Impact of theoretical perspectives on the design of mathematical modelling tasks

Referencias

Ärlebäck, J. B., & Doerr, H. M. (2015). At the core of modelling: Connecting, coordinating and integrating models. In K. Krainer, & N. Vondrová (Eds.), Proceedings of CERME9 (pp. 802–808). Prague, Czech Republic: Charles University. Ärlebäck, J. B., & Doerr, H. M. (2018). Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence. ZDM Mathematics Education, 50(1-2), 187-200. Barquero, B., & Bosch, M. (2015). Didactic Engineering as a research methodology: From fundamental situations to study and research paths. In A. Watson, & M. Ohtani (Eds.), Task design in mathematics education (pp. 249–272). Cham, Switzerland: Springer. Barquero, B., Bosch, M., & Gascón, J. (2019). The unit of analysis in the formulation of research problems: The case of mathematical modelling at university level. Research in Mathematics Education, 21(3), 314–330. 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 International Congress on Mathematical Education (pp. 73–96). Cham, Switzerland: Springer. Blum, W., & Leiß, D. (2007). How do students and teachers deal with mathematical modelling problems? The example Sugarloaf and the DISUM project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics. ICTMA 12 (pp. 222–231). Chichester, England: Horwood. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68. Borromeo Ferri, R. (2007). Modeling from a cognitive perspective: Individual modeling routes of pupils. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 260–270). Chichester, England: Horwood. Bosch, M. (2018). Study and Research Paths: A model for inquiry. Proceedings of the International Congress of Mathematics (pp. 4001–4022). Rio de Janeiro, Brazil: ICM. Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51-65. Burkhardt, H. (2018). Ways to teach modelling. A 50 year study. ZDM Mathematics Education, 50(1-2), 61–75. Cai, J., Cirillo, M., Pelesko, J. A., Borromeo Ferri, R., et al. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional, and teacher education perspectives. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of PME38 (Vol. 1, pp. 145–172). Vancouver, Canada: PME. Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266. Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of CERME4 (pp. 21–30). Barcelona: FUNDEMI- IQS. Chevallard, Y. (2015). Teaching mathematics in tomorrow’s society: A case for an oncoming counter paradigm. In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 173–187). Cham, Switzerland: Springer. Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. English L. D., Ärlebäck J. B., & Mousoulides N. (2016). Reflections on progress in mathematical modelling research. In Á. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education. The journey continues (pp. 383–413) Rotterdam, the Netherlands: Sense Publishers. Czocher, J.A. (2017). Mathematical modelling cycles as task design heuristics. The Mathematics Enthusiast, 14(1), 129-140. Fonseca, C., Gascón, J., & Lucas, C. (2014). Desarrollo de un modelo epistemológico de referencia en torno a la modelización funcional. RELIME, 17(3), 289-318. Galbraith, P. L., Henn, H., Blum , W., & Niss, M. (2007). Modeling and applications in mathematics education The 14th ICMI Study. New York: Springer. García, F. J., Barquero, B., Florensa, I., & Bosch, M. (2019). Diseño de tareas en el marco de la Teoría Antropológica de lo Didáctico. Avances de Investigación en Educación Matemática, 15, 75–94. García, F. J., Gascón, J., Higueras, L. R., & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM Mathematics Education, 38(3), 226–246. Greefrath G. (2020). Mathematical modelling competence. Selected current research developments. Avances de Investigación en Educación Matemática, 17, 38–51. Jessen, B. E., Kjeldsen, T. H., & Winsløw, C. (2015). Modelling: From theory to practice. In K. Krainer, & N. Vondrová (Eds.), Proceedings of CERME9 (pp. 876– 882). Prague, Czech Republic: Charles University. Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 110–119). Chichester, England: Horwood. Kaiser, K., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM Mathematics Education, 38(2), 196–208. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM Mathematics Education, 38, 302-310. Kieran, C., Doorman, M., & Ohtani, M. (2015). Frameworks and principles for task design. In A. Watson, & M. Ohtani (Eds.), Task design in mathematics education: The 22nd ICMI Study (pp. 19–81). New York: Springer. Lesh, R. A., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. A. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching and learning (pp. 35–58). Mahwah, NJ: Lawrence Erlbaum. Lesh, R., & Doerr, H. (2003). Foundations of a model and modeling perspective on mathematics teaching, learning, and problem solving. In R. A. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum. Lesh, R., & Fennewald, T. (2013). Introduction to Part I Modeling: What is it? Why do it? In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modelling competencies (pp. 5–10). New York: Springer. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. A. Lesh, & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–646). Mahwah, NJ: Lawrence Erlbaum. Lucas, C. (2015). Una posible razón de ser del cálculo diferencial elemental en el ámbito de la modelización funcional. PhD Manuscript. Universidad de Vigo. Lucas, C., Fonseca, C., Gascón, J., & Schneider, M. (2020). The phenomenotechnical potential of reference epistemological models: The case of elementary differential calculus. In M. Bosch, Y. Chevallard, J. García, & J. Monaghan (Eds.), Working with the Anthropological Theory of the Didactic in mathematics education: A comprehensive casebook (pp. 77–97). London, England: Routledge. Maaß, K. (2010). Classification scheme for modeling tasks. Journal für Mathematik- Didaktik, 31(2), 285–311. Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D., & Schukajlow, S. (2019). Mathematical modelling. In H. N. Jahnke, & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 91–114). Cham, Switzerland: Springer.