Abstract
This work aims to analyze the responses of a group of engineering students related to problems about tangents in a teaching learning process of derivative in a differential calculus course. The methodological design, oriented to a group of 161 students from two Chilean universities, considers different onto-semiotic configurations in problem-situations about tangents. The methodology implemented integrates information and communication technologies in differentiated activities, favoring the use of languages and progressive approach to the meaning of the derivative. The exploratory-type analysis was carried out applying some tools of the onto-semiotic Approach of mathematical knowledge and instruction. Difficulties were found in the concept of function and the Euclidean conception of the tangent line, which brings with it a weak interpretation of the derivative function and its geometric representation. It is concluded that the implementation of the geometric interpretation through information and communication technologies makes it possible to improve the teaching of the derivative.
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Article Type: Research Article
EURASIA J Math Sci Tech Ed, Volume 18, Issue 7, July 2022, Article No: em2130
https://doi.org/10.29333/ejmste/12162
Publication date: 15 Jun 2022
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Article Downloads: 1228
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- Aguilera, C., Manzano, A., Martínez, I., Lozano M., & Casiano, C. (2017). El modelo flipped classroom. Universidad de Almería [The flipped classroom model. University of Almeria]. International Journal of Developmental and Educational Psychology, 4(1), 261-266. https://doi.org/10.17060/ijodaep.2017.n1.v4.1055
- Ahumada, M. E. (2013). Las tic en la formación basada en competencias [ICT in training based on competences]. Revista Universidad de la Salle [La Salle University Magazine], (60), 141-157.
- Alvarado, H., Galindo, M., & Retamal, L. (2013). Evaluación del aprendizaje de la estadística orientada a proyectos en estudiantes de ingeniería [Project-oriented evaluation of statistics learning in engineering students]. Revista Educación Matemática [Mathematics Education Magazine], 30(3), 151-183. https://doi.org/10.24844/em3003.07
- Antonio, R., Escudero, D., & Flores, E. (2019). Una introducción al concepto de derivada en estudiantes de bachillerato a través de análisis de situaciones de variación [An introduction to the concept of derivative in high school students through analysis of variation situations]. Educación Matemática [Mathematics Education], 31(1), 258-280. https://doi.org/10.24844/EM3101.10
- Artigue, M. (1995). La enseñanza de los principios del cálculo: Problemas epistemológicos, cognitivos y didácticos [Teaching the principles of calculus: Epistemological, cognitive and didactic problems]. In P. Gómez (Ed.), Ingeniería didáctica en educación matemática (un esquema para la investigación y la innovación en la enseñanza y el aprendizaje de las matemáticas) [Didactic engineering in mathematics education (an outline for research and innovation in the teaching and learning of mathematics)] (pp. 97-140).
- Artigue, M. (1998). Enseñanza y aprendizaje del análisis elemental: ¿Qué se puede aprender de las investigaciones didácticas y los cambios curriculares? [Teaching and learning of elemental analysis: What can be learned from didactic investigations and curricular changes?] Revista Latinoamericana de investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 1(1), 40-55.
- Asiala, M., Cottrill, J., Dubinsky, E., & Schwingendorf, K. (1997). The development of student’s graphical understanding of the derivate. Journal of Mathematical Behavior, 16(4), 399-431. https://doi.org/10.1016/S0732-3123(97)90015-8
- Azcárate, C. (1990). La velocidad: Introducción al concepto de derivada [Velocity: Introduction to the concept of derivative] [PhD thesis, Universitat Autònoma de Barcelona].
