Beginning early mathematical modelling in Early Childhood Education: how do 3-year-olds think and what do they do?
DOI:
https://doi.org/10.24197/edmain.1.2022.1-38Keywords:
Early mathematical modelling, modelling cycle, concrete model, mathematics teaching, Early Childhood EducationAbstract
Early mathematical modelling, defined as a process that helps to create the first models to analyse, explain and understand reality, is an ideal framework for developing mathematical competence. From this point of view, the activity "we build houses with pieces of wood", which has been implemented with 20 3-year-old children, is presented. In order to analyse the modelling cycle, the indicators of the "Rubric for the Evaluation of Mathematical Modelling Processes" were used. The results show that 3-year-olds begin to develop skills of comprehension, structuring, mathematization, mathematical work, interpretation, validation and exposition and, therefore, create the first concrete models. It is concluded that, in future studies, it is necessary to determine the influence of several variables on children's actions, such as the type of task or the knowledge of the Early Childhood Education teacher to carry out early mathematical modelling activities.
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Alsina, Á. (2012). Más allá de los contenidos, los procesos matemáticos en Educación Infantil. Edma 0-6: Educación Matemática en la Infancia, 1(1), 1-14.
Alsina, Á. (2016). Diseño, gestión y evaluación de actividades matemáticas competenciales en el aula. Épsilon, Revista de Educación Matemática, 33(1), 7-29.
Alsina, Á. (2020). Cinco prácticas productivas para una enseñanza de las matemáticas a través de los procesos. Saber & Educar, 28, 1-13.
Alsina, Á., y Salgado, M. (2021a). Introduciendo la Modelización Matemática Temprana en Educación Infantil: un marco para resolver problemas reales. Modelling in Science Education and Learning, 14(1), 33-56. https://doi.org/10.4995/msel.2021.14024
Alsina, Á., y Salgado, M. (2021b). Understanding Early Mathematical Modelling: First Steps in the Process of Translation Between Real-world Contexts and Mathematics. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-021-10232-8
Alsina, Á., Maurandi-Lopez, A., Ferre, E., y Coronata, C. (2021a). Validating an Instrument to Evaluate the Teaching of Mathematics Through Processes. International Journal of Science and Mathematics Education, 19, 559–577. https://doi.org/10.1007/s10763-020-10064-y
Alsina, Á., Toalongo-Guamba, X., Trelles-Zambrano, C., y Salgado, M. (2021b). Desarrollando habilidades de modelización matemática temprana en Educación Infantil: un análisis comparativo en 3 y 5 años. Quadrante, 30(1), 74–93. https://doi.org/10.48489/quadrante.23654
Andrade, H. G. (2000). Using rubrics to promote thinking and learning. Educational Leadership, 57(5), 13-18.
Blum, W., y Leiß, D. (2007). How do students and teachers deal with modelling problems? En C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12). Education, engineering and economics (pp. 222–231). Ellis Horwood.
Blum, W., y Kirsch, A. (1989). The problem of the graphic artist. En W. Blum, J. S. Berry, R. Biehler, I. D. Huntley, G. Kaiser-Meßner, y L. Profke (Eds.), Applications and Modelling in Learning and Teaching Mathematics (pp. 129-135). Ellis Horwood.
Carreira, S., Amado, N., y Lecoq, F. (2011). Mathematical Modeling of Daily Life in Adult Education: Focusing on the Notion of knowledge. En G. Kaiser, W. Blum, R. Borromeo Ferri, y G. Stillman (Eds.), Trends in teaching and Learning of Mathematical Modeling (pp. 199-210). Springer.
Chevallard, Y. (1999). El análisis de las prácticas docentes en la teoría antropológica de los didáctico. Recherches en Didáctique des Mathématiques, 19(2), 221-266.
Common Core State Standards Initiative [CCSSI] (2010). Common Core State Standards for Mathematics. Recuperado de http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Freudenthal, H. (1991), Revising mathematics education. Dordrecht: Kluwer Academic Publishers.
Geiger, V. (2011). Factors Affecting Teachers' Adoption of Innovative Practices with Technology and Mathematical Modeling. En G. Kaiser, W. Blum, R. Borromeo Ferri y G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling ICTMA 14 (pp. 305-314). Springer.
Girnat, B., y Eichler, A. (2011). Secondary Teacher`s Beliefs on Modeling in Geometry and Stochastics. En G. Kaiser, W. Blum, R. Borromeo Ferri, y G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling ICTMA 14 (pp. 75-84). Springer.
Greefrath, G. (2011). Using Technologies: New Possibilities of Teaching and learning Modeling - Overview. En G. Kaiser, W. Blum, R. Borromeo Ferri y G. Stillman (Eds.), Trends in teaching and Learning of Mathematical Modeling ICTMA 14 (pp. 301-304). Springer.
Greefrath, G. (2019). Mathematical modelling – Background and current projects in Germany. En J. M. Marbán, M. Arce, A. Maroto, J. M. Muñoz-Escolano y Á. Alsina (Eds.), Investigación en Educación Matemática XXIII (pp. 23-41). SEIEM.
Kaiser, G. (1995). Realitätsbezüge im Mathematikunterricht - Ein Überblick über die aktuelle und. En G. Graumann, T. Jahnke, G. Kaiser, y J. Meyer (Eds.), Materialen für einen realitätsbezogenen (pp. 64-84). Franzbecker.
Maaß, K. (2004). Mathematisches Modellieren im Unterricht. Ergebnisse einer empirischen Studie. Franzbecker.
Ministry of Education Singapore (2012). Mathematics Syllabus. Primary One to Six. Curriculum Planning and Development Division.
National Council of Teachers of Mathematics [NCTM] (2003). Principios y estándares para la educación matemática. Servicio de Publicaciones de la SAEM Thales.
National Research Council [NRC] (2001). Adding It Up: Helping Children Learn Mathematics. The National Academies Press.
Ortlieb, C. P. (2004). Mathematische Modelle und Naturerkenntnis. Mathematica didactica, 27(1), 23–40.
Ruiz-Higueras, L., García, F. J., y Lendínez, E. M. (2013). La actividad de modelización en el ámbito de las relaciones espaciales en la Educación Infantil. Edma 0-6: Educación Matemática en la Infancia, 2(1), 95-118.
Ruiz-Higueras, L., y García, F. J. (2011). Análisis de praxeologías didácticas en la gestión de procesos de Modelización Matemática en la Escuela Infantil. Revista Latinoamericana de Investigación en Matemática Educativa, 14(1), 41-70.
Toalongo-Guamba, X., Alsina, Á., Trelles-Zambrano, C., y Salgado, M. (2021). Creando los primeros modelos matemáticos: análisis de un ciclo de modelización a partir de un problema real en Educación Infantil. CADMO, Giornale Italiano di Pedagogia Sperimentale 1/2021, 81-98. https://doi.org/10.3280/CAD2021-001006
Toalongo-Guamba, X., Trelles-Zambrano, C. y Alsina, Á. (2020). Design, construction and validation of a rubric to evaluate mathematical modeling in the different educational stages. Artículo entregado para la publicación.
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