Covariational Reasoning and Instrumented Techniques in the Resolution of an Optimization Problem Mediated by GeoGebra

Authors

  • Mihály André Martínez-Miraval Pontificia Universidad Católica del Perú
  • Daysi Julissa García-Cuéllar Universidad Antonio Ruiz de Montoya
  • Martha Leticia García-Rodríguez Instituto Politécnico Nacional

https://doi.org/10.17583/redimat.11419

Keywords:


Number of words in the article:

8137

Abstract

The aim of this study was to document how different instrumental techniques are related to different mental actions during the work of university students in an optimization activity mediated by GeoGebra. To minimize the length of the fence of a rectangular plot, the students put into play mental actions, which were visible in the manipulations with GeoGebra, associated with different levels of covariational reasoning, and which allowed us to identify different instrumented techniques. It is concluded that the use of instrumented techniques involving concepts related to the derivative, such as the slope of the tangent line or the derivative function, make visible behaviors associated with mental actions of a more sophisticated covariational reasoning.

Downloads

Download data is not yet available.

References

Antonio, R., Escudero, D. I. y Flores, E. (2019). Una introducción al concepto de derivada en estudiantes de bachillerato a través del análisis de situaciones de variación. Educación Matemática, 31(1), 258-280. https://doi.org/10.24844/em3101.10

Google Scholar Crossref

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274. https://doi.org/10.1023/A:1022103903080

Google Scholar Crossref

Avgerinos, E. & Remoundou, D. (2021). The Language of “Rate of Change” in Mathematics. Eur. J. Investig. Health Psychol. Educ., 11(4) 1599–1609. https://doi.org/10.3390/ejihpe11040113

Google Scholar Crossref

Bataineh, H., Zoubi, A. y Khataybeh, A. (2019). Utilizing MATHEMATICA software to improve students’ problem solving skills of derivative and its applications. International Journal of Education and Research, 7(11), 57-70.

Google Scholar Crossref

Carlson, M., Jacobs, S., Coe, E., Larsen, S. y Hsu, E. (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

Google Scholar Crossref

Chevallard, Y. (1999). El análisis de las prácticas docentes en la teoría antropológica de lo didáctico. Recherches en didactique des mathématiques, 19(2), 221-266.

Google Scholar Crossref

Denzin, N. K. y Lincoln, Y. S. (2011). The SAGE handbook of qualitative research. Sage Publications.

Google Scholar Crossref

Galindo-Illanes, M., Breda, A., Chamorro-Manríquez, D., & Alvarado-Martínez, H. (2022). Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmste/12162

Google Scholar Crossref

Johnson, H. y McClintock, E. (2018). A link between students’ discernment of variation in unidirectional change and their use of quantitative variational reasoning. Educational Studies in Mathematics, 97(3), 299-316. https://doi.org/10.1007/s10649-017-9799-7

Google Scholar Crossref

Kouropatov, A. y Dreyfus, T. (2014). Learning the integral concept by constructing knowledge about accumulation. ZDM Mathematics Education, 46(4), 533–548. https://doi.org/10.1007/s11858-014-0571-5

Google Scholar Crossref

LaRue, R. y Infante, N. E. (2015). Optimization in first semester calculus: A look at a classic problem. International Journal of Mathematical Education in Science and Technology, 46(7), 1021-1031. https://doi.org/10.1080/0020739X.2015.1067844

Google Scholar Crossref

Martínez-Miraval, M. A., y García-Rodríguez, M. L. (2022). Razonamiento Covariacional de Estudiantes Universitarios en un Acercamiento al Concepto de Integral Definida mediante Sumas de Riemann. Formación Universitaria, 15(4), 105-118. http://dx.doi.org/10.4067/S0718-50062022000400105

Google Scholar Crossref

Medrano, I. & Pino-Fan, L.R. (2016). Estadios de comprensión de la noción matemática de límite finito desde el punto de vista histórico. REDIMAT, 5(1), 287-323. https://doi.org/10.17583/redimat.2016.1854

Google Scholar Crossref

Mkhatshwa, T. y Doerr, H. (2018). Undergraduate students' quantitative reasoning in economic contexts. Mathematical Thinking and Learning, 20(2), 142-161. https://doi.org/10.1080/10986065.2018.1442642

Google Scholar Crossref

Orts, A., Boigues, F. J., y Llinares, S. (2018). Génesis Instrumental del Concepto de Recta Tangente. Acta Scientiae, 20(2), 72-83. https://doi.org/10.17648/acta.scientiae.v20iss2id3833

Google Scholar Crossref

Roorda, G., Vos, P., Drijvers, P., y Goedhart, M. (2016). Solving Rate of Change Tasks with a Graphing Calculator: a Case Study on Instrumental Genesis. Digit Exp Math Educ 2, 228–252. https://doi.org/10.1007/s40751-016-0022-8

Google Scholar Crossref

Rojas-Escribano, L., Báez-Rojas, J. J. y Corona-Galindo, M. G. (2017). Propuesta didáctica para la enseñanza del tema de optimización, apoyado con Excel y Geogebra, para estudiantes de bachillerato. El cálculo y su enseñanza. Enseñanza de las Ciencias y la Matemática, 9(1), 52-63.

Google Scholar Crossref

Sánchez-Matamoros, G., García, M. y Llinares, S. (2008). La comprensión de la derivada como objeto de investigación en didáctica de la matemática. Revista Latinoamericana de Investigación en Matemática Educativa, 11(2), 267-296

Google Scholar Crossref

Thompson, P. y Carlson, M. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. En J. Cai (Ed.), Compendium for research in mathematics education (pp. 421–456). National Council of Teachers of Mathematics.

Google Scholar Crossref

Villa-Ochoa, J., González-Gómez, D., y Carmona-Mesa, J. (2018). Modelación y Tecnología en el Estudio de la Tasa de Variación Instantánea de Matemáticas. Formación Universitaria, 11(2), 25-34. http://dx.doi.org/10.4067/S0718-50062018000200025

Google Scholar Crossref

Published

2023-02-24

Almetric

Dimensions

Issue

Section

Articles