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Artículos

Vol. 25 No. 2 (2022): July

INTUITIVE AND FORMAL MEANINGS OF THE DEFINITE INTEGRAL IN ENGINEERING EDUCATION

DOI
https://doi.org/10.12802/relime.22.2521
Submitted
June 7, 2023
Published
2022-07-31

Abstract

The definite integral is a central concept in the applications of calculus to experimental sciences and engineering, and consequently, a relevant didactic research topic. This paper analyses the different meanings of the definite integral by applying theoretical tools of the ontosemiotic approach to mathematical knowledge and instruction, particularly, the interpretation of meaning in terms of systems of operational and discursive practices related to the resolution of types of problems and the algebraization levels model of mathematical activity. Types of problem-situations and configurations of practices, objects, and processes are identified that allow us to characterize and articulate the various partial meanings of the definite integral (geometric-intuitive, as a limit of Riemann sums and cumulative function) as well as its extensions to the case of the double integral (as a particular case of the multiple) and the line, from the most intuitive to the most formal. The analysis allows us to identify the generality degrees of the objects of integral calculus and the role of algebra in the characterization of the meanings of the definite integral, which must be considered in the planning and management of the processes of teaching and learning of integral calculus in engineering degrees.

References

  1. Alpers, B. (Ed.). (2013). A framework for mathematics curricula in engineering education (a report of the mathematics working group). Brussels: European Society for Engineering Education.https://www.sefi.be/publication/a-framework-for-mathematics-curricula-inengineering-education/
  2. Boigues, F., Llinares, S. y Estruch, V. (2010). Desarrollo de un esquema de la integral definida en estudiantes de ingenierías relacionadas con las ciencias de la naturaleza. Revista Latinoamericana de Investigación en Matemática Educativa, 13(3), 255-282.
  3. Bressoud, D., Ghedams, I., Martinez-Luances, V. y Törner, G. (2016). Teaching and learning of Calculus. Berlin: Springer.
  4. Brito-Vallina, M. L., Alemán-Romero, I., Fraga-Guerra, E., Para-García, J. L. y Arias-De Tapia, R. I. (2011). Papel de la modelación matemática en la formación de los ingenieros. Ingeniería Mecánica, 14(2), 129-139.
  5. Burgos, M., Bueno, S., Godino, J. D. y Pérez, O. (2021). Onto-semiotic complexity of the Definite Integral. Implications for teaching and learning Calculus. REDIMAT – Journal of Research in Mathematics Education, 10(1), 4-40. https://doi.org/10.17583/redimat.2021.6778
  6. Carracelas, G. G., García, S. B. y Oca, N. M. de. (2022). Situaciones didáctico-matemáticas para el tratamiento de los procesos de variación y acumulación del cálculo integral en problemas ingenieriles. PARADIGMA, 43(2),341-363. https://doi.org/10.37618/PARADIGMA.10112251.2022.p341-363.id1249
  7. Carvalho, P. y Oliveira, P. (2018). Mathematics or mathematics for engineering? Proceedings of 2018 3rd International Conference of the Portuguese Society for Engineering Education (CISPEE), Aveiro, Portugal. https://ria.ua.pt/bitstream/10773/25337/1/CISPEE2018_final.pdf
  8. Contreras, A. y Ordóñez, L. (2006). Complejidad ontosemiótica de un texto sobre la introducción a la integral definida. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 65-84. https://www.scielo.org.mx/scielo.php?pid=S1665-24362006000100004&script=sci_abstract
  9. Contreras, A., Ordóñez, L. y Wilhelmi, M. R. (2010). Influencia de las pruebas de acceso a la universidad en la enseñanza de la integral definida en el bachillerato. Enseñanza de las Ciencias, 28(3), 367-384. https://doi.org/10.5565/rev/ec/v28n3.63
  10. Ellis, B., Larsen, S., Voigt, M. y Kristeen, W. (2021). Where calculus and engineering converge: an analysis of curricular change in calculus for engineers. International Journal of Research in Undergraduate Mathematics Education, 7, 379–399. https://doi.org/10.1007/s40753-020-00130-9
  11. Font, V., Godino, J. D. y Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97–124. https://doi.org/10.1007/s10649-012-9411-0.
  12. Godino, J. D. (2002). Un enfoque ontológico semiótico de la cognición matemática. Recherches en Didactique des Mathématiques 22 (2-3), 237-284.
  13. Godino, J. D., Aké, L., Gonzato, M. y Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 32(1), 199-219. http://dx.doi.org/10.5565/rev/ensciencias.965
  14. Godino, J. D. y Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325-355. https://www.ugr.es/~jgodino/funciones-semioticas/03_SignificadosIP_RDM94.pdf
