Demandas matemáticas para el desarrollo de la formulación de problemas en Educación Infantil

• Carmona Medeiro, Enrique ^[1] ; Climent Rodríguez, Nuria ^[2]
  1. [1] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
  2. [2] Universidad de Huelva

     Universidad de Huelva

     Huelva, España

     
• Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 19, Nº. 1, 2024 (Ejemplar dedicado a: (October, 2024)), págs. 25-51
• Idioma: español
• DOI: 10.30827/pna.v19i1.28408
• Títulos paralelos:
  • Demandas Matemáticas para o desenvolvimiento da formulaçao de problemas na sala de aula da Primeira Infância
  • Mathematical demands for the development of problem formulation in the early childhood classroom
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Esta investigación se centró en la gestión de aula que una maestra realiza durante una tarea de formulación de problemas con alumnado de Educación Infantil (4-5 años). Mediante un estudio de caso único, nos enfocamos en identificar las demandas matemáticas que la maestra establece para favorecer el avance en la formulación de un problema, la actividad del alumnado que las detona y las relaciones entre ambas. Los resultados indican que la mayoría de las demandas matemáticas están orientadas a favorecer el desarrollo del contexto del problema y, revelan que las dificultades que las detonan están ligadas al significado no matemático de problema que prevalece en el alumnado.

  • English

    This research focused on the classroom management that a teacher performs during a problem formulation task with students in Early Childhood Education (4-5 years old). By means of a single case study, we focused on identifying the mathematical demands that the teacher establishes to favor progress in the formulation of a problem, the students' activity that triggers them and the relationships between both. The results indicate that most of the mathematical demands are oriented to favor the development of the context of the problem and reveal that the difficulties that trigger them are linked to the non-mathematical meaning of problem that prevails in the students.

  • português

    Esta investigação centrou-se na gestão da sala de aula que um professor realiza durante uma tarefa de formulação de problemas com alunos da Educação Infantil (4-5 anos de idade). Através de um estudo de caso único, procurámos identificar as exigências matemáticas que o professor estabelece para favorecer o progresso na formulação de um problema, a atividade do aluno que as desencadeia e as relações entre ambas. Os resultados indicam que a maioria das exigências matemáticas são orientadas para favorecer o desenvolvimento do contexto do problema e revelam que as dificuldades que as desencadeiam estão ligadas ao significado não matemático de problema que prevalece nos alunos.

