Justificaciones matemáticas motivadas por la modelización de un fenómeno físico

Referencias

Apostol, T. M. (1969). Calculus, vol. 1 y 2. Reverté. Baird, D. C. (1991). Experimentación. Una introducción a la teoría de mediciones y al diseño de experimentos. Prentice Hall. Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18(2), 147–176. http://doi.org/10.1007/BF00314724 Balacheff, N. (1991). The Benefits and Limits of Social Interaction: The Case of Mathematical Proof. En A. J. Bishop, et al. (Eds.), Mathematical Knowledge: Its Growth Through Teaching. Mathematics Education Library, vol 10. Springer. https://doi.org/10.1007/978-94-017-2195-0_9 Balacheff, N. (2019) Contrôle, preuve et démonstration. Trois régimes de la validation. In: Pilet J., Vendeira C. (Eds.) Actes du séminaire national de didactique des mathématiques 2018 (pp.423-456). ARDM et IREM de Pris - Université de Pari Diderot. Barbosa, J. C. (2019). Commentary on Affect, Cognition and Metacognition in Mathematical Modelling. In Scott A.Chamberlin & Bharath Sriraman (Eds.) Affect in Mathematical Modeling (pp. 3-13). Springer. https://doi.org/10.1007/978-3-030- 04432-9_1 Barwell, R. (2013). Formal and informal language in mathematics classroom interaction: a dialogic perspective. In A. M. Lindmeier y A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the PME, Vol. 2 (pp. 73–80). http://www.lettredelapreuve.org/pdf/PME37/Barwell.pdf Bell, W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1), 23–40. https://doi.org/10.1007/BF00144356 Blum W. (2011). ¿Can modelling be taught and learnt? Some answers from empirical research. In Kaiser G., Blum W., Borromeo Ferri R. & Stillman G. (Eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, Vol 1 (pp. 15-30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3 Boero, P. (1999). Argumentación y demostración: una relación compleja, productiva, e inevitable en las matemáticas y en la educación matemática. Prueba. http://www.lettredelapreuve.org/OldPreuve/Newsletter/990708Theme/990708Them eES.html Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In Christian R. Hirsch & Amy Roth McDuffie (Eds). Annual perspectives in mathematics education 2016: Mathematical modeling and modeling mathematics (pp. 3-16). National Council of Teachers of Mathematics. Duval, R. (1993). Registres de représentation sémiotique et le fonctionnement cognitif de la pensé. Annales de Didactique et de Sciences Cognitives, (5), 37- 65. Duval, R. (1999). Semiosis y pensamiento humano. Universidad del Valle. Fischbein, E. (1982). Intuition and Proof. For the Learning of Mathematics, 3(2), 9–18. Halliday, D., Resnick, R., & Walker, J. (2001). Fundamentos de Física, volúmenes 1 y 2. CECSA Halloun, I. A. (2007). Mediated modeling in science education. Science & Education, 16(7), 653-697. https://doi.org/10.1007/s11191-006-9004-3 Hanna, G., & Barbeau, E. (2002). What Is a Proof? In B. Baigrie (Ed.), History of Modern Science and Mathematics, Vol. 1, (pp. 36–48). Charles Scribner’s Sons. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Shoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education. Vol 3 (pp. 234–283). American Mathematical Society. Hemmi, K., Lepik, M., & Viholainen, A. (2013). Analysing proof-related competences in Estonian, Finnish and Swedish mathematics curricula -- towards a framework of developmental proof. Journal of Curriculum Studies, 45(3), 354-378. https://doi.org/10.1080/00220272.2012.754055 Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310. https://doi.org/10.1007/BF02652813 Kelly, G., Druker, S., & Chen, C. (1998). Students’ reasoning about electricity: Combining performance assessments with argumentation analysis. International Journal of Science Education, 20(7), 849–871. https://doi.org/10.1080/0950069980200707 Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113-142. https://doi.org/10.1007/BF02655885 Malafosse D., Lerouge A. & Dusseau J.M. (2000), Étude en inter-didactique des mathématiques et de la physique de l’acquisition de la loi d’Ohm au collège : espace de réalité, Didaskalia,16, 81–106 Marrades, R., & Gutiérrez, Á. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1–2), 87–125. http://doi:10.1023/A:1012785106627 Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66, 23-41. https://doi.org/10.1007/s10649-006-9057-x Protter, M., & Morrey, C. (1964). Modern Mathematical Analysis. Addison-Wesley Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50(1), 301-314. https://doi.org/10.1007/s11858-017-0898-9 Toulmin, S. E. (1969). The uses of argument. Cambridge University Press Touma, G. (2009). Une étude sémiotique sur l'activité cognitive d'interprétation. Annales de didactique et de sciences cognitives. (14): 79-101 Umland, K., & Sriraman, B. (2014). Argumentation in Mathematics. In Stephen Lerman (Ed.) Encyclopedia of Mathematics Education (pp. 44–46). Springer. https://doi.org/10.1007/978-94-007-4978-8 Watson, F. (1980). The role of proof and conjecture in mathematics and mathematics teaching. International Journal of Mathematical Education in Science and Technology, 11(2), 163-167. https://doi.org/10.1080/0020739800110202