Historia de las matemáticas para la formación inicial de maestros
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Sep 16, 2019
Palabras clave:
matemáticas, didáctica, grado universitario, enseñanza primaria, historia
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Gran parte del alumnado que nos encontramos en las aulas del grado de maestro o maestra en educación primaria es desconocedor de los hechos históricos que ocurrieron alrededor del personaje que produjo el contenido matemático que trabajamos, ni tampoco las consecuencias que se han plasmado en el currículo que trabajarán con sus futuros alumnos y alumnas. Siguiendo la teoría de Jankvist (2009) y la experiencia de Furinghetti (2007), emulamos una pequeña experiencia con nuestro alumnado para observar cómo es de útil la historia matemática en el momento de enseñar y aprender matemáticas La consecuencia principal ha sido que nuestro alumnado fue más consciente del proceso histórico-evolutivo de las matemáticas y su perfil más humano y dinámico reforzando así las múltiples miradas que su futuro alumnado pueda tener sobre los contenidos matemáticos.
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Santágueda Villanueva, M., & Lorenzo-Valentín, G. (2019). Historia de las matemáticas para la formación inicial de maestros. Matemáticas, educación Y Sociedad, 2(2), 19–32. Recuperado a partir de https://journals.uco.es/mes/article/view/12842
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Esta obra está bajo una Licencia Creative Commons Atribución 3.0 España
Bibliografía
Alcalde, M., Pérez, I., & Lorenzo, G. (2014). Los Números Naturales en el aula de Primaria. Castellón. Ed. Universitat Jaume I. Recuperado de: http://repositori.uji.es/xmlui/handle/10234/89550
Arcavi, A., y Bruckheimer, M. (2000). Didactical uses of primary sources from the history of mathematics. Themes in Education, 1, 55–74.
Bakker, A. (2004). Design research in statistics education—on symbolizing and computer tools. (Tesis de doctorado) The Freudenthal Inistitute, Utrecht.
Bakker, A., y Gravemeijer, K. P. E. (2006). An historical phenomenology of mean and median. Educational Studies in Mathematics, 62, 149–168.
Barbin, E. (2007). On the argument of simplicity in ‘elements’ and schoolbooks of geometry. Educational Studies in Mathematics, 66, 225–242. Special issue on the history of mathematics in mathematics education.
Bartolini Bussi, M. G., y Bazzini, L. (2003). Research, practice and theory in didactics of mathematics: Towards dialogue between different fields. Educational Studies in Mathematics, 54, 203–223.
Barabash, M., y Guberman-Glebov, R. (2004). Seminar and graduate project in the history of mathematics as a source of cultural and intercultural enrichment of the academic teacher education program. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 73–88. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Barillé, A. (1994). Érase una vez…, los inventores. https://www.youtube.com/watch?v=cZI1issfSPE (última visualización el 17-04-2018)
Chevallard, Y. (1991). La trasposición didáctica: del saber sabido al saber enseñado. Argentina: Aique Grupo Editorial S.A.
Farmaki, V., y Paschos, T. (2007). Employing genetic ‘moments’ in the history of mathematics in classroom activites. Educational Studies in Mathematics, 66, 83–106.
Fauvel, J. (1991). Using history in mathematics education. Learning of Mathematics, 11(2), 3–6. Special Issue on History in Mathematics Education.
Freudenthal, H. (1981). Educ Stud Math 12: 133. Recuperado de: https://doi.org/10.1007/BF00305618
Fung, C.-I. (2004). How history fuels teaching for mathematising: Some personal reflections. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 125–146. Special doublé issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Furinghetti, F. (2000). The History of mathematics as a coupling link between secondary and university teaching. International Journal of Mathematical Education in Science and Technology, 31(1), 43–51.
Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66, 131-143.
Gómez, C. M. (1994). Historia de las matemáticas y su enseñanza: un análisis. SUMA, 17-26.
González-Urbaneja, P. M. (2004). La historia de las matemáticas como recurso didáctico e instrumento para enriquecer culturalmente su enseñanza. SUMA, 45, 17–28.
Gravemeijer, K., y Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111–129.
