Designing the encounter of teachers with meanings and levels of understanding of the derivative

Alan Basilio Pizarro-Ayavire; Juan Luis Prieto-González; Rafael Enrique Gutiérrez-Araujo

doi:10.29333/iejme/15520

Designing the encounter of teachers with meanings and levels of understanding of the derivative

Full Text (PDF)

Alan Basilio Pizarro-Ayavire ¹ , Juan Luis Prieto-González ¹ ^* , Rafael Enrique Gutiérrez-Araujo ²

More Detail

¹ Facultad de Ciencias Humanas, Universidad Arturo Prat, Tarapacá, CHILE² Coordinación de Formación, Asociación Aprender en Red, Zulia, VENEZUELA^* Corresponding Author

Abstract

Previous research has shown that mathematics teachers face difficulties teaching the derivative of a function at a point. One of these difficulties revolves around the lack of materials and specialized information on this topic that allows teachers to carry out this task. Seeking to contribute to overcoming this difficulty, we describe the design of an activity oriented towards the encounter of mathematics teachers with meanings and levels of understanding of the derivative of a function at a point. The design is theoretically founded on the concepts of learning and activity of the theory of objectification and incorporates relevant information in the analytical, analytical-numerical, and geometric meanings of the derivative as well as the intra, inter, and trans levels of understanding of the concept. Based on these references, we describe the tasks that make up our design. We see our design as contributing to the field of mathematics education regarding the promotion of in-service teachers’ learning from an historical-cultural educational perspective.

Keywords

professional development
task design
derivative
joint labor

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 19, Issue 4, November 2024, Article No: em0798