• Referencias bibliográficas
  • Aktaş, M. C. (2022). Problem-posing research in mathematics education: A bibliometric analysis. Journal of Pedagogical Research, 6(4), 217-233....
  • Ayllón, M. F., Castro, E. y Molina, M. (2010). Conocimiento aritmético informal puesto de manifiesto por una pareja de alumnos (6-7 años)...
  • Bardin, L. (1986). El Análisis del Contenido. Akal.
  • Baumanns, L. y Rott B. (2020). Rethinking problem-posing situations: A review. Investigations in Mathematics Learning 13(2), 59-76. https://doi.org/10.1080/19477503.2020.1841501
  • Baumanns, L. y Rott, B. (2022). Developing a framework for characterising problem-posing activities: a review. Research in Mathematics Education,...
  • Bassey, M. (1999). Case study research in educational settings. Open University Press.
  • Brown, S. I. y Walter, M. I. (2005). The art of problem posing (3rd edition). Lawrence Erlbaum Associates Publishers.
  • Bryman, A. (2001). Social Research Methods. Oxford University Press.
  • Cai, J. (2022). What Research Says About Teaching Mathematics Through Problem Posing. Éducation & didactique, 16(3), 31-50. https://doi.org/10.4000/educationdidactique.10642
  • Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L. y Song, N. (2019). Exploring the impact of a problem-posing workshop on elementary...
  • Cai, J., Hwang, S., Jiang, C. y Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions....
  • Cai, J. y Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions...
  • Cai, J. y Hwang, S. (2022). Seeing Algebra in Arithmetic Through Mathematical Problem Posing. Journal of Educational Research in Mathematics,...
  • Cai, J. y Hwang, S. (2023). Making Mathematics Challenging Through Problem Posing in the Classroom. En R. Leikin (Ed.), Mathematical Challenges...
  • Cai, J., Koichu, B., Rott, B., Zazkis, R. y Jiang, C. (2022). Mathematical problem posing: tasks variables, processes, and products. En C....
  • Çakır, A. y Akkoc, H. (2020). Examining socio-mathematical norms related to problem posing: A case of gifted and talented mathematics classrooms....
  • Carmona-Medeiro, E. y Cardeñoso, J. M. (2021). Social interaction: A crucial means to promote sustainability in initial teacher training....
  • Carrillo, J. y Cruz, J. (2016). Problem-Posing and Questioning: Two Tools to Help Solve Problems. En P. Felmer, E. Pehkonen y J. Kilpatrick....
  • Charmaz, K. (2008). Reconstructing Grounded Theory. En P. Alasuutari, L. Bickman y J. Brannen (Eds.). The Sage Handbook of Social Research...
  • Charnay, R. (2002). Aprender (por medio de) la resolución de problemas. En C. Parra e I. Saiz (Eds.), Didáctica de matemáticas: Aportes y...
  • Chi, M. (2011). Theoretical Perspectives, Methodological Approaches, and Trends in the Study of Expertise. En Y. Li y G. Kaiser (Eds.), Expertise...
  • Crespo, S. y Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems....
  • Decreto 100/2023, de 9 de mayo, por el que se establece la ordenación y el currículo de la etapa de Educación Infantil en la Comunidad Autónoma...
  • Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics,...
  • Ellerton, N. F., Singer, F. M. y Cai, J. (2015). Problem Posing in Mathematics: Reflecting on the Past, Energizing the Present, and Foreshadowing...
  • Flick, U. (2007). Introducción a la investigación cualitativa (2ª ed.). Morata.
  • Fosse, T., Lange, T. y Meaney, T. (2020). Kindergarten Teachers’ Stories About Young Children’s Problem Posing and Problem Solving. En M....
  • Font, V. (2008). Enseñanza de la Matemática. Tendencias y perspectivas. En C. Gaita (Ed.) Actas del III Coloquio Internacional sobre la Enseñanza...
  • García-García, F. J., Quesada-Armenteros, A., Romero, M. y Abril, A. M. (2019). Promover la indagación en matemáticas y ciencias: desarrollo...
  • Godino, J. D., Batanero, C., Cañadas, G. R. y Contreras, J. M. (2015). Articulación de la indagación y transmisión de conocimientos en la...
  • Husén, T. (1988). Paradigmas de la investigación en educación: un informe del estado de la cuestión. En I. Dendaluce (Ed.), Aspectos metodológicos...
  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? En A. H. Schoenfeld (Ed.), Cognitive science and mathematics...
  • Kvale, S. (1996). Interviews: An Introduction to Qualitative Research Interviewing. SAGE Publications.
  • Lee, SY. (2021). Research Status of Mathematical Problem Posing in Mathematics Education Journals. International Journal of Science and Mathematics...
  • Lee, Y., Capraro, R. y Capraro, M. (2018). Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing....
  • Lerman, S. (2010). Theories of mathematics education: Is plurality a problem? En B. Sriraman y L. English (Eds.), Theories of mathematics...
  • Lester, F. y Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. En P. Felmer, E. Pehkonen...
  • Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: challenges and strategies. Educational Studies in...
  • Leikin, R. y Elgrably, H. (2019). Problem posing through investigations for the development and evaluation of proof-related skills and creativity...
  • Li, X., Sun, X. y Cai, J. (2022). Integrating problem posing into the mathematics classroom: current advances and future directions of research....
  • Malaspina, U. (2021). Creación de problemas y de juegos para el aprendizaje de las matemáticas. Edma 0-6: Educación Matemática en la Infancia,...
  • Martín-Díaz, J. P. (2022). Conocimiento especializado del profesor de matemáticas en contextos de formulación de problemas [Tesis doctoral]....
  • Mason, J. (2016). When Is a Problem…? “When” Is Actually the Problem! En P. Felmer, E. Pehkonen y J. Kilpatrick. (Eds.) Posing and Solving...
  • National Council of Teachers of Mathematics (2003). Principios y estándares para la educación matemática. SAEM Thales.
  • Orden de 30 de mayo de 2023, por la que se desarrolla el currículo correspondiente a la etapa de Educación Infantil en la Comunidad Autónoma...
  • Palmér, H. y van Bommel, J. (2020). Young students posing problem-solving tasks: what does posing a similar task imply to students? ZDM Mathematics...
  • Polya, G. (1985). How to solve it (2ª ed.). Princeton University Press.
  • Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A. (2013). Problem-posing research in mathematics education: looking back, looking around, and looking ahead. Educational Studies...
  • Silver, E. A. y Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education,...
  • Singer, F. M., Ellerton, N. y Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational...
  • Stake, R. (1995). The art of case study research. Sage Publications.
  • Stoyanova, E. y Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. En P. C. Clarkson (Ed.),...
  • Strauss, A. L. y Corbin, J. (1990). Basics of Qualitative Research: Grounded Theory Procedures and Techniques. SAGE Publications.
  • Weber, K. y Leikin, R. (2016). Recent advances in research on problem solving and problem posing. En A. Gutiérrez, G. Leder y P. Boero (Eds.),...
  • Yackel, E. y Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education,...
  • Yin, R. K. (2009). Case study research. Design and methods (4.ª ed.). SAGE Publications.