Moving beyond descriptive models: Research issues for design and implementation

• Jonas Bergman Ärlebäck ^[1] ; Helen M. Doerr ^[2]
  1. [1] Linköping University

     Linköping University

     Linköpings S:t Lars, Suecia

     
  2. [2] Syracuse University

     Syracuse University

     City of Syracuse, Estados Unidos

     
• Localización: Avances de investigación en educación matemática, ISSN-e 2254-4313, Nº. 17, 2020, págs. 5-20
• Idioma: inglés
• DOI: 10.35763/aiem.v0i17.307
• Títulos paralelos:
  • Más allá de modelos descriptivos: Cuestiones de investigación sobre diseño e implementación
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En este artículo nos situamos en la perspectiva teórica ‘models and modeling’ para describir el diseño de una secuencia de tareas, conocida como secuencia de desarrollo de modelos, utilizada para investigar la enseñanza y aprendizaje de las matemáticas. Un objetivo central de la investigación desde esta perspectiva es desarrollar principios para el diseño de secuencias de tareas de modelización y para su enseñanza. En este trabajo nos proponemos ampliar nuestras investigaciones anteriores elaborando la forma en la que una secuencia de desarrollo de modelos puede servir para apoyar a los estudiantes al desarrollar modelos que no sean sólo descriptivos, sino también explicativos, especialmente cuando se conectan a los modelos matemáticos existentes. Para ello, elaboramos cuestiones de lenguaje sobre representaciones y contexto, así como estrategias de implementación del profesor.

  • English

    In this paper, we draw on a models and modeling perspective to describe the design of a sequence of tasks, known as a model development sequence, that has been used to research the teaching and learning of mathematics. A central research goal of a models and modeling perspective is the development of principles for the design of sequences of modeling tasks and for the teaching of such sequences. We extend our earlier research by elaborating how a model development sequence can be used to support students in developing models that are not only descriptive but also have explanatory power when connected to existing mathematical models. In so doing, we elaborate language issues about representations and context as well as the implementation strategies used by the teacher

• Referencias bibliográficas
  • Ärlebäck, J. B., & Doerr, H. M. (2015). Preserving students’ independence by encouraging students self-evaluation. In H. Silfverberg,...
  • Ärlebäck, J. B., & Doerr, H. M. (2018). Students’ interpretations and reasoning about phenomena with negative rates of change throughout...
  • Ärlebäck, J. B., Doerr, H. M., & O’Neil, A. H. (2013). A modeling perspective on interpreting rates of change in context. Mathematical...
  • Barquero, B., Bosch, M., & Gascón, J. (2013). The ecological dimension in the teaching of mathematical modelling at university. Recherches...
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of the 12th...
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application,...
  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher,...
  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks,...
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith,...
  • Doerr, H. M, Ärlebäck, J. B., & Stanic, A. C. (2014). Design and effectiveness of modelling-based mathematics in a summer bridge program....
  • Doerr, H. M., Ärlebäck, J. B., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. A. Stillman, W. Blum,...
  • Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in...
  • Doerr, H. M., & Lesh, R. A. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century....
  • Hestenes, D. (2010). Modeling theory for math and science education. In R. A. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds). Modeling...
  • Lesh, R. A., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. (2003). Model development sequences. In R. A. Lesh & H. M. Doerr...
  • Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching...
  • Lesh, R. A., & Doerr, H. M. (Eds.) (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning,...
  • Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92-107.
  • Maass, K. (2011). How can teachers’ beliefs affect their professional development? ZDM Mathematics Education, 43(4), 573–586.
  • Niss, M. (2015). Prescriptive modelling. Challenges and opportunities. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.). Mathematical...
  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H.- W. Henn, & M. Niss (Eds.), Modelling and applications...
  • Pollak, H. O. (1979). The interaction between mathematics and other school subjects. New trends in mathematics teaching (Vol. 4, pp. 232–248)....
  • Rosa, M, & Orey, D. (2015). Social-critical dimensions of mathematical modelling. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.)....
  • Temple, C., & Doerr, H. M. (2012). Developing fluency in the mathematical register through conversation in a tenth-grade classroom. Educational...
  • Wake, G. (2011). Teachers’ professional learning: Modelling at the boundaries. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman...