Creating the first mathematical models: analysis of a mod¬eling cycle from a real problem in Early Childhood Education

Journal title CADMO
Author/s Ximena Toalongo-Guamba, Ángel Alsina, César Trelles-Zambrano, María Salgado
Publishing Year 2021 Issue 2021/1
Language Spanish Pages 18 P. 81-98 File size 253 KB
DOI 10.3280/CAD2021-001006
DOI is like a bar code for intellectual property: to have more infomation click here

Below, you can see the article first page

If you want to buy this article in PDF format, you can do it, following the instructions to buy download credits

Article preview

FrancoAngeli is member of Publishers International Linking Association, Inc (PILA), a not-for-profit association which run the CrossRef service enabling links to and from online scholarly content.

The modelling process carried out by 19 children aged 5-6 years in the context of a real problem is analysed to understand how temperature works and how it is measured. To carry out the analysis, the previously validated instrument "Rubric to Evaluate Mathematical Modeling Processes" (REM¬MOP) is used, which includes seven components related to the modeling cycle (understanding, structuring, mathematization, mathematical work, in¬terpretation, validation and presentation) and the corresponding indicators. The results show that, during this cycle: 1) children develop a first model to determine where the numbers are on the thermometer and how they are interpreted, based on the mathematical knowledge they mobilize; 2) they present important deficits especially in the last phases of the modeling cycle. It is concluded that it is necessary to promote the professional development of teachers to incorporate this type of activity from an early age.

Keywords: mathematical modelling, modelling cycle, assessment in math¬ematics, teaching practices, Early Childhood Education.