https://doi.org/10.29333/iejme/15520

Publication date: 24 Oct 2024

Article Views: 548

Article Downloads: 225

Open Access References How to cite this article

References

Cuevas Vallejo, C. A., & Pluvinage, F. (2009). Cálculo y tecnología [Calculation and technology]. El Cálculo y su Enseñanza, 1(1), 45-60. https://doi.org/10.61174/recacym.v1i1.164
Desfitri, R. (2016). In-service teachers’ understanding on the concept of limits and derivatives and the way they deliver the concepts to their high school students. Journal of Physics: Conference Series, 693, Article 012016. https://doi.org/10.1088/1742-6596/693/1/012016
Fuentealba, C., Trigueros, M., Sánchez-Matamoros, G., & Badillo, E. (2022). Los mecanismos de asimilación y acomodación en la tematización de un esquema de derivada [The mechanisms of assimilation and accommodation in the thematization of a derivative scheme]. Avances de Investigación en Educación Matemática, (21), 23-44. https://doi.org/10.35763/aiem21.4241
García-Cuéllar, D. J., & Martínez-Miraval, M. A. (2023). Pendiente de recta tangente: Elemento de conexión de la derivada como límite o razón de cambio mediado por GeoGebra [Slope of tangent line: Connection element of the derivative as a limit or rate of change mediated by GeoGebra]. Revista Ibérica de Sistemas e Tecnologias de Informação, (E56), 289-302. https://doi.org/10.17583/redimat.11419
Gavilán Izquierdo, J. M. (2005). El papel del profesor en la enseñanza de la derivada. Análisis desde una perspectiva cognitiva [The role of the teacher in teaching derivatives. Analysis from a cognitive perspective] [PhD thesis, Universidad de Sevilla]. https://doi.org/10.24844/EM1802.07
Gavilán-Izquierdo, J. M., & Gallego-Sánchez, I. (2021). How an upper secondary school teacher provides resources for the transition to university: A case study. International Electronic Journal of Mathematics Education, 16(2), Article em0634. https://doi.org/10.29333/iejme/10892
González, J. L., Ruiz, O., Loera, E. J., Barrón, J. V., & Salazar, M. C. (2013). Comprensión del concepto de la derivada como razón de cambio [Understanding the concept of the derivative as a rate of change]. CULCyT: Cultura Científica y Tecnológica, 10(51), 4-14.
González-García, A., Muñiz-Rodríguez, L., & Rodríguez-Muñiz, L. J. (2018). Un estudio exploratorio sobre los errores y las dificultades del alumnado de bachillerato respecto al concepto de derivada [An exploratory study on the errors and difficulties of high school students regarding the concept of derivative]. Aula Abierta, 47(4), 449-462. https://doi.org/10.17811/rifie.47.4.2018.449-462
Gutiérrez Mendoza, L., Buitrago Alemán, M. R., & Ariza Nieves, L. M. (2017). Identificación de dificultades en el aprendizaje del concepto de la derivada y diseño de un OVA como mediación pedagógica [Identification of difficulties in learning the concept of the derivative and design of an OVA as a pedagogical mediation]. Revista Científica General José María Córdova, 15(20), 137-153. https://doi.org/10.21830/19006586.170
Hitt, F. (2003). Dificultades en el aprendizaje del cálculo [Difficulties in learning calculus]. In Proceedings of the XI Meeting of Middle-Higher Level Mathematics Teachers.
Hitt, F. (2017). El aprendizaje del cálculo y nuevas tendencias en su enseñanza en el aula de matemáticas [Learning calculus and new trends in teaching it in the mathematics classroom]. Eco Matemático, 8(S1), 6-15. https://doi.org/10.22463/17948231.1374
Ímaz Jahnke, C., & Moreno Armella, L. (2009). Sobre el desarrollo del cálculo y su enseñanza [On the development of calculus and its teaching]. El Cálculo y su Enseñanza, 1(1), 99-112. https://doi.org/10.61174/recacym.v1i1.168
Leontiev, A. N. (1984). Actividad, conciencia y personalidad [Activity, consciousness and personality]. Editora Cartago de México, S. A.
MINEDUC. (2021). Programa de estudio 3° o 4° medio. Formación diferenciada matemática. Límites, derivadas e integrales [Study program for 3^rd or 4^th year of high school. Differentiated mathematical training. Limits, derivatives and integrals]. Ministerio de Educación. https://www.curriculumnacional.cl/614/articles-140143_programa_feb_2021_final_s_disegno.pdf
Moreno, M. (2005). El papel de la didáctica en la enseñanza del cálculo: Evolución, estado actual y retos futuros [The role of didactics in teaching calculus: Evolution, current status and future challenges]. In A. Maz, B. Gómez, & M. Torralbo (Eds.), Proceedings of the IX Symposium of the Spanish Society for Research in Mathematics Education (pp. 81-96). Universidad de Córdoba.
Moreno-Armella, L. (2021). The theory of calculus for calculus teachers. ZDM Mathematics Education, 53, 621-633. https://doi.org/10.1007/s11858-021-01222-9
Orhun, N. (2012). Graphical understanding in mathematics education: Derivative functions and students’ difficulties. Procedia-Social and Behavioral Sciences, 55, 679-684. https://doi.org/10.1016/j.sbspro.2012.09.551
Panero, M., Arzarello, F., & Sabena, C. (2016). The mathematical work with the derivative of a function: Teachers’ practices with the idea of “generic”. Bolema, 30(54), 265-286. https://doi.org/10.1590/1980-4415v30n54a13
Radford, L. (2014). De la teoría de la objetivación [From the theory of objectification]. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.
Radford, L. (2015). Methodological aspects of the theory of objectification. Perspectivas da Educação Matemática, 8(18), 547-567.
Radford, L. (2017). A teoria da objetivação e seu lugar na pesquisa sociocultural em educação matemática [Objectification theory and its place in sociocultural research in mathematics education]. In V. D. Moretti, & W. L. Cedro (Eds.), Educação matemática e a teoria histórico-cultural: Um olhar sobre as pesquisas (pp. 229-261). Mercado de Letras.
Radford, L. (2020). ¿Cómo sería una actividad de enseñanza-aprendizaje que busca ser emancipadora? La labor conjunta en la teoría de la objetivación [What would a teaching-learning activity that seeks to be emancipatory look like? Joint work in the theory of objectification]. Revista Colombiana de Matemática Educativa, 5(2), 15-31.
Radford, L. (2021). The theory of objectification: A vygotskian perspective on knowing and becoming in mathematics teaching and learning. Brill. https://doi.org/10.1163/9789004459663
Sánchez-Matamoros, G. (2004). Análisis de la comprensión en los alumnos de bachillerato y primer año de universidad sobre la noción matemática de derivada (desarrollo del concepto) [Analysis of understanding of the mathematical concept of derivative in high school and first-year university students (development of the concept)] [PhD thesis, Universidad de Sevilla].
Sánchez-Matamoros, G. (2014). Adoptando diferentes perspectivas de investigación sobre el concepto de derivada [Adopting different research perspectives on the concept of derivative]. In M. T. González, M. Codes, D. Arnau, & T. Ortega (Eds.), Investigación en educación matemática XVIII (pp. 41-53). SEIEM.
Sánchez-Matamoros, G., & Fernández, C. (2016). Secuencias de actividades sobre derivada desde una trayectoria de aprendizaje [Sequences of activities derived from a learning path]. Uno. Revista de Didáctica de las Matemáticas, (72), 40-45.
Sánchez-Matamoros, G., Fernández, C., Valls, J., García, M., & Llinares, S. (2012). Cómo estudiantes para profesor interpretan el pensamiento matemático de los estudiantes de bachillerato. La derivada de una función en un punto [How student teachers interpret high school students’ mathematical thinking. The derivative of a function at a point]. In A. Estepa, Á. Contreras, J. Deulofeu, M. C. Penalva, F. J. García, & L. Ordóñez (Eds.), Investigación en educación matemática XVI (pp. 497-508). SEIEM.
Sánchez-Matamoros, G., García, M., & Llinares, S. (2008). La comprensión de la derivada como objeto de investigación en didáctica de la matemática [Understanding the derivative as an object of research in mathematics education]. Revista Latinoamericana de Investigación en Matemática Educativa, 11(2), 267-296.
Saraza, D., & Prada-Núñez, R. (2017). Estado del arte alrededor de la comprensión conceptual de la derivada [State of the art around the conceptual understanding of the derivative]. In R. Prada-Núñez, P. Ramírez, C. Hernández, H. Gallardo, S. Mendoza, & G. Rincón (Eds.), Proceedings of the II International Meeting on Mathematics Education (pp. 122-128). Universidad Francisco de Paula Santander.
Tapiero, K. J. (2020). Análisis de una propuesta para el aprendizaje del concepto de derivada a través de la razón de cambio [Analysis of a proposal for learning the concept of derivative through the rate of change] [Master’s thesis, Universidad del Valle].
Vargas-Plaça, J. S., & Radford, L. (2023). Uma reconceituação do professor a partir da teoria da objetivação [A reconceptualization of the teacher based on the theory of objectification]. Olhares: Revista do Departamento de Educação da Unifesp, 11(1), 1-16. https://doi.org/10.34024/olhares.2023.v11.14453
Wenzelburger, E. (1993). Introducción de los conceptos fundamentales del cálculo diferencial e integral–Una propuesta didáctica [Introduction to the fundamental concepts of differential and integral calculus–A didactic proposal]. Educación Matemática, 5(3), 93-123. https://doi.org/10.24844/EM0503.06