- Badillo, E., Azcárate, C., & Font, V. (2011). Análisis de los niveles de comprensión de los objetos f´(a) y f’(x) de profesores de matemáticas [Analysis of the levels of understanding of the objects f´(a) and f’(x) of mathematics teachers]. Revista Enseñanza de las Ciencias [Science Teaching Magazine], 29(2), 191-206. https://doi.org/10.5565/rev/ec/v29n2.546
- Balcaza, T., Contreras, A., & Font, V. (2017). Análisis de libros de texto sobre la optimización en el bachillerato [Analysis of textbooks on optimization in high school]. Bolema: Boletim de Educação Matemática [Bolemma: Mathematics Education Bulletin], 31(59), 1061-1081. https://doi.org/10.1590/1980-4415v31n59a11
- Berry, J., & Nyman, M. (2003). Promoting students` graphical understanding of the calculus. Journal of Mathematical Behavior, 22, 481-497. https://doi.org/10.1016/j.jmathb.2003.09.006
- Biza, I., & Zacharides, T. (2010). First year mathematics undergraduates’ settled images of tangent line. The Journal of Mathematical Behavior, 29(4), 218-229. https://doi.org/10.1016/j.jmathb.2010.11.001
- Borgen, K., & Manu, S. (2002). What do students really understand? Journal of Mathematical Behavior, 21, 151-165. https://doi.org/10.1016/S0732-3123(02)00115-3
- Breda, A., Font, V., & Pino-Fan, L. R. (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica [Evaluative and normative criteria in the didactics of mathematics: The case of the didactic suitability construct]. Bolema: Boletim de Educação Matemática [Bolemma: Mathematics Education Bulletin], 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
- Cuesta, A., Deulofeu, J., & Méndez, M. (2010). Análisis del proceso de aprendizaje de los conceptos de función y extremo de una función en estudiantes de economía [Analysis of the learning process of the concepts of function and extreme of a function in economics students]. Educación Matemática [Mathematics Education], 22(3), 5-21. https://doi.org/10.24844/EM3003.07
- Esnaola, G. H., & Ansó, M. B. (2019). Competencias digitales lúdicas y enseñanza [Playful digital skills and teaching]. ReiDoCrea, 8, 399-410. https://doi.org/10.30827/Digibug.57800
- Flores, A. (2014). Enfoque conceptual del cálculo en la formación de docentes: Ejemplos con uso de tecnología interactiva [Conceptual approach to calculus in teacher training: Examples with the use of interactive technology]. Revista El Cálculo y su Enseñanza [Calculus and Its Teaching Magazine], 5(5), 1-26.
- Font, V. (2000a). Procediments per obtenir expressions simbòliques a partir de gràfiques. Aplicacions a la derivada [Procedures for obtaining symbolic expressions from graphs. Derivative applications] [PhD thesis, Universitat de Barcelona].
- Font, V. (2000b). Representaciones ostensivas que pueden ser activadas en el cálculo de f’(x). El caso de la función seno [Ostensive representations that can be activated in the calculation of f’(x). The case of the sine function]. Uno. Revista de Didáctica de las Matemáticas [One. Journal of Didactics of Mathematics], 25, 21-40.
- Font, V. (2005). Una aproximación ontosemiótica a la didáctica de la derivada [An ontosemiotic approach to the didactics of the derivative]. In A. Maz, B. Gómez, & M. Torralbo (Eds.), Investigación en educación matemática [Research in mathematics education] (pp. 109-128). SEIEM.
- Font, V. (2008). Rappresentazioni attivate nel calcolo della derivata [Representations activated in the calculation of the derivative]. In Proceedings of the Congress of Didactic of Mathematics (pp. 13-24).
- Font, V. (2009). Formas de argumentación en el cálculo de la función derivada de la función f(x)=x^2 sin usar la definición por límites [Forms of argumentation in the calculation of the derivative function of the function f(x)=x^2 without using the definition by limits]. Unión, (18), 15-18.
- Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97–124. https://doi.org/10.1007/s10649-012-9411-0
- Font, V., Godino, J., & D’Amore, B. (2007). An onto‐semiotic approach to representations in mathematics education. For the Learning of Mathematics, 27(2), 2‐7. https://doi.org/10.1007/s11858-006-0004-1
- Galindo, M., & Breda, A. (2020). Interpretación geométrica de la derivada en estudiantes de ingeniería comercial [Geometric interpretation of the derivative in commercial engineering students]. In Proceedings of the V International Meeting on Mathematics Education (pp. 158-163). Universidad del Atlántico.
- García, M., & Flores, C. D. (2016). Diseño de una situación de aprendizaje para la comprensión de la derivada [Design of a learning situation for understanding the derivative]. Unión, (46), 49-70.
- Godino, J. D. (2014). Síntesis del enfoque ontosemiótico del conocimiento y la instrucción matemática: Motivación, supuestos y herramientas teóricas [Synthesis of the ontosemiotic approach to mathematical knowledge and instruction: Motivation, assumptions and theoretical tools]. Universidad de Granada. http://www.ugr.es/~jgodino/eos/sintesis_EOS_24agosto14.pdf
- Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos [Institutional and personal meaning of mathematical objects]. Recherches en Didactique des Mathématiques [Research in Mathematics Didactics], 14(3), 325-355.
- Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37-42.
- Godino, J., Batanero, C., & 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
- Gómez, E., Hernández, H., & Chaucanés, A. (2015). Dificultades en el aprendizaje y el trabajo inicial con funciones en estudiantes de educación media [Difficulties in learning and initial work with functions in high school students]. Scientia et Technica [Science and Technology], 20(3), 278-285. https://doi.org/10.22517/23447214.10141
- González, D., Jeong, J. S., Cañada, F., & Gallego, A. (2017). La enseñanza de contenidos científicos a través de un modelo «flipped»: Propuesta de instrucción para estudiantes del grado de educación primaria [The teaching of scientific content through a “flipped” model: Instructional proposal for students of the primary education degree]. Enseñanza de las Ciencias [Science Education], 35(2), 71-87. https://doi.org/10.5565/rev/ensciencias.2233
- Gustafsson, G., Newman, D. J., Stafström, S., & Wallin, H. P. (2002). First-year introductory courses as a means to develop conceive-design-implement-operate skills in engineering education programmes. In Proceedings of the SEFIrenze 2002. Florence, Italy.
- Gutiérrez, L., Buitrago, M. R., & Ariza, 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 pedagogical mediation]. General José María Córdova, 15(20), 137-153. https://doi.org/10.21830/19006586.170
- Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, (25), 57-72. https://doi.org/10.1016/j.jmathb.2005.11.004
- Hernández, C., & Tecpan, S. (2017). Aula invertida mediada por el uso de plataformas virtuales: un estudio de caso en la formación de profesores de física [Inverted classroom mediated by the use of virtual platforms: a case study in the training of physics teachers]. Estudios Pedagógicos [Pedagogical Studies], 43(3), 193-204. https://doi.org/10.4067/S0718-07052017000300011
- Hernández, C., Prada, R. & Ramírez, P. (2018). Perspectivas actuales de los docentes de educación básica y media acerca de la aplicación de las competencias tecnológicas en el aula [Current perspectives of basic and secondary education teachers about the application of technological skills in the classroom]. Revista ESPACIOS [SPACES Magazine], 49(43), 19.
- Hitt, F. (2005). Dificultades en el aprendizaje del cálculo. En Reflexiones sobre el aprendizaje del cálculo y su enseñanza [Difficulties in learning calculus. In reflections on learning calculus and its teaching]. In Proceedings of the 11th Meeting of Mathematics Teachers of the Intermediate-Superior Level. Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico.
- Hitt, F., & Dufour, S. (2014). Un análisis sobre el concepto de derivada en el nivel preuniversitario, del rol de un libro de texto y su conexión con el uso de tecnología [An analysis of the concept of derivative at the pre-university level, of the role of a textbook and its connection with the use of technology]. In A. Cuevas, & F. Pluvinage (Eds.), La enseñanza del cálculo diferencial e integral [The teaching of differential and integral calculus] (pp. 19-42). Pearson Education.
- Inglada, N., & Font, V. (2003). Significados institucionales y personales de la derivada. Conflictos semióticos relacionados con la notación incremental [Institutional and personal meanings of the derivative. Semiotic conflicts related to incremental notation]. In Proceedings of the XIX Conference of the SI-IDM (pp. 1-18). Córdoba, Spain.
- Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14-26. https://doi.org/10.3102/0013189X033007014
- Lagrange, J., Artigue, M., Laborde, C., & Trouche, L. (2001). A meta study on ICT in education. Towards a multidimensional framework to tackle their integration. In Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (pp. 111-122). Freudenthal Institute, Utrecht, Netherlands.
- Letelier, M., López, L., Carrasco, R., & Pérez, P. (2005). Sistema de competencias sustentables para el desempeño profesional en ingeniería [System of sustainable competencies for professional performance in engineering]. Revista Facultad de Ingenieria [Faculty of Engineering Magazine], 13(2), 91-96. https://doi.org/10.4067/S0718-13372005000200011
- Londoño, N., Kakes, A., & Decena, V. (2013). Algunas dificultades en la resolución de problemas con derivadas [Some difficulties in solving problems with derivatives]. In R. Flores (Ed.), Acta Latinoamericana de matemática educativa [Latin American act of educational mathematics] (pp. 935-942).
- López, R. (2008). Nuevas tecnologías en la enseñanza aprendizaje del cálculo: Una aproximación al estado de la cuestión [New technologies in teaching-learning calculus: An approach to the state of the art]. TFM_Rubi-1.
- López, R., & Hernández, M. (2016). Principios para elaborar un modelo pedagógico universitario basado en las TIC. Estado del arte [Principles for developing a university pedagogical model based on ICT. State of the art]. UNIANDES EPISTEME, Revista de Ciencia, Tecnología e Innovación [UNIANDES EPISTEME, Journal of Science, Technology and Innovation], 3(4), 1-19.
- Marqués, P. (2012). Impacto de las TIC en la educación: Funciones y limitaciones [Impact of ICT in education: Functions and limitations]. 3Ciencias [3Science], 1(3), 14-29.
- Martín, D., & Tourón, J. (2017). El enfoque flipped learning en estudios de magisterio: Percepción de los alumnus [The flipped learning approach in teacher studies: Student perception]. RIED. Revista Iberoamericana de Educación [RIED. Ibero-American Journal of Education], 20(2), 187-211. https://doi.org/10.5944/ried.20.2.17704
- Martín, M., Hernández, C., & Mendoza, S. (2017). Ambientes de aprendizaje basados en herramientas web para el desarrollo de competencias TIC en la docencia [Learning environments based on web tools for the development of ICT skills in teaching]. Perspectivas [Perspectives], 2(1), 97-104. https://doi.org/10.22463/25909215.1282
- Martínez, C., Muñoz, M., Cárdenas, C., & Cepeda, M. (2013). Adopción de la Iniciativa CDIO en los planes de estudio de las carreras de la Facultad de Ingeniería de la UCSC [Adoption of the CDIO Initiative in the study plans of the careers of the Faculty of Engineering of the UCSC]. In Proceedings of the 11th Latin American and Caribbean Conference for Engineering and Technology. Cancún, México.
- Mercado, L., Aguas, N., & Arrieta, W. (2010). Comprensión del concepto de función a través de situaciones problema relacionadas con el contexto [Understanding of the concept of function through problem situations related to the context]. In P. Lestón (Ed.), Acta Latinoamericana de matemática educative [Latin American act of educational mathematics] (pp. 495-503).
- Moreno, H. (2017). Valoración de la idoneidad didáctica de un proceso de estudio de cálculo diferencial por los estudiantes [Assessment of the didactic suitability of a differential calculus study process by students]. In Proceedings of the Second Virtual International Congress on the Onto-Semiotic Approach to Knowledge and Mathematical Instruction.
- Núñez, A., & Gutiérrez, I. (2016). Flipped classroom para el aprendizaje del inglés: Estudio de caso en Educación Primaria [Flipped classroom for learning English: Case study in Primary Education]. Revista Electrónica de Tecnología Educativa [Electronic Magazine of Educational Technology], (56), 89-102. https://doi.org/10.21556/edutec.2016.56.654
- Orton, A. (1983). Student’s understanding of differentiation. Educational Studies in Mathematics, 14(3), 235-250. https://doi.org/10.1007/BF00410540
- Orts, A., Llinares, S., & Boiges, F. (2016). Elementos para una descomposición genética del concepto de recta tangente [Elements for a genetic decomposition of the tangent line concept]. AIEM. Avances de Investigación en Educación Matemática [AIEM. Research Advances in Mathematics Education], 10, 111-134. https://doi.org/10.35763/aiem.v0i10.164
- Pico, R., Díaz, F., & Escalona, M. (2017). Enseñanza y aprendizaje del cálculo diferencial aplicando el asistente matemático derive [Teaching and learning of differential calculus applying the mathematical assistant derive]. Tecnología Educativa [Educative technology], 2(1), 24-31.
- Pineda, W. B., Hernández, C. A., & Avendaño, W. R. (2020). Propuesta didáctica para el aprendizaje de la derivada con derive [Didactic proposal for learning the derivative with derive]. Praxis & Saber [Praxis & Knowledge], 11(26), e9845. https://doi.org/10.19053/22160159.v11.n26.2020.9845
- Pino-Fan, L., Castro, W. F., Godino, J. D., & Font, V. (2013). Idoneidad epistémica del significado de la derivada en el currículo de bachillerato [Epistemic suitability of the meaning of the derivative in the high school curriculum]. Paradigma, 34(2), 123-150.
- Pino-Fan, L., Godino, J. D., & Font, V. (2011). Faceta epistémica del conocimiento didáctico matemático sobre la derivada [Epistemic facet of mathematical didactic knowledge about the derivative]. Educação Matemática Pesquisa [Mathematics Education Research], 13(1), 141-178.
