Treatment and conversion of the register of representation of the definite integral by engineers in training
Keywords:
Definite integral, register of semiotic representation, engineering educationAbstract
This article explores the treatment and conversion of the semiotic representation registers mobilized by agronomy engineering students about the mathematical object 'definite integral' when they try to appropriate its meaning, supported using GeoGebra. With the support of the Theory of Semiotic Representation Register and a qualitative analysis of a case study, the developments generated by the students in the task of modeling the definite integral of a contextualized situation are shown. Within the results it is identified that the use of the software supported, mainly, the mediation between the tabular and graphic treatment, and in turn, the conversion of these to an algebraic language outside the computer.
Downloads
References
Aranda, C., y Callejo, M. L. (2017). Construcción de la Función Integral y Razonamiento Covariacional: Dos Estudios de Casos. Bolema: Boletim de Educação Matemática, 31(58), 777-798. https://doi.org/10.1590/1980-4415v31n58a13
Bajracharya, R. R., Wemyss, T. M., y Thompson, J. R. (2012, febrero). Student interpretation of the signs of definite integrals using graphical representations [ponencia]. AIP Conference Proceedings (Vol. 1413, No. 1, pp. 111-114). American Institute of Physics. https://doi.org/10.1063/1.3680006
Camacho, M., Depool, R., y Garbín, S. (2008). Integral definida en diversos contextos: Un estudio de casos. Educación matemática, 20(3), 33-57. http://www.revista-educacion-matematica.org.mx/descargas/Vol20/3/vol20-3-03_REM_20-2.pdf
Carli, M., Lippiello, S., Pantano, O., Perona, M., y Tormen, G. (2020). Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context. Physical Review Physics Education Research, 16(1), 010111. https://doi.org/10.1103/PhysRevPhysEducRes.16.010111
Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., y Hsu. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education, 33(5), 352-378. https://doi.org/10.2307/4149958
Cohen, L., Manion, L., y Morrison, K. (2018). Research methods in education (8a ed.). Routledge.
Depool, R. (2005). La enseñanza y aprendizaje del Cálculo Integral en un entorno computacional. Actitudes de los estudiantes hacia el uso de un Programa de Cálculo Simbólico (PCS). Números, 62, 3-31. http://sinewton.es/revista_numeros/062/
Dominguez, M., Barniol, P., y Zavala, G. (2019). Evaluación del entendimiento gráfico de derivada e integral definida mediante un examen en castellano de opción múltiple. Formación Universitaria, 12(6), 41-56. http://dx.doi.org/10.4067/S0718-50062019000600041
Dreyfus, T., Kouropatov, A., y Ron, G. (2021). Research as a resource in a high-school calculus curriculum. ZDM–Mathematics Education, 53(3), 679-693. https://doi.org/10.1007/s11858-021-01236-3
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics, Educational Studies in Mathematics, 61(1-2), 103-131. http://www.jstor.org/stable/25472062
Duval, R. (1995). Sémiosis et pensée humaine: registres sémiotiques et apprentissages intellectuels. Peter Lang.
Duval, R. (2017). Understanding the Mathematical way of Thinking-The Registers of Semiotic Representations. Springer International Publishing. https://doi.org/10.1007/978-3-319-56910-9
Godino, J. D., Wilhelmi, M. R., Blanco, T. F., Contreras, Á., y Giacomone, B. (2016). Análisis de la actividad matemática mediante dos herramientas teóricas: Registros de representación semiótica y configuración ontosemiótica. Avances de investigación en educación matemática, (10), 91-110. https://doi.org/10.35763/aiem.v0i10.144
Jones, S. R. (2018). Prototype images in mathematics education: The case of the graphical representation of the definite integral. Educational Studies in Mathematics, 97(3), 215-234. https://doi.org/10.1007/s10649-017-9794-z
Johnson, D., y Johnson, R. (2014). La evaluación en el aprendizaje cooperativo: cómo mejorar la evaluación individual a través del grupo. España: Biblioteca Innovación Educativa.