  1. Lesh, R., Hoover, M., Hole, B., Kelly, A., Post, T. (2000), Principles for developing thought-revealing activities for students and teachers. En A. Kelly, R. Lesh, A. Kelly, R. Lesh (Eds), Handbook of Research Desing in Mathematics and Science Education. Mahwah: Lawrence Erlbaum, pp. 591-645.
  2. McMillan, J.H., Schumacher, S. (2005), Investigacion educativa. Madrid: Pearson Educación SA.
  3. National Governors Association Center for Best Practices, Council of Chief State School Officers (2010), Common Core State Standards Mathematics. National Governors Association Center for Best Practices; Council of Chief State School Officers.
  4. NCTM – National Council of Teachers of Mathematics (2000), Principles and Standards for School Mathematics. NCTM.
  5. NCTM – National Council of Teachers of Mathematics (2014), Principles to actions: Ensuring mathematical success for all. NCTM.
  6. NCTM –National Council of Teachers of Mathematics (1989), Curriculum and Evaluation Standars for School Matematics. NCTM.
  7. Ortiz, J., Rico, L., Castro, E. (2007), Mathematical Modelling: A teacher`s training study. En C. Haines, P. Galbraith, W. Blum, S. Khan (Eds), Mathematical Modelling: Education, Engineering and Economics. Cambridge: Woodhead Publishing Limited, pp. 249-441.
  8. Peter-Koop, A. (2009), Teaching and Understanding Mathematical Modelling through Fermi-Problems. En B. Clarke, B. Grevholm, R. Millman (Eds), Education Mathematics Teacher 4. Tasks in Primary Mathematics Teacher Education: Purpose, Use and Exemplars. Secaucus (NJ): Springer, pp. 131-145.
  9. Porras-Lizano, K., Fonseca-Castro, J. (2015), “Aplicación de actvidades de modelización matemática en la educación secundaria costarricense”, Uniciencia, 29 (1), pp. 42-57. Reeuvijk, M.V. (1997), “Las matemáticas en la vida cotidiana y la vida cotidiana en las matemáticas”, UNO, Revista de Didáctica de las Matemáticas, 12, pp. 9-16.
  10. Ruiz-Higueras, L. (2005), La construcción de los primeros conocimientos numéricos. En M.C. Chamorro, Didáctica de las Matemáticas para Educación Infantil. Madrid: Pearson Educación, pp. 181-219.
  11. Wess, R., Greefrath, G. (2019), Professional competencies for teaching mathematical modelling-supporting the modelling-especific task competency of prospective teachers in the teaching laboratory. En U.T. Jankvist, M. van den Heuvel-Panhuizen, M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht (NL): Grupo Freudenthal, Instituto Freudenthal, Universidad de Utrecht y ERME, pp. 1276-1283.
  12. Alsina, Á. (2012), “Más allá de los contenidos, los procesos matemáticos en Educación Infantil”, Edma 0-6: Educación Matemática en la Infancia, 1 (1), pp. 1-14.
  13. Alsina, Á. (2016), “Diseño, gestión y evaluación de actividades matemáticas competenciales en el aula”, Épsilon, Revista de Educación Matemática, 33 (1), pp. 7-29.
  14. Alsina, Á., Liñán-García, M., Muñoz-Catalán, M.C. (2018), El número y las operaciones matemáticas en Educación Infantil. En M.C. Múñoz-Catalán, J. Carillo (ed. por), Didáctica de las Matemáticas para maestros de Educación Infantil. Madrid: Paraninfo, pp. 81-144.
  15. Alsina, C., García, L.M., Gómez, J., Romero, S. (2007), “Modelling in science education and learning”, SUMA, 54, pp. 51-53.
  16. Bliss, K., Libertini, J. (2019), What is mathematical modeling? En S. Garfunkel, M. Montgomery (Eds), Guidelines for assessment & instruction in mathematical modeling education. Philadelphia: Consortium for Mathematics and Its Applications and Society for Industrial and Applied Mathematics, pp. 7-21.
  17. Blum, W. (2015), Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do?. En S. Cho (Ed), Proceeding of the 21th International Congress on Mathematical Education. Cham: Springer, pp. 73-96.
  18. Blum, W., Borromeo, R. (2009), “Mathematical Modelling: Can I Be Taught And Learn?”, Journal of Mathematical Modeling and Application, 1 (1), pp. 45-58. Blum, W., Leiβ, D. (2007), How do students and teachers deal with modelling problems? En C. Haines, P. Galbraith, W. Blum, S. Khan (Eds), Mathematical Modelling: Education, Engineering and Economics. Cambridge: Woodhead Publishing Limited, pp. 222-231.
  19. Borromeo, R. (2010), “On the influence of mathematical thinking styles on learners’ modelling behaviour”, Journal für Mathematik Didaktik, 31 (1), pp. 99-118.
  20. Carreira, S., Amado, N., 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, G. Stillman (Eds), Trends in teaching and Learning of Mathematical Modeling. Heidelberg: Springer, pp. 199-210.
  21. Corbalán, F. (2011), Los recursos que utilizar. En J.M. Goñi (ed. por), Didáctica de las matemáticas. Barcelona: Graó, pp. 53-74.
  22. English, L.D. (1996), Children’s reasoning in solving novel problems of deduction. En L. Puig, Á. Gutiérrez (Eds), Proceedings of the 20th PME International Conference 2, pp. 329-336.