- Pino-Fan, L., Godino, J. D., & Font, V. (2015). Una propuesta para el análisis de las prácticas matemáticas de futuros profesores sobre derivadas [A proposal for the analysis of the mathematical practices of future teachers on derivatives]. Bolema, 29(51), 60-89. https://doi.org/10.1590/1980-4415v29n51a04
- Robles, M., Del Castillo, A., & Font, V. (2010). La función derivada a partir de una visualización de la linealidad local [The derived function from a visualization of local linearity]. In M. Moreno, A. Estrada, J. Carrillo, & T. Sierra (Eds.), Investigación en educación matemática XIV [Research in mathematics education XIV] (pp. 523-532). SEIEM.
- Salas-Rueda, R.A., & Lugo-García, J.L. (2019). Impacto del aula invertida durante el proceso educativo superior sobre las derivadas considerando la ciencia de datos y el aprendizaje automático [Impact of the flipped classroom during the higher educational process on derivatives considering data science and machine learning]. EDMETIC, Revista de Educación Mediática y TIC [EDMETIC, Journal of Media and ICT Education], 8(1), 147-170. https://doi.org/10.21071/edmetic.v8i1.9542
- Sánchez-Matamoros, G. (2004). Análisis de la comprensión en los alumnos de bachillerato y primer año de la universidad sobre la noción matemática de derivada (desarrollo del concepto) [Analysis of understanding in high school and first year university students about the mathematical notion of derivative (development of the concept)] [PhD thesis, Universidad de Sevilla].
- Sánchez-Matamoros, G., García, M., & Llinares, S. (2006). El desarrollo del esquema de derivada [The development of the derivative scheme]. Enseñanza de las Ciencias [Science Education], 24(1), 85-98. https://doi.org/10.5565/rev/ensciencias.3816
- Sánchez-Matamoros, G., García, M., & Llinares, S. (2008). La comprensión de la derivada como objeto de investigación en didáctica de la matemática [The understanding of the derivative as an object of research in mathematics education]. Revista Latinoamericana de Investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 11(2), 267-296.
- Santi, A. (2011). Objectification and semiotic function. Educational Studies in Mathematics, 77(2-3), 285-311. https://doi.org/10.1007/s10649-010-9296-8
- Tall, D. (2001). Natural and formal infinities. Educational Studies in Mathematics, 48(2-3), 200-238. https://doi.org/10.1023/A:1016000710038
- Tourón, J., & Santiago, R. (2015). El modelo flipped learning y el desarrollo del talento en la escuela [The flipped learning model and the development of talent at school]. Revista de Educación [Education Magazine], 368, 196-231.
- Zandieth, M. (2000). A theorical framework for analyzing student understanding of the concept of derivate. In E. Dubinsky, A. Shoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education (pp. 103-127). American Mathematical Society. https://doi.org/10.1090/cbmath/008/06
- Zuñiga, L. (2007). El cálculo en carreras de ingeniería: Un estudio cognitivo [Calculus in engineering careers: A cognitive study]. Relime, 10(1), 145-175.
How to cite this article
APA
Galindo Illanes, M. K., Breda, A., Chamorro Manríquez, D. D., & Alvarado Martínez, H. A. (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
Vancouver
Galindo Illanes MK, Breda A, Chamorro Manríquez DD, Alvarado Martínez HA. Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA J Math Sci Tech Ed. 2022;18(7):em2130. https://doi.org/10.29333/ejmste/12162
AMA
Galindo Illanes MK, Breda A, Chamorro Manríquez DD, Alvarado Martínez HA. Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA J Math Sci Tech Ed. 2022;18(7), em2130. https://doi.org/10.29333/ejmste/12162
Chicago
Galindo Illanes, Maritza Katherine, Adriana Breda, Denise Deyanira Chamorro Manríquez, and Hugo Alejandro Alvarado Martínez. "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 2022 18 no. 7 (2022): em2130. https://doi.org/10.29333/ejmste/12162
Harvard
Galindo Illanes, M. K., Breda, A., Chamorro Manríquez, D. D., and Alvarado Martínez, H. A. (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
MLA
Galindo Illanes, Maritza Katherine et al. "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, vol. 18, no. 7, 2022, em2130. https://doi.org/10.29333/ejmste/12162