Ir al contenido

Documat

An approach to teach with variations: using typical problems

  • Ban Heng Choy [1] ; Jaguthsing Dindyal [1]
    1. [1] Nanyang Tecnological University
  • Localización: Avances de investigación en educación matemática, ISSN-e 2254-4313, Nº. 13, 2018, págs. 21-38
  • Idioma: inglés
  • DOI: 10.35763/aiem.v0i13.227
  • Títulos paralelos:
    • Uma abordagem para ensinar com variações: usando problemas típicos
    • Une approche pour enseigner avec des variations: utilisation des problèmes typiques
    • Una aproximación para enseñar con variaciones: usando problemas típicos
  • Enlaces
  • Resumen
    • español

      Los profesores de matemáticas usan problemas típicos desde propuestas de exámenes anteriores y desde los libros de texto para desarrollar destrezas procedimentales. En este articulo, discutimos otros usos de los problemas típicos. Nos centramos en las oportunidades que un profesor experimentado, John, percibe en los problemas típicos y cómo los usa para potenciar el aprendizaje de sus estudiantes aprovechando las variaciones del problema(o bianshi). A partir de los datos de una investigación con enfoque cualitativo centrada en la competencia “mirar profesionalmente” del profesor, presentamos una instantánea de la práctica de John para mostrar lo que observa de las posibles variaciones en los problemas típicos y cómo las usa con los estudiantes para promover tanto las destrezas procedimentales como la comprensión conceptual. Los resultados subrayan el potencial de apoyar a los profesores para que aprovechen las variaciones de los problemas típicos, lo cual tienen implicaciones para la formación inicial y continua de profesores.

    • português

      Os professores de matemática usam problemas típicos de propostas de exames anteriores e de livros didáticos para desenvolver procedimentos. Neste artigo, discutimos outros usos de problemas típicos. Nós nos concentramos nas oportunidades que um professor experiente, John, percebe nos problemas típicos e como ele os usa para melhorar a aprendizagem de seus alunos aproveitando as variações do problema (ou bianshi). A partir dos dados de uma pesquisa qualitativa voltada para a competência “olhar profissionalmente” do professor, apresentamos um instantâneo da prática de John para mostrar o que ele observa de possíveis variações em problemas típicos e como ele os usa com os alunos para promover habilidades processuais e compreensão conceitual. Os resultados destacam o potencial de apoiar os professores para tirar proveito das variações de problemas típicos, que têm implicações para a formação inicial e contínua dos professores

    • English

      Mathematics teachers use typical problems from past examination papers and textbook exercises to develop procedural skills. In this paper, we discuss other uses of typical problems. We focus on the affordances that an experienced teacher, John, perceives in typical problems and how he uses them to enhance student learning by harnessing the idea of teaching with variations or bianshi. Drawing on data from a larger qualitative design-based research on investigating teacher noticing, we present snapshots of John’s classroom practices to show what he noticed about the variations afforded by typical problems and how he used these problems with students to promote both procedural skills and conceptual understanding. Findings suggest the value of supporting teachers in harnessing variations of typical problems, which has implications for teacher education and professional development.

    • français

      Les professeurs de mathématiques utilisent des problèmes typiques des propositions d'examen précédentes et des manuels pour développer des compétences procédurales. Dans cet article, nous discutons d'autres utilisations de problèmes typiques. Nous nous concentrons sur les opportunités qu'un enseignant expérimenté, John, perçoit dans les problèmes typiques et comment il les utilise pour améliorer l'apprentissage de ses étudiants en profitant des variations du problème (ou bianshi). À partir des données d'une recherche qualitative axée sur la compétence «noticing» de l'enseignant, nous présentons un aperçu de la pratique de John pour montrer ce qu'il observe des variations possibles dans les problèmes typiques et comment il les utilise avec les élèves promouvoir les compétences procédurales et la compréhension conceptuelle. Les résultats soulignent la possibilité d'aider les enseignants à tirer parti des variations de problèmes typiques, qui ont des implications pour la formation initiale et continue des enseignants.