  23. English, L.D. (2004). Promoting the development of young children’s mathematical and analogical reasoning. En L.D. English (Ed.), Mathematical and analogical reasoning of young learners. Mahwah: Lawrence Erlbaum, pp. 210-215.
  24. English, L.D. (2006), “Mathematical Modeling in the Primary School: Children’s construction of a consumer guide”, Educational Studies in Mathematics, 63, pp. 303-323.
  25. English, L.D. (2010), “Young Children’s Early Modelling with Data”, Mathematics Education Research Journal, 22 (2), pp. 24-47.
  26. English, L.D. (Ed) (1997), Mathematical reasoning: Analogies, metaphors, and images. Mahwah: Lawrence Erlbaum.
  27. English, L.D., Watson, J. (2018), “Modelling with authentic data in sixth grade”, ZDM Mathematics Education, 50, pp. 103-115.
  28. English, L.D., Watters, J.J. (2005), “Mathematical Modelling in the Early School Years”, Mathematics Education Research Journal, 16 (3), pp. 58-79.
  29. Ferrer, M., Fortuny, J.M., Morera, L. (2014), “Efectos de la actuación docente en la generación de oportunidades de aprendizaje matemático”, Enseñanza de las ciencias, 32 (3), pp. 385-405.
  30. Gallart, C., Ferrando, I., García-Raffi, L. (2015), “Análisis competencial de una tarea de modelización abierta”, Números, 88, pp. 93-103.
  31. Gallart, C., Ferrando, I., García-Raffi, L. (2019), “Modelización matemática en la educación secundaria: manual de uso”, Modelling in Science Education and Learning, 12 (1), pp. 71-86.
  32. Geiger, V. (2011), Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modeling. En G. Kaiser, W. Blum, R. Borromeo Ferri, G. Stillman (Eds), Trends in Teaching and Learning of Mathematical Modeling ICTMA 14. Heidelberg: Springer, pp. 305-314.
  33. Girnat, B., 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. Heidelberg: Springer, pp. 75-84.
  34. Greefrath, G. (2011). Using Technologies: New Possibilities of Teaching and learning Modeling - Overview. En G. Kaiser, W. Blum, R. Borromeo Ferri, G. Stillman (Eds), Trends in teaching and Learning of Mathematical Modeling ICTMA 14. Heidelberg: Springer, pp. 301-304.
  35. Kaiser, G. (1995), Realitätsbezüge im Mathematikunterricht – Ein Überblick über die aktuelle und. En G. Graumann, T. Jahnke, G. Kaiser, J. Meyer (hrsg.), Materialen für einen realitätsbezogenen. Hildesheim: Franzbecker, pp. 64-84.
  36. Kaiser, G., Blomhøj, M., Sriraman, B. (2006), “Towards a didactical theory for mathematical modeling”, ZDM Mathematics Education, 38 (2), pp. 82-85.
  37. Kaiser, G., Sriraman, B. (2006), “A global survey of international perspectives on modelling in mathematics education”, Zentralblatt Für Didaktik Der Mathematik, 38 (3), pp. 302-310.
  38. Lawshe, C.H. (1975), “A quantitative approach to content validity”, Personnel Psychology, 28 (4), pp. 563-575.
  39. Ruiz-Higueras, L., 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), pp. 41-70.
  40. Ruiz-Higueras, L., García, F.J., 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), pp. 95-118.
  41. Toalongo-Guamba, X., Trelles-Zambrano, C., Alsina, Á. (2020), Design, construction and validation of a rubric to evaluate mathematical modeling in the different educational stages, manuscrito presentado para su publicación.
  42. Trelles-Zambrano, C., Alsina, Á. (2017), “Nuevos Conocimientos para una Educación Matemática del S. XXI: panorama internacional de la modelización en el currículo”, UNIÓN, Revista Iberoamericana de Educación Matemática, 51, pp. 140-163.
  43. Trigueros, M. (2009), “El uso de la modelación en la enseñanza de las matemáticas”, Innovación Educativa, 9 (46), pp. 75-87.
  44. Tristán-López, A. (2008), “Modificación al modelo de Lawshe para el dictámen cuantitativo de la validez de contenido de un instrumento objetivo”, Avances en Medición, 6, pp. 37-48.

  • Orientaciones didácticas para introducir la modelización matemática temprana en Educación Infantil Angel Alsina, María Salgado, in Modelling in Science Education and Learning /2022 pp.83
    DOI: 10.4995/msel.2022.17226
  • Understanding Early Mathematical Modelling: First Steps in the Process of Translation Between Real-world Contexts and Mathematics Ángel Alsina, María Salgado, in International Journal of Science and Mathematics Education /2022 pp.1719
    DOI: 10.1007/s10763-021-10232-8
  • Design, Construction and Validation of a Rubric to Evaluate Mathematical Modelling in School Education Ximena Toalongo, César Trelles, Ángel Alsina, in Mathematics /2022 pp.4662
    DOI: 10.3390/math10244662

Ximena Toalongo-Guamba, Ángel Alsina, César Trelles-Zambrano, María Salgado, Creando los primeros modelos matemáticos: análisis de un ciclo de modelización a partir de un problema real en Educación Infantil in "CADMO" 1/2021, pp 81-98, DOI: 10.3280/CAD2021-001006