  15. Godino, J. D. Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education 39 (1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  16. Godino, J. D., Neto, T., Wilhelmi, M. R., Aké, L., Etchegaray, S. y Lasa, A. (2015). Niveles de algebrización de las prácticas matemáticas escolares. Articulación de las perspectivas ontosemiótica y antropológica. Avances de Investigación en Educación Matemática, 8, 117-142. https://doi.org/10.35763/aiem.v1i8.105
  17. González-Martín, A. S. (2021). The Use of Integrals in Engineering Programmes: a Praxeological Analysis of Textbooks and Teaching Practices in Strength of Materials and Electricity and Magnetism Courses. International Journal of Research in Undergraduate Mathematics Education, 7, 211–234. https://doi.org/10.1007/s40753-021-00135-y
  18. González-Martín, A. S., Gueudet, G., Barquero, B. y Romo-Vázquez, A. (2021). Mathematics and other disciplines, and the role of modelling. En V. Durand-Guerrier, R. Hochmut, E. Nardi, y C. Winsløw (Eds.), Research and Development in University Mathematics Education (pp. 169–189). Routledge ERME Series: New Perspectives on Research in Mathematics Education. https://doi.org/10.4324/9780429346859-12
  19. González-Martin, A. S y Hernandes, G. (2017). How are Calculus notions used in engineering? An example with integrals and bending moments. CERME 10. Dublin, Ireland. https://hal.archives-ouvertes.fr/hal-01941357
  20. Gordillo, W. y Pino-Fan, L. (2016). Una propuesta de reconstrucción del significado holístico de la antiderivada. BOLEMA: Boletim de Educação Matemática, 30 (55), 535-558. http://dx.doi.org/10.1590/1980-4415v30n55a12
  21. Jones, S. R. (2020). Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding. Journal of Mathematical Behavior, 59, 100801. https://doi.org/10.1016/j.jmathb.2020.100801
  22. Jones, S. R. y Dorko (2015). Students’ understandings of multivariate integrals and how they may be generalized from single integral conceptions. Journal of Mathematical Behavior, 40, 154-170. https://doi.org/10.1016/j.jmathb.2020.100801
  23. Kouropatov, A. y Dreyfus, T. (2013). Constructing the integral concept on the basis of the idea of accumulation: Suggestions for a high school curriculum. International Journal of Mathematical Education in Science and Technology, 44(5), 641–651. https://doi.org/10.1080/0020739X.2013.798875
  24. Ministerio de Educación Superior (2017). Plan de Estudios “E”. Carrera Ingeniería Informática.
  25. Ministerio de Educación Superior (2018). Plan de Estudios “E”. Carrera Ingeniería Industrial.
  26. Muñoz, O. G. (2000). Elementos de enlace entre lo conceptual y lo algorítmico en el Cálculo Integral. Revista Latinoamericana de Investigación en Matemática Educativa, 3(2), 131-170. http://funes.uniandes.edu.co/9599/1/Mu%C3%B1oz2000Elementos.pdf
  27. Pepin, B., Biehler, R. y Gueudet, G. (2021). Mathematics in engineering education: a review of the recent literature with a view towards innovative practices. International Journal of Research in Undergraduate Mathematics Education, 7,163–188. https://doi.org/10.1007/s40753-02100139-8
  28. Pino-Fan, L., Font, V., Gordillo, W., Larios, V. y Breda, A. (2018). Analysis of the meanings of the antiderivative used by students of the first engineering courses. International Journal of Science and Mathematics Education, 16(6), 1091-1113. https://doi.org/10.1007/s10763-017-9826-2
  29. Puga, K. y Miranda, E (2021). Construcción del esquema mental para la apropiación del concepto de la integral. Acta Latinoamericana de Matemática Educativa, 25, 113-122. http://funes.uniandes.edu.co/4136/1/PugaConstrucci%C3%B3nALME2012.pdf
  30. Robles, M. G., Tellechea, E. y Font, V. (2014). Una propuesta de acercamiento alternativo al teorema fundamental del cálculo. Educación Matemática, 26(2), 69-109. https://www.redalyc.org/pdf/405/40532665004.pdf
  31. Rooch, A., Junker, P., Härterich, J. y Hackl, K. (2016). Linking mathematics with engineering applications at an early stage – implementation, experimental set-up and evaluation of a pilot project. European Journal of Engineering Education, 41(2), 172–191. https://doi.org/10.1080/03043797.2015.1056095
  32. Serhan, D. (2015). Students’ understanding of the definite integral concept. International Journal of Research in Education and Science, 1(1), 84-88. http://dx.doi.org/10.21890/ijres.00515
  33. Starbird, M. (2006). Change and motion: Calculus made clear, 2nd Edition. Chantilly, Virginia: The Teaching Company.
  34. Stewart, J. (2016). Calculus. Early transcendentals. Boston: Cengage Learning.
  35. Stewart, J. (2012a). Cálculo de una variable. Trascendentes tempranas. (7ª edición). México: Cendage Learning.
  36. Stewart, J. (2012b). Cálculo de varias variables. Trascendentes tempranas. (7ª edición). México: Cendage Learning.
  37. Viol, J. y Jacques, A. (2019). Ensino e Aprendizagem do Teorema Fundamental do Cálculo: algumas reflexões a partir de uma revisão sistemática de literatura. Educacão Matemática Pesquisa, 21(2), 239–263. https://doi.org/10.23925/1983-3156.2018v21i2p239-263

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