Evolution of Non-Institutional Representations in a Modeling Process of Teaching (ACODESA)

Referencias

Alsina, C. (2007). Less chalk, less words, less symbols… more objects, more context, more actions. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 35–44). Springer. https://doi.org/10.1007/978-0-387-29822-1_2 Bourdieu, P. (1980). Le sens pratique. Éditions de Minuit. Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématiques. Recherches en Didactique des Mathématiques, 4(2), 164-198. Cerqueira, J. (2009). Mathematical modelling, the socio-critical perspective and the reflexive discussions. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics (pp. 133–144). Roskilde Universitet. Cole, M. (1996). Cultural psychology. A once and future discipline. The Belknap Press of Harvard University Press. Creswell, J. (2007). Qualitative inquiry and research design. Sage. D’Ambrosio, U. (2000). A historiographical proposal for non-western mathematics. In H. Selin (Ed.), Mathematics across cultures science across cultures: The history of non-western mathematics (pp. 79–92). Springer. https://doi.org/10.1007/978-94-011-4301-1_6 diSessa, A., Hammer, D., Sherin, B., & Kolpakowski, T. (1991). Inventing graphing: MetaRepresentational expertise in children. Journal of Mathematical Behavior, 10(2), 117–160. Duval, R. (1995). Sémiosis et pensée humaine: Registres sémiotiques et apprentissages intellectuels. Peter Lang. Eco, U. (1992). La production des signes. Livre de Poche. (Original published in 1975) Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamäki (Eds.), Perspectives on activity theory (pp. 19–38). Cambridge University Press. https://doi.org/10.1017/CBO9780511812774.003 Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Kluwer Academic Publishers Group. Hernández, R., Baptista, P., & Fernández, C. (2010). Metodología de la investigación. McGraw-Hill. Hitt, F. (2013). Théorie de l’activité, interactionnisme et socioconstructivisme. Quel cadre théorique autour des représentations dans la construction des connaissances mathématiques ? Annales de Didactique et de Sciences Cognitives, 18(1), 9–27. https://doi.org/10.4000/12dwu Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process: The ACODESA (Collaborative learning, Scientific debate and Self-reflexion) method. Educational Studies in Mathematics, 88(2), 201–219. https://doi.org/10.1007/s10649-014-9578-7 Hitt, F., & Quiroz, S. (2017). Aprendizaje de la modelación matemática en un medio sociocultural. Revista Colombiana de Educación, 73, 153–177. https://doi.org/10.17227/01203916.73rce151.175 Hitt, F., Quiroz, S., Saboya, M., & Lupiáñez, J. (2023). Une approche socioculturelle pour la construction d’habiletés de généralisation arithmético-algébriques dans les écoles québécoises et mexicaines. Educación Matemática, 35(3), 112–150. https://doi.org/10.24844/em3503.04 Ikeda, T. (2007). Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 457–463). Springer. https://doi.org/10.1007/978-0-387-29822-1_51 Imm, K., & Lorber, M. (2013). The footprint problem: A pathway to modeling. Mathematics Teaching in the Middle School, 19(1), 46–54. https://doi.org/10.5951/mathteacmiddscho.19.1.0046 Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Lawrence Erlbaum Associates. Karsenty, R. (2003). What adults remember from their high school mathematics? The case of linear functions. Educational Studies in Mathematics, 51, 117–144. https://doi.org/10.1023/A:1022429504802 Koellner-Clark, K., & Lesh, R. (2003). Whodunit? Exploring proportional reasoning through the footprint problem. School Science and Mathematics, 103(2), 92–98. https://doi.org/10.1111/j.1949-8594.2003.tb18224.x Legrand, M. (2001). Scientific debate in mathematics courses. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI Study (pp. 127–135). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_12 Leontiev, A. (1978). Activity, consciousness, and personality. Prentice Hall. Lesh, R., & Doerr, H. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. LEA publishers. https://doi.org/10.4324/9781410607713 Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modelling perspectives on mathematics problem solving, learning, teaching? In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI Study (pp. 161–170). Springer. https://doi.org/10.1007/978-0-387-29822-1_15 Lombardo, D. H., & Jacobini, O. R. (2009). Mathematical modelling: From classroom to the real world. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics (pp. 35–46). Roskilde University. Perkins, D., & Simmons, R. (1988). Patterns of misunderstanding: An integrative model for science, math, and programming. Review of Educational Research, 58(3), 303–326. https://doi.org/10.3102/003465430580033 Powell, A., Francisco, J., & Maher, C. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22(4), 405–435. https://doi.org/10.1016/j.jmathb.2003.09.002 Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70. https://doi.org/10.1207/S15327833MTL0501_02 Soto, J., Hitt, F., & Quiroz, S. (2019). Distinción entre ejercicio, problema y situación problema en un medio tecnológico y ejemplos en diferentes niveles educativos. In S. Quiroz, E. Nuñez, M. Saboya, & J. Soto (Eds.), Investigaciones teórico prácticas sobre la modelación matemática en un mundo tecnológico (pp. 31–50). Editorial Amiutem. Thompson, P. (2002). Some remarks on conventions and representations. In F. Hitt (Ed.), Mathematics visualisation and representations (pp. 199–206). Scientific Research. Voloshinov, V. N. (1973). Marxism and the philosophy of language. Harvard University Press. von Glasersfeld, E. (2001). Questions et réponses au sujet du constructivisme radical. In P. Jonnaert & D. Masciotra (Eds.), Constructivisme choix contemporains (pp. 291–323). Presses de l’Université du Québec. Vygotsky, L. (1962). Thought and language. Boston Review. https://doi.org/10.1037/11193-000 Warren, E. (2006). Teachers actions that assist young students write generalizations in words and in symbols. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 377–384). PME. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. https://doi.org/10.2307/749877 Yin, R. (2014). Case study research design and methods. Sage Publications. https://doi.org/10.3138/cjpe.30.1.10