Desarrollo del sentido estructural en alumnos universitarios mediante el uso de la Teoría de la Variación en el manejo de expresiones algebraicas racionales

Referencias

Banerjee, R., & Subramaniam, K. (2005). Developing procedure and structure sense of arithmetic expressions. En H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 121–128). Melbourne: PME. Burgell, F., & Ochoviet, C. (2015). Significados del signo de igual y aspectos de su enseñanza. Un estudio realizado con estudiantes de primer año de enseñanza secundaria y sus profesores. Enseñanza de las Ciencias, 33(3), 77. doi:10.5565/rev/ensciencias.1561. Chinnappan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26(4), 871–896. doi: 10.1007/s13394-014-0131-x Eccius-Wellmann, C. C. C. (2011). Implications of a lack in structure sense for business school students. En Proceedings of the 6th Annual Meeting of the Academy of Business Education. Orlando, USA. Eccius-Wellmann, C. C. C. (2013). The role of structure sense in recognizing term structure. En C. O. Trejo-Pech, R. Manley, & A. Jaiswal-Dale (Eds.), Proceedings of the XII Inter- national Business and Economy Conference (Vol. 12, pp. 114–125). Caen, France. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. New York: Kluwer Academic/Plenum Publishers. Godino, J. D., Aké, L., Contreras, Á., Estepa, A., Fernandez, T., Neto, T., ... Lasa, A. (2015). Diseño de un cuestionario para evaluar conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental. Enseñanza de las Ciencias. Revista de investigación y experiencias didácticas, 33(1), 127–150. Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A chinese way of promoting effective mathematics learning. En L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How chinese learn mathematics: Perspectives from insiders (Vol. 1, pp. 309–347). Singapore: World Scientific. Häggström, J. (2008). Teaching systems of linear equations in Sweden and China: What is made possible to learn? (Doctoral thesis). University of Gothenburg, Göteborg, Sweden. Recuperado de https://gupea.ub.gu.se/handle/2077/17286 Harel, G. (2013). Dnr-based curricula: The case of complex numbers. Journal of Humanistic Mathematics, 3(2), 2–61. doi: 10.5642/jhummath.201302.03. Harel, G., & Soto, O. (2017). Structural reasoning. International Journal of Research in Under- graduate Mathematics Education, 3(1), 225–242. doi: 10.1007/s40753-016-0041-2 Hoch, M. (2003). Structure sense. En M. A. Mariotti (Ed.), Proceedings of the 3rd Conference for European Research in Mathematics Education (Vol. 3, pp. 1–3). Bellaria, Italia. Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: The effect of brackets. En M. Johnsen Hoines & A. Berit Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 49–56). Bergen, Norway. Hoch, M., & Dreyfus, T. (2006). Structure sense versus manipulation skills: an unexpected result. En J Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 305–312). Prague, Czech Republic. Hoch, M., & Dreyfus, T. (2007). Recognising an algebraic structure. En D. Pitta, P. Philipou, & G. Philipou (Eds.), Proceedings of the Fifth Congress of European Research in Mathematics Education (Vol. 5, pp. 436–445). Larnaca, Cyprus. Huang, R., & Li, Y. (Eds.). (2017). Teaching and learning mathematics through variation: Confucian heritage meets western theories. Rotterdam: Sense Publishers. Jupri, A., & Sispiyati, R. (2017). Expert strategies in solving algebraic structure sense problems: The case of quadratic equations. Journal of Physics: Conference Series, 812, 012093. doi:10.1088/1742-6596/812/1/012093 Kieran, C. (2018). Seeking, using, and expressing structure in numbers and numerical operations: a fundamental path to developing early algebraic thinking. En Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 79–105). Springer, Cham. Kullberg, A., Kempe, U. R., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM, 49(4), 559–569. doi:10.1007/s11858-017-0858-4 Lai, M. Y., & Murray, S. (2012). Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics. International Journal for Mathematics Teaching and Learning, 1–25. Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173–196. Lo, M. L. (2012). Variation theory and the improvement of teaching and learning. Göteborg: Acta Universitatis Gothoburgensis. Lüken, M. M. (2012). School starters’ early structure sense. PNA, 7(1), 41–50. Marton, F. (2015). Necessary conditions of learning. New York: Routledge. Marton, F., & Booth, S. (1997). Learning and awareness. New York: Routledge. Marton, F., Runesson, U., & Tsui, A. B. M. (2004). The space of learning. En F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 3–24). New York: Routledge. Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32. Molina, M. (2010). Una visión estructural del trabajo con expresiones aritméticas y algebraicas. Revista Suma, 65, 7–15. Novotná, Jarmila, Stehlíková, N., & Hoch, M. (2006). Structure sense for university algebra. En Jarmila Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 249–256). Prague, Czech Republic. Olteanu, C., & Olteanu, L. (2012). Equations, functions, critical aspects and mathematical communication. International Education Studies, 5(5), 69–78. doi:10.5539/ies.v5n5p69 Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. Sfard, A. (2001). Equilibrar algo desequilibrado: Los estándares del NCTM a la luz de las teorías del aprendizaje de las matemáticas. Revista EMA, 6(2), 95–140. Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–16. Vega-Castro, D. C. (2010). Sentido estructural de estudiantes de bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables (Tesis de maestría no publicada). Universidad de Granada, Granada, España. Recuperado de http://digibug.ugr.es/handle/10481/23888 Vega-Castro, D. C. (2013). Perfiles de alumnos de Educación Secundaria relacionados con el sentido estructural manifestado en experiencias con expresiones algebraicas (Tesis de doctorado no publicada). Universidad de Granada, Granada, España. Recuperado de http://digibug.ugr.es/handle/10481/31311 Vega-Castro, D., Molina, M., & Castro, E. (2012). Sentido estructural de estudiantes de bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables. Revista latinoamericana de investigación en matemática educativa, 15(2), 233–258.