Aspectos históricos del teorema fundamental del cálculo y posibles mediaciones tecnológicas
| Issue | Vol. 5 Núm. 1 (2021): Ciencia y Educación |
| DOI | |
| Publicado | mar 4, 2021 |
|
Estadísticas |
Universidad Distrital Francisco José de Caldas, Colombia.
Resumen
Este artículo presenta aspectos históricos del Teorema Fundamental del Cálculo (TFC) que podrían ser mediados por herramientas tecnológicas. Esta exploración pretende identificar en los argumentos de Newton y de Leibniz, un potencial heurístico para ser incorporados en ambientes de aprendizaje del cálculo en las universidades. Se presentan los resultados de una exploración de actualización de los argumentos de Newton y de Leibniz con la mediación del software matemático Geogebra. Los resultados de esta exploración articulan factores históricos y tecnológicos del TFC, que podrían usarse de manera curricular, por ejemplo, en el diseño de tareas para la formación universitaria.
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Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3–6. http://www.jstor.org/stable/40248010
Fernandez, F. (2002). El análisis de contenido como ayuda metodológica para la investigación. Revista de Ciencias Sociales (San José), II(96), 35–53. https://www.redalyc.org/pdf/153/15309604.pdf
Font, V. (2011). Competencias profesionales en la formación inicial de profesores de matemáticas. Revista Iberoamericana de Educación Matemática, 26.
Godino, J., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema Rio Claro, 31(57), 90–113. https://doi.org/10.1590/1980-4415v31n57a05
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Hodgson, B. R. (n.d.). La contribución de la Historia de las Matemáticas a la Formación de Profesores de Matemáticas de Educación. 91–108.
Hohenwarter, M., Kreis, Y., & Lavicza, Z. (2008). Teaching and calculus with free dynamic mathematics software GeoGebra. 11th International Congress on Mathematical Education, January, 1–9. https://doi.org/10.1080/0020739X.2017.1298855
ICMI. (2002). History in mathematics education (International Commission on Mathematical Instruction) (J. Fauvel & A. Van Maanen (eds.)). Kluwer Academic Publishers.
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Kouropatov, A., & Dreyfus, T. (2013). Constructing the Fundamental Theorem of Calculus. Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education Methodology and Methods in Mathematics Education, 3, 201–208.
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Berry, J. S., & Nyman, M. A. (2003). Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior, 22(4), 481–497. https://doi.org/10.1016/j.jma thb.2003.09.006
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Capote, G. E., Rizo, N., & Bravo, G. (2016). La formación de ingenieros en la actualidad. Una explicación necesaria. Revista Universidad y Sociedad, 8(1), 21–28.
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Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3–6. http://www.jstor.org/stable/40248010
Fernandez, F. (2002). El análisis de contenido como ayuda metodológica para la investigación. Revista de Ciencias Sociales (San José), II(96), 35–53. https://www.redalyc.org/pdf/153/15309604.pdf
Font, V. (2011). Competencias profesionales en la formación inicial de profesores de matemáticas. Revista Iberoamericana de Educación Matemática, 26.
Godino, J., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema Rio Claro, 31(57), 90–113. https://doi.org/10.1590/1980-4415v31n57a05
Golden, J. (2011). Second Fundamental Theorem of Calculus. Geogebra.Org. https://www.geogebra.org/m/tFXTp3ar
Gorgone, H., Galli, D., Acevedo, F., Guillen, G., Diab, J., & Voda, D. (2010). Nuevo enfoque en la enseñanza de la ingenieria. In UNNOBA.
Guicciardini, N. (2008). Analysis and synthesis in Newton’s mathematical work. In The Cambridge Companion to Newton (pp. 308–328). https://doi.org/10.1017/ccol0521651778.xml.010
Guicciardini, N. (2009). Isaac Newton on mathematical certainty and method. https://doi.org/10.1007/s10086-013-1369-8
Guicciardini, N. (2011). Newton. Carocci Editore
Hazzan, O., & Leron, U. (1996). Students’ use and misuse of mathematical theorems: The case of Lagrange’s Theorem. For the Learning of Mathematics, 16(1), 23–26. https://doi.org/10.1006/anbe.2000.1610
Hodgson, B. R. (n.d.). La contribución de la Historia de las Matemáticas a la Formación de Profesores de Matemáticas de Educación. 91–108.