Gulikers, I., y Blom, K. (2001). ‘A historical angle’, a survey of recent literature on the use and value of the history in geometrical education. Educational Studies in Mathematics, 47, 223–258.
Guzmán, M. (1992). Tendències innovadores en educació matemàtica. Butlletí de La Societat Catalana de Matemàtiques.
Helfgott, M. (2004). Two examples from the natural sciences and their relationship to the history and pedagogy of mathematics. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 147–164. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Jankvist, U.T. (2009).A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71, 235-261.
Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Dynnikov, C., Furinghetti, et al. (2000). The use of original sources in the mathematics classroom. En J. Fauvel & J. van Maanen (Eds.), History in mathematics education – The ICMI Study (pp. 291–328). Boston, MA: Kluwer.
Jahnke, H. N. (2001). Cantor’s cardinal and ordinal infinies: An epistemological and didactic view. Educational Studies in Mathematics, 48, 175–197.
Katz, V. (2000). Using history to teach mathematics: An international perspective. Washington, DC: The Mathematical Association of America.
Kenschaft, P. C. (2005). Change is possible: Stories of women and minorities in mathematics. Providence, RI: American Mathematical Society.
Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational Studies in Mathematics, 48, 137–174.
Klyve, D., y Stemkoski, L. (2009). The Euler archive. Recuperado de: http://math.dartmouth.edu/*euler/. Accessed 21 May 2012.
Knoebel, A., Laubenbacher, R., Lodder, J., & Pengelley, D. (2007). Mathematical masterpieces: Further chronicles by the explorers. New York: Springer.
Lorenzo, G., Alcalde, M., & Pérez, I. (2015). La geometría y la estadística en el aula de primaria. Castelló de la Plana (Espanya). Ed. Universitat Jaume I. Recuperado de: http://repositori.uji.es/xmlui/handle/10234/143825
Lupiáñez, L. (2002). Reflexiones didácticas sobre la Historia de la Matemática. SUMA, 40, 59–63.
Mac y Bhaird, C. (2009) Introducing the history of mathematics to third level students with weak mathematical backgrounds: a case study. In: CETL-MSOR Conference 2008. The Maths, Stats & OR Network, pp. 63-68.
Niss, M., y Jensen, T. H. (Eds.) (2002). Kompetencer og matematiklæring—ideer og inspiration til udvikling af matematikundervisning i Danmark. Undervisningsministeriet. Uddannelsesstyrelsens temahæfteserie nr. 18. English translation of title: Competencies and Learning of Mathematics—Ideas and Inspiration for the Development of Mathematics Education in Denmark.
Pérez, I., Alcalde, M., & Lorenzo, G. (2014). Los números enteros y racionales, las magnitudes y la medida en el aula de primaria. Castelló. Ed. Universitat Jaume I. Recuperado de: http://repositori.uji.es/xmlui/handle/10234/108118.
Philippou, G. N., y Christou, C. (1998). The effects of a preparatory mathemtics program in changing prospective teachers’ attitudes towards mathematics. Educational Studies in Mathematics, 35, 189–206.
Radford, L. (2000b). Signs and measuring in students’ emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42, 237–268.
Russ, S., Ransom, P., Perkins, P., Barbin, E., Arcavi, A., Brown, G., et al. (1991). The experience of history in mathematics education. Learning of Mathematics, 11(2), 7–16. Special Issue on History in Mathematics Education.
Sánchez, J. d. (1997). Historia de la matemática: implicaciones didácticas. SUMA, 33-38.
Streefland, L. (2003). Learning from history for teaching in the future. Educational Studies in Mathematics, 54, 37–62.
Taimina, D. (2004). History of mathematics and mechanics in digital Reuleaux kinematic mechanism collection. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 89–102. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Tattersall, J., y McMurran, S. L. (2004). Using the ‘educational times’ in the classroom. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 103–114. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Thomaidis, Y., y Tzanakis, C. (2007). The notion of historical ‘parallelism’ revisited: Historical evolution and students’ conception of the order relation on the number line. Educational Studies in Mathematics, 66, 165–183. Special issue on the history of mathematics in mathematics education.
