Fases del razonamiento inductivo que presentan profesores de matemáticas al resolver un problema de generalización

Referencias

Alajmi, A. H. (2016). Algebraic generalization strategies used by Kuwaiti preservice teachers. International Journal of Science and Mathematics Education, 14(8), 1517–1534. https://doi.org/10.1007/s10763-015-9657-y AMTE (2017). Standards for preparing teachers of mathematics. Recuperado el 18 de mayo de 2017, de https://amte.net/standards. Bills, L. y Rowland, T. (1999). Examples, generalisation and proof. Advances in Mathematics Education, 1(1), 103-116. https://doi.org/10.1080/14794809 909461549 Cañadas, M. C. y Castro, E. (2007). A proposal of categorisation for analysing inductive reasoning. PNA, 1(2), 67-78. https://doi.org/10.1227/01.NEU. 0000032542.40308.65 Cañadas, M. C., Castro, E. y Castro, E. (2008). Patrones, generalización y estrategias inductivas de estudiantes de 3° y 4° de educación secundaria obligatoria en el problema de las baldosas. PNA, 2(3), 137-151. Cañadas, M. C., Castro, E. y Castro, E. (2009). Utilización de un modelo para describir el razonamiento inductivo de los estudiantes en la resolución de problemas. Electronic Journal of Research in Educational Psychology, 7(1), 261-278. Cañadas, M. C. y Castro, E. (2013). Análisis didáctico en una investigación sobre razonamiento inductivo. En L. Rico, J. L. Lupiáñez y M. Molina (Eds.), Análisis Didáctico en Educación Matemática. Metodología de Investigación, Formación de profesores e Innovación Curricular (pp. 333-348). Granada, España: Editorial Comares. Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D. y Yevdokimov, O. (2007). The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55-72. Castro, E., Cañadas, M. C. y Molina, M. (2010). El Razonamiento Inductivo como Generador de Conocimiento Matemático. UNO, 54, 55-67. https://doi.org/ 10.1017/CBO9781107415324.004 Davydov, V. (1990). Type of generalization in instruction: Logical and psychological problems in the structuring of school curricula. En J. Kilpatrick (Ed.), Soviet Studies in Mathematics Education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics. Davydov, V. (2008). Problems of developmental instruction: A theoretical and experimental psychological study. Nueva York, NY: Nova Science Publishers. Demonty, I., Vlassis, J. y Fagnant, A. (2018). Algebraic thinking, pattern activities and knowledge for teaching at the transition between primary and secondary school. Educational Studies in Mathematics, 99(1), 1-19. https://doi.org/10.1007/s10649-018-9820-9 El Mouhayar, R. y Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379-396. https://doi.org/10.1007/s10649-012-9434-6 Glaser, R. y Pellegrino, J. (1982). Improving the skills of learning. En D. K. Detterman y R. J. Sternberg (Eds.), How and How Much can Intelligence be Increased (pp. 197-212). Norwood, NJ: Ablex. Hallagan, J. E., Rule, A. C., y Carlson, L. F. (2009). Elementary school preservice teachers’ understandings of algebraic generalizations. The Mathematics Enthusiast, 6(1), 201-206. Haverty, L., Koedinger, K., Klahr, D. y Alibali, M. (2000). Solving Inductive Reasoning Problems in Mathematics: Not-so-Trivial Pursuit. Cognitive Science, 24(2), 249–298. Herbert, S., Vale, C., Bragg, L. A., Loong, E. y Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26-37. http://dx.doi.org/ 10.1016/j.ijer.2015.09.005 Hernández, R., Fernández, C. y Baptista, P. (2006). Metodología de la investigación (4a ed.). D.F., México: McGraw-Hill. Hodnik, T. y Manfreda, V. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283–306. https://doi.org/10.1007/s10649-015- 9598-y Klauer, K. (1996). Teaching inductive reasoning: some theory and three experimental studies. Learning and Instruction, 6(1), 37–57. https://doi.org/10.1016/0959-4752(95)00015-1 Manfreda, V., Slapar, M. y Hodnik, T. (2012). Comparison of competences in inductive reasoning between primary teachers' students and mathematics teachers' students. En B. Maj-Tatsis y K. Tatsis (Eds.), Generalization in mathematics at all educational levels. Rzeszów, Polonia: Wydawnictwo Uniwersytetu Rzeszowskiego. Molnár, G. (2011). Playful fostering of 6-to 8-year-old students’ inductive reasoning. Thinking Skills and Creativity, 6(2), 91-99. https://doi.org/10.1016/j.tsc.2011.05.002 Molnár, G., Greiff, S. y Csapó, B. (2013). Inductive reasoning, domain specific and complex problem solving: Relations and development. Thinking Skills and Creativity, 9, 35-45. https://doi.org/10.1016/j.tsc.2013.03.002 Mousa, M. (2017). The influence of inductive reasoning thinking skill on enhancing performance. International Humanities Studies, 4(3), 37–48. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Neubert, G. A. y Binko, J. B. (1992). Inductive reasoning in the secondary classroom. Washington, D.C.: National Education Association. Papageorgiou, E. (2009). Towards a teaching approach for improving mathematics inductive reasoning problem solving. En M. Tzekaki, M. Kaldrimidou y H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 313–320). Thessaloniki, Grecia: PME. Pólya, G. (1957). How to solve it. A New aspect of mathematical method. Nueva York, NY: Doubleday & Company, Inc. Pólya, G. (1966). Matemáticas y razonamiento plausible. Madrid, España: Tecnos. Rivera, F. D. y Becker, J. R. (2003). The effects of numerical and figural cues on the induction processes of preservice elementary teachers. En N. Pateman, B. Dougherty y J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education Held Jointly with the 25th PME-NA Conference (Vol.4, pp. 63–70). Honolulu, HI: International Group for the Psychology of Mathematics Education. Rivera, F. D. y Becker, J. R. (2007). Abduction-induction (generalization) processes of elementary majors on figural patterns in algebra. Journal of Mathematical Behavior, 26(2), 140–155. https://doi.org/10.1016/j.jmathb. 2007.05.001 Secretaría de Educación Pública [SEP] (2017). Aprendizajes clave para la educación integral. Plan y programas de estudio para la educación básica. Ciudad de México, México: Autor. Sosa, L. y Cabañas, G. (2017). Analytical framework to study inductive reasoning in mathematical teachers while solving task. En E. Galindo y J. Newton (Eds.), Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1415-1418). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators. Sriraman, B. y Adrian, H. (2004). The pedagogical value and the interdisciplinary nature of inductive processes in forming generalizations: Reflections from the classroom. Interchange, 35(4), 407–422. Stylianides, G., Stylianides, A. y Shilling-Traina, L. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490. https://doi.org/10.1007/ s10763-013-9409-9 Tomic, W. (1995). Training in inductive reasoning and problem solving. Contemporary Educational Psychology, 20(4), 483–490. https://doi.org/10.1006/ceps.1995.1036 Warren, E., Trigueros, M. y Ursini, S. (2016). Research on the learning and teaching of algebra. In A. Gutiérrez, G. Leder, y P. Boero (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education. The Journey Continues (pp. 73–108). Rotterdam, Países Bajos: Sense Publishers.