. Eurasia Journal of Mathematics, Science & Technology Education, 12(8), 2155-2170. https://doi.org/10.12973/eurasia.2016.1295a
  27. Lo, J. y Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15, 481-500. https://doi.org/10.1007/s10857-012-9221-4
  28. Mason, J. (2002). Researching your own practice: the discipline of noticing. Routledge. https://doi.org/10.4324/9780203471876
  29. Montero, E. y Callejo, M. L. (2019). Cambios en cómo estudiantes para maestro anticipan respuestas de niños de primaria. En J. M. Marbán, M. Arce, A. Maroto, J. M. Muñoz-Escolano y Á. Alsina (Eds.), Investigación en Educación Matemática XXIII (pp. 433-442). Valladolid: SEIEM. https://doi.org/10.26754/actas.seim21
  30. Nillas, L. (2003). Division of fractions: Preservice teachers’ understanding and use of problem solving strategies. The mathematics educator 7(2), 96-113.
  31. Olanoff, D., Lo, J. y Tobias, J. (2014). Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions. The Mathematics Enthusiast, 11(2), 267-310. https://doi.org/10.54870/1551-3440.1304
  32. Sánchez-Matamoros, G., Moreno, M., Perez-Tyteca, P. y Callejo, M.L. (2018). Trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual usado por futuros maestros de educación infantil. RELIME. Revista Latinoamericana de Investigación en Matemática Educativa, 21(2), 203-228. https://doi.org/10.12802/relime.18.2124
  33. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for research in mathematics education, 26(2) 114-145. https://doi.org/10.5951/jresematheduc.26.2.0114
  34. Smith, M. S. y Stein, M.K. (2011). 5 practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics.
  35. Stahnke, R., Schueler, S. y Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM Mathematics Education, 48, 1-27. https://doi.org/10.1007/s11858-016-0775-y
  36. Steffe, L. P. y Olive, J. (2010). Children’s fractional knowledge. Springer.
  37. Stein, M. K., Engle, R. A., Smith, M. S. y Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
  38. Stevens, A., Wilkins, J., Lovin, L., Siegfried, J., Norton, A. y Busi, R. (2020). Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers. Journal of Mathematics Teacher Education, 23, 153-181. https://doi.org/10.1007/s10857-018-9415-5
  39. Stockero, S. L. (2014). Transitions in prospective mathematics teacher noticing. En J. J. Lo, K. Leatham y L. Van Zoest (Eds.), Research Trends in Mathematics Teacher Education (pp. 239-259). Springer. https://doi.org/10.1007/978-3-319-02562-9_13
  40. Teuscher, D., Leatham, K. R. y Peterson, B. E. (2017). From a framework to a lens: Learning to notice student mathematical thinking. En E. Schack, M. Fisher y J. Wilhelm (Eds), Teacher noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 31-48). Springer. https://doi.org/10.1007/978-3-319-46753-5_3
  41. Tirosh, D. y Graeber, A. O. (1989). Preservice elementary teachers' explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96. https://doi.org/10.1007/bf00356042
  42. Tyminski, A. M., Simpson, A. J., Land, T. J., Drake, C. y Dede, E. (2021). Prospective elementary mathematics teachers ‘noticing of childrens’ mathematics: a focus on extending moves. Journal of Mathematics Teacher Education, 24, 533–561. https://doi.org/10.1007/s10857-020-09472-2
  43. Vula, E. y Kingji-Kastrati, J. (2018). Pre-service teacher procedural and conceptual knowledge of fractions. En G. J. Stylianides y K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers (pp. 111-123). Springer. https://doi.org/10.1007/978-3-319-68342-3
  44. Wilson, P. H.; Mojica, G. F. y Confrey, J. (2013). Learning trajectories in teacher education: supporting teachers’ understanding of students’ mathematical thinking. Journal of Mathematical Behavior, 32(2), 103-121. https://doi.org/10.1016/j.jmathb.2012.12.003
  45. Wilson, P. H., Sztajn, P., Edgington, C. y Confrey, J. (2014). Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory. Journal of Mathematics Teacher Education, 17, 149-175. https://doi.org/10.1007/s10857-013-9256-1
  46. Wilson, P. H., Sztajn, P., Edgington, C. y Myers, M. (2015). Teachers’ uses of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66(3), 227-244. https://doi.org/10.1177/0022487115574104
  47. Zimmerman, B. J. (1989). A social cognitive view of self-regulated academic learning. Journal of Educational Psychology, 81(3), 329. https://psycnet.apa.org/doi/10.1037/0022-0663.81.3.329
  48. Zimmerman, B. J. (1998). Developing self-fulfilling cycles of academic regulation: An analysis of exemplary instructional models. En D. Schunk y B. Zimmerman (Eds.), Self regulated learning: From teaching to self-reflective practice (pp. 1–19). Guilford Publications."

Descargas

Los datos de descargas todavía no están disponibles.

Artículos similares

1 2 3 4 5 6 7 8 9 10 > >> 

También puede {advancedSearchLink} para este artículo.