Thompson, A. (1992). Teachers’ beliefs: a Synthesis of the research. In D. A. Grouws (Ed.), Handbook on research in mathematics education (pp. 127–146). New York: Macmillan Publishing Co.
Tzanakis, C., y Thomaidis, Y. (2000). Integrating the close historical development of mathematics and physics in mathematics education: Some methodological and epistemological remarks. Learning of Mathematics, 20(1), 44–55.
Van Amerom, B. A. (2003). Focusing on informal stragies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54, 63–75.
Van Maanen, J. (1997). New maths may profit from old methods. Learning of Mathematics, 17(2), 39–46.
Verillon, P., y Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 77–101.
Weldeana, H.N. y Abraham, S.T. (2014). The effect of an historical perspective on prospective teachers’ beliefs in learning mathematics. Journal of Mathematics Teacher Education, 17, 303–330
Arcavi, A., y Bruckheimer, M. (2000). Didactical uses of primary sources from the history of mathematics. Themes in Education, 1, 55–74.
Bakker, A. (2004). Design research in statistics education—on symbolizing and computer tools. (Tesis de doctorado) The Freudenthal Inistitute, Utrecht.
Bakker, A., y Gravemeijer, K. P. E. (2006). An historical phenomenology of mean and median. Educational Studies in Mathematics, 62, 149–168.
Barbin, E. (2007). On the argument of simplicity in ‘elements’ and schoolbooks of geometry. Educational Studies in Mathematics, 66, 225–242. Special issue on the history of mathematics in mathematics education.
Bartolini Bussi, M. G., y Bazzini, L. (2003). Research, practice and theory in didactics of mathematics: Towards dialogue between different fields. Educational Studies in Mathematics, 54, 203–223.
Barabash, M., y Guberman-Glebov, R. (2004). Seminar and graduate project in the history of mathematics as a source of cultural and intercultural enrichment of the academic teacher education program. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 73–88. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Barillé, A. (1994). Érase una vez…, los inventores. https://www.youtube.com/watch?v=cZI1issfSPE (última visualización el 17-04-2018)
Chevallard, Y. (1991). La trasposición didáctica: del saber sabido al saber enseñado. Argentina: Aique Grupo Editorial S.A.
Farmaki, V., y Paschos, T. (2007). Employing genetic ‘moments’ in the history of mathematics in classroom activites. Educational Studies in Mathematics, 66, 83–106.
Fauvel, J. (1991). Using history in mathematics education. Learning of Mathematics, 11(2), 3–6. Special Issue on History in Mathematics Education.
Freudenthal, H. (1981). Educ Stud Math 12: 133. Recuperado de: https://doi.org/10.1007/BF00305618
Fung, C.-I. (2004). How history fuels teaching for mathematising: Some personal reflections. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 125–146. Special doublé issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Furinghetti, F. (2000). The History of mathematics as a coupling link between secondary and university teaching. International Journal of Mathematical Education in Science and Technology, 31(1), 43–51.
Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66, 131-143.
Gómez, C. M. (1994). Historia de las matemáticas y su enseñanza: un análisis. SUMA, 17-26.
González-Urbaneja, P. M. (2004). La historia de las matemáticas como recurso didáctico e instrumento para enriquecer culturalmente su enseñanza. SUMA, 45, 17–28.
Gravemeijer, K., y Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111–129.
Gulikers, I., y Blom, K. (2001). ‘A historical angle’, a survey of recent literature on the use and value of the history in geometrical education. Educational Studies in Mathematics, 47, 223–258.
Guzmán, M. (1992). Tendències innovadores en educació matemàtica. Butlletí de La Societat Catalana de Matemàtiques.
Helfgott, M. (2004). Two examples from the natural sciences and their relationship to the history and pedagogy of mathematics. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 147–164. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Jankvist, U.T. (2009).A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71, 235-261.
Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Dynnikov, C., Furinghetti, et al. (2000). The use of original sources in the mathematics classroom. En J. Fauvel & J. van Maanen (Eds.), History in mathematics education – The ICMI Study (pp. 291–328). Boston, MA: Kluwer.
Jahnke, H. N. (2001). Cantor’s cardinal and ordinal infinies: An epistemological and didactic view. Educational Studies in Mathematics, 48, 175–197.