How to cite this article

APA

Pizarro-Ayavire, A. B., Prieto-González, J. L., & Gutiérrez-Araujo, R. E. (2024). Designing the encounter of teachers with meanings and levels of understanding of the derivative. International Electronic Journal of Mathematics Education, 19(4), em0798. https://doi.org/10.29333/iejme/15520

Vancouver

Pizarro-Ayavire AB, Prieto-González JL, Gutiérrez-Araujo RE. Designing the encounter of teachers with meanings and levels of understanding of the derivative. INT ELECT J MATH ED. 2024;19(4):em0798. https://doi.org/10.29333/iejme/15520

AMA

Pizarro-Ayavire AB, Prieto-González JL, Gutiérrez-Araujo RE. Designing the encounter of teachers with meanings and levels of understanding of the derivative. INT ELECT J MATH ED. 2024;19(4), em0798. https://doi.org/10.29333/iejme/15520

Chicago

Pizarro-Ayavire, Alan Basilio, Juan Luis Prieto-González, and Rafael Enrique Gutiérrez-Araujo. "Designing the encounter of teachers with meanings and levels of understanding of the derivative". International Electronic Journal of Mathematics Education 2024 19 no. 4 (2024): em0798. https://doi.org/10.29333/iejme/15520

Harvard

Pizarro-Ayavire, A. B., Prieto-González, J. L., and Gutiérrez-Araujo, R. E. (2024). Designing the encounter of teachers with meanings and levels of understanding of the derivative. International Electronic Journal of Mathematics Education, 19(4), em0798. https://doi.org/10.29333/iejme/15520

MLA

Pizarro-Ayavire, Alan Basilio et al. "Designing the encounter of teachers with meanings and levels of understanding of the derivative". International Electronic Journal of Mathematics Education, vol. 19, no. 4, 2024, em0798. https://doi.org/10.29333/iejme/15520