Hohenwarter, M., Kreis, Y., & Lavicza, Z. (2008). Teaching and calculus with free dynamic mathematics software GeoGebra. 11th International Congress on Mathematical Education, January, 1–9. https://doi.org/10.1080/0020739X.2017.1298855
ICMI. (2002). History in mathematics education (International Commission on Mathematical Instruction) (J. Fauvel & A. Van Maanen (eds.)). Kluwer Academic Publishers.
Iliffe, R. (Cambridge U. N. P. (2011). The October of 1666 Tract on Fluxions. MS Add. 3958.3, Ff. 48v-63v, Cambridge University Library, Cambridge, UK. http://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00100
Katz, V. (1993). Using the History of Calculus to Teach Calculus. 243–249.
Katz, V. (2008). A History of Mathematics. Pearson.
Klisinska, A. (2005). The Fundamental Theorem of Calculus_ A case study into the didactic transposition of proof. In Integration The Vlsi Journal. https://doi.org/10.2307/2307007
Kouropatov, A., & Dreyfus, T. (2013). Constructing the Fundamental Theorem of Calculus. Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education Methodology and Methods in Mathematics Education, 3, 201–208.
Kumar, R. (2015). Fundamental Theorem of Calculus. Geogebra.Org. https://www.geogebra.org/m/JUpgHnhs
Lacoste, P. (2016). Fundamental Theorem of Calculus. Geogebra.Org. https://www.geogebra.org/m/wdUED3wy
Lopez, J. (2011). Reflexions On Leibniz’ Proof Of The Fundamental Theorem Of Calculus. Research Gate. https://doi.org/10.13140/RG.2.1.4804.2405
Macdonald, A. (1998). The fundamental theorem of geometric calculus via a generalized riemann integral. Advances in Applied Clifford Algebras, 8(1), 5–16. https://doi.org/10.1007/bf03041922
Macduffee, C. (1947). Objectives in Calculus. The American Mathematical Monthly, 94(4), 335 –337. www.jstor.org/stable/2305209
Majerek, D. (2014). Application of Geogebra for Teaching Mathematics. Advances in Science and Technology Research Journal, 8(January), 51–54. https://doi.org/10.12913/22998624/567
McCullough, J. (2017). Fundamental Theorem of Calculus. Geogebra.Org. https://www.geogebra.org/m/fAyYZYm2
Mena, R. (2014). The Fundamental Theorem of Calculus. http://web.csulb.edu/~rmena/410/Section8.pdf
Moreno, I. (2007). Consideraciones para una enseñanza de calidad en ingeniería. Revista Pedagogía Universitaria, XII(1), 38–46.
Najwa, A., Kamin, Y., & Khair, M. (2018). Competencies of Engineering Graduates: What are the Employer’s Expectations? International Journal of Engineering & Technology, 7(2.29), 519. https://doi.org/10.14419/ijet.v7i2.29.13811
Olaya, C. (2013). Más ingeniería y menos ciencia por favor. XI Congreso Latinoamericano de Dinámica de Sistemas Instituto Tecnológico y de Estudios Superiores de Monterrey, 6.
Palma, C. (2012). Nuevos retos para el ingeniero en el siglo XXI. ING-NOVACIÓN., 4, 61–65. http://www.redicces.org.sv/jspui/bitstream/10972/1973/1/4-nuevos-retos-para-el-ingeniero-en-el-siglo-xxi.pdf
Panza, M. (2000). Newton et les origines de l’analyse : 1664-1666. Sciences de l’Homme et Société. Ecole des Hautes Etudes en Sciences Sociales. https://tel.archives-ouvertes.fr/tel-00116744/file/MsPr.pdf
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Teorema fundamental del cálculo
competencia
Geogebra
Newton
Leibniz
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Weimar Muñoz Villate
Universidad Distrital Francisco José de Caldas, Colombia.
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Muñoz Villate, W. (2021). Aspectos históricos del teorema fundamental del cálculo y posibles mediaciones tecnológicas. Ciencia Y Educación, 5(1), 189–204. https://doi.org/10.22206/cyed.2021.v5i1.pp189-204