Katz, V. (2000). Using history to teach mathematics: An international perspective. Washington, DC: The Mathematical Association of America.
Kenschaft, P. C. (2005). Change is possible: Stories of women and minorities in mathematics. Providence, RI: American Mathematical Society.
Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational Studies in Mathematics, 48, 137–174.
Klyve, D., y Stemkoski, L. (2009). The Euler archive. Recuperado de: http://math.dartmouth.edu/*euler/. Accessed 21 May 2012.
Knoebel, A., Laubenbacher, R., Lodder, J., & Pengelley, D. (2007). Mathematical masterpieces: Further chronicles by the explorers. New York: Springer.
Lorenzo, G., Alcalde, M., & Pérez, I. (2015). La geometría y la estadística en el aula de primaria. Castelló de la Plana (Espanya). Ed. Universitat Jaume I. Recuperado de: http://repositori.uji.es/xmlui/handle/10234/143825
Lupiáñez, L. (2002). Reflexiones didácticas sobre la Historia de la Matemática. SUMA, 40, 59–63.
Mac y Bhaird, C. (2009) Introducing the history of mathematics to third level students with weak mathematical backgrounds: a case study. In: CETL-MSOR Conference 2008. The Maths, Stats & OR Network, pp. 63-68.
Niss, M., y Jensen, T. H. (Eds.) (2002). Kompetencer og matematiklæring—ideer og inspiration til udvikling af matematikundervisning i Danmark. Undervisningsministeriet. Uddannelsesstyrelsens temahæfteserie nr. 18. English translation of title: Competencies and Learning of Mathematics—Ideas and Inspiration for the Development of Mathematics Education in Denmark.
Pérez, I., Alcalde, M., & Lorenzo, G. (2014). Los números enteros y racionales, las magnitudes y la medida en el aula de primaria. Castelló. Ed. Universitat Jaume I. Recuperado de: http://repositori.uji.es/xmlui/handle/10234/108118.
Philippou, G. N., y Christou, C. (1998). The effects of a preparatory mathemtics program in changing prospective teachers’ attitudes towards mathematics. Educational Studies in Mathematics, 35, 189–206.
Radford, L. (2000b). Signs and measuring in students’ emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42, 237–268.
Russ, S., Ransom, P., Perkins, P., Barbin, E., Arcavi, A., Brown, G., et al. (1991). The experience of history in mathematics education. Learning of Mathematics, 11(2), 7–16. Special Issue on History in Mathematics Education.
Sánchez, J. d. (1997). Historia de la matemática: implicaciones didácticas. SUMA, 33-38.
Streefland, L. (2003). Learning from history for teaching in the future. Educational Studies in Mathematics, 54, 37–62.
Taimina, D. (2004). History of mathematics and mechanics in digital Reuleaux kinematic mechanism collection. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 89–102. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Tattersall, J., y McMurran, S. L. (2004). Using the ‘educational times’ in the classroom. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 103–114. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
Thomaidis, Y., y Tzanakis, C. (2007). The notion of historical ‘parallelism’ revisited: Historical evolution and students’ conception of the order relation on the number line. Educational Studies in Mathematics, 66, 165–183. Special issue on the history of mathematics in mathematics education.
Thompson, A. (1992). Teachers’ beliefs: a Synthesis of the research. In D. A. Grouws (Ed.), Handbook on research in mathematics education (pp. 127–146). New York: Macmillan Publishing Co.
Tzanakis, C., y Thomaidis, Y. (2000). Integrating the close historical development of mathematics and physics in mathematics education: Some methodological and epistemological remarks. Learning of Mathematics, 20(1), 44–55.
Van Amerom, B. A. (2003). Focusing on informal stragies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54, 63–75.
Van Maanen, J. (1997). New maths may profit from old methods. Learning of Mathematics, 17(2), 39–46.
Verillon, P., y Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 77–101.
Weldeana, H.N. y Abraham, S.T. (2014). The effect of an historical perspective on prospective teachers’ beliefs in learning mathematics. Journal of Mathematics Teacher Education, 17, 303–330