Kartika, C., Umi, I., Machromah, I., Sri, N., y Zakiyyah, Z. (2019, 7 de agosto). The Existence of The Definite Integral: Students’ Understanding [ponencia]. Proceedings of the 4th Progressive and Fun Education International Conference. http://dx.doi.org/10.4108/eai.7-8-2019.2289033
Kohen, Z., & Orenstein, D. (2021). Mathematical modeling of tech-related real-world problems for secondary school-level mathematics. Educational Studies in Mathematics, 107, 71-91. https://doi.org/10.1007/s10649-020-10020-1
Leithold, L. (1994). El Cálculo (7a ed.) Oxford University Press.
Martínez-Miraval, M. A., y García-Cuéllar, D. J. (2020). Estudio de las aprehensiones en el registro gráfico y génesis instrumental de la integral definida. Formación universitaria, 13(5), 177-190. http://dx.doi.org/10.4067/S0718-50062020000500177
Peña, C. A., Ramírez-Sánchez, M., y Rivas-Trujillo, E. (2019). La integración numérica en la integral definida: caso de estudio. Espacios, 40(19), 23-30. https://revistaespacios.com/a19v40n19/19401923.html
Presmeg, N., Radford, L., Roth, W-M., y Kadunz, G. (2016). Semiotic in mathematics education. Springer Cham. https://doi.org/10.1007/978-3-319-31370-2
Rasslan, S., y Tall, D. (2002, julio). Definitions and images for the definite integral concept [ponencia]. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 89-96).
Rodríguez, R. (2017). Repensando la enseñanza de las matemáticas para futuros ingenieros: actualidades y desafíos. IE Revista de investigación educativa de la REDIECH, 8(15), 69-85.
Serhan, D. (2015). Students' understanding of the definite integral concept. International Journal of Research in Education and Science, 1(1), 84-88. https://www.ijres.net/index.php/ijres/article/view/20
Smith, J., y Thompson, P. W. (2007). Quantitative reasoning and the development of algebraic reasoning. En J. J. Kaput, D. W. Carraher, y M. L. Blanton (Eds.), Algebra in the early grades (pp. 95-132). Erlbaum.
Tall, D. (1996). Functions and Calculus. En Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J., y Laborde, C. (Eds.) International Handbook of Mathematics Education. Kluwer International Handbooks of Education (vol 4, pp. 289-325). Springer. https://doi.org/10.1007/978-94-009-1465-0_9
Tallman, M. A., Reed, Z., Oehrtman, M., y Carlson, M. P. (2021). What meanings are assessed in collegiate calculus in the United States? ZDM–Mathematics Education, 53(3), 577-589. https://doi.org/10.1007/s11858-020-01212-3
Tatar, E., y Zengin, Y. (2016). Conceptual understanding of definite integral with Geogebra. Computers in the Schools, 33(2), 120-132. https://doi.org/10.1080/07380569.2016.1177480
Downloads
Published
How to Cite
Issue
Section
License
This journal provides free, immediate access to its content under the principle of making research freely available to the public, which fosters a greater exchange of global knowledge.
Authors who publish in Areté, Revista Digital del Doctorado en Educación, agree to the following terms:
- Authors retain copyright and grant the journal the right to be the first publication of the work, as well as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of authorship of the work and initial publication in this journal.
- Authors may separately establish additional agreements for the non-exclusive distribution of the version of the work published in the journal (for example, placing it in an institutional repository or publishing it in a book), with an acknowledgement of its initial publication in this journal and not to be used for commercial purposes.
- The contents and images included in the articles are the responsibility of the author(s). Areté, Revista Digital del Doctorado en Educación, is not responsible for the information included in them.
- Authors agree with the license of use used by the journal, with the self-archiving conditions and with the open access policy.
- Authors are allowed to disseminate electronically (e.g., in institutional repositories or on their own website) the published version of their work, as it favors its earlier circulation and dissemination and thus a possible increase in its citation and reach among the academic community.
- In case of reuse of published works, the existence and specifications of the license of use must be mentioned, as well as the authorship and original source of publication.