  • Referencias bibliográficas
    • Askew, M., Rhodes, V., Brown, M., William, D., & Johnson, D. (1997). Effective teachers of numeracy: report of a study carried out for...
    • Backhouse, J., Haggarty, L., Pirie, S., & Stratton, J. (1992). Improving the learning of mathematics. London, UK: Cassell.
    • Bryman, A. (2012). Social research methods (4th ed.). New York: Oxford University Press.
    • Choy, B. H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28(3), 421-440.
    • Choy, B. H., & Dindyal, J. (2017a). Noticing affordances of a typical problem. In B. Kaur, W. K. Ho, T. L. Toh & B. H. Choy (Eds.),...
    • Choy, B. H., & Dindyal, J. (2017b). Snapshots of productive noticing: orchestrating learning experiences using typical problems. In A....
    • Choy, B. H., Thomas, M. O. J., & Yoon, C. (2017). The FOCUS framework: characterising productive noticing during lesson planning, delivery...
    • Design-Based Research Collective (2003). Design-based research: an emerging paradigm for educational inquiry. Educational Researcher, 32(1),...
    • Foong, P. Y. (2009). Review of research on mathematical problem solving in Singapore. In K. Y. Wong, P. Y. Lee, B. Kaur, P. Y. Foong &...
    • Franke, M. L., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practice in mathematics. In J. F. K. Lester (Ed.),...
    • Gibson, J. J. (1986). The theory of affordances. The ecological approach to visual perception. Hillsdale, USA: Lawrence Erlbaum Associates.
    • Greeno, J. G. (2003). Situative research relevant to standards for school mathematics. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.),...
    • Grootenboer, P. (2009). Rich mathematical tasks in the Maths in the Kimberly (MITK) project. In R. Hunter, B. Bicknell & T. Burgess (Eds.),...
    • Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: a Chinese way of promoting effective mathematics learning. In L. Fan,...
    • Henningsen, M., & Stein, M. K. (1997). Mathematics tasks and student cognition: classroom-based factors that support and inhibit high-level...
    • Ho, K. F., & Hedberg, J. G. (2005). Teachers’ pedagogies and their impact on students’ mathematical problem solving. The Journal of Mathematical...
    • Lee, M. Y., & Choy, B. H. (2017). Mathematical teacher noticing: the key to learning from Lesson Study. In E. O. Schack, M. H. Fisher...
    • Loughran, J., Keast, S., & Cooper, R. (2016). Pedagogical reasoning in teacher education. In J. Loughran & M. L. Hamilton (Eds.),...
    • Marton, F. (2014). Necessary conditions of learning. London, UK: Routledge.
    • Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. The Jounal of the Learning Sciences, 15(2), 193-220.
    • Mason, J. (2002). Researching your own practice: the discipline of noticing. London, UK: Routledge Falmer.
    • Mason, J. (2011). Noticing: Roots and branches. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: seeing...
    • Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. Saint Albans, UK: Tarquin Publications.
    • Sánchez, V., & Llinares, S. (2003). Four student teachers' pedagogical reasoning on functions. Journal of Mathematics Teacher Education,...
    • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: seeing through teachers' eyes. New York:...
    • Shulman, L. S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
    • Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: from research to practice. Mathematics Teaching in the...
    • Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, USA: NCTM.
    • Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: five practices for...
    • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: an analysis...
    • Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2014). Supporting teachers in structuring mathematics...
    • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: learners generating examples. Mahwah, USA: Lawrence Erlbaum Associates.
    • Watson, A., & Thompson, D. (2015). Design issues related to text-based tasks. In A. Watson & M. Ohtani (Eds.), Task design in mathematics...
    • Wong, N.-Y. (2008). Confucian heritage culture learner’s phenomenon: from “exploring the middle zone” to “constructing a bridge”. ZDM, 40(6),...
    • Wong, N.-Y., Lam, C. C., & Chan, A. M. Y. (2013). Teaching with variation: bianshi mathematics teaching. In Y. Li & R. Huang (Eds.),...
    • Wong, N.-Y., Lam, C. C., Sun, X., & Chan, A. M. Y. (2009). From "exploring the middle zone" to "constructing a bridge":...
    • Wood, T. (1998). Alternative patterns of communication in mathematics classes: funnelling or focusing? In H. Steinbring, M. G. Bartolini...
    • Yang, Y., & Ricks, T. E. (2012). How crucial incidents analysis support Chinese Lesson Study. International Journal for Lesson and Learning...
    • Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers' professional development. For the Learning of Mathematics,...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno