Analyzing the mathematical connections of a future mathematics teacher when solving problems in a Didactics of Calculus course.
Article Sidebar
Main Article Content
Abstract
The mathematical connections established by a pre-service mathematics teacher when problem-solving an application on derivatives were analyzed and how their pre-service mathematics teacher identifies them in the classroom. The study was based on the Extended Theory of Connections (ETC) and the methodology was qualitative developed in three stages: 1) selection of participants, 2) performance of a participant observation in a Calculus Didactics course in a Colombian public University, 3) execution of a thematic analysis of the data. The main results show that the future teacher established connections oriented to instruction, meaning, modeling, procedural, feature, different representations and, implication, in order to solve and explain an application problem about the volume of a box and are the special evidence of your understanding. It is important that both the teacher and the students (pre-service mathematics teachers) foster connections when problems-solving, which will allow them to reflect a high level of understanding of Calculus concepts. In fact, when a person does not make a mathematical connection, it is the cause of difficulties and errors in mathematics problems-solving.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
Alsina, Á. (2020). Conexiones matemáticas a través de actividades STEAM en Educación Infantil. UNIÓN-Revista Iberoamericana de Educación Matemática, 16(58), 168-190.
Amaya, T. (2020). Evaluación de la faceta epistémica del conocimiento didáctico-matemático de futuros profesores de matemáticas en el desarrollo de una clase utilizando funciones. Bolema-Mathematics Education Bulletin, Rio Claro (SP), 34(66), 110-131.
Braun, V. y Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa
Berry, J. y Nyman, M. (2003). Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior, 22(4), 479-495.
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. [Unpublished PhD thesis, Simon Fraser University, Canada].
Campo-Meneses, K. G. y García-García, J. (2020). Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes universitarios colombianos. Educación matemática, 32(3), 209-240.
Caviedes-Barrera, S.; De Gamboa-Rojas, G. y Badillo-Jiménez, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida y comparación de áreas. Praxis, 15(1), 69-87.
Charria-Castaño, L. (2017). Los derechos básicos de aprendizaje y la Narrativa Transmedia, otra forma de aprender en clase de matemáticas. Revista Educación y Ciudad, 33, 87-98.
Cohen, L.; Manion, L. y Morrison, K. (2018). Research methods in education. London and New York: Routledge.
Dolores-Flores, C. y García-García, J. (2017). Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior. Bolema - Mathematics Education Bulletin, Rio Claro SP, 31(57), 158–180.
Dolores-Flores, C. (2013). La variación y la derivada. 2. ed. México: Ediciones Díaz de Santos.
Dray, T.; Giré, E.; Kustusch, M.; Manogue.; Corinne A. y Roundy, D. (2019). Interpreting Derivatives. Primus, 29(8), 830-850.
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. [Unpublished dissertation, Doctor of philosophy, Pennsylvania State University College of Education. EE. UU].
Eli, J.; Mohr-schroeder, M. y Lee, C. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319.
Fuentealba, C.; Badillo-Jiménez, E. y Sánchez-Matamoros, G. (2019). Identificación y caracterización de los subniveles de desarrollo del esquema de derivada. Enseñanza de las ciencias: revista de investigación y experiencias didácticas, v. 37(2), 63-84.
García-García, J. (2019). Escenarios de exploración de conexiones matemáticas. Números: revista de didácticas de las matemáticas, 100, 129-133.
García-García, J. y Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing calculus tasks. Int.J.Math.Educ.Sci.Technol, 49(2), 227–252.
García-García, J. y Dolores-Flores, C. (2019). Conexión entre derivada e integral en el registro algebraico en bachillerato. Investigación e Innovación en Matemática Educativa, 4, 11-30.
García-García, J. y Dolores-Flores, C. (2020). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, v. 52(6), 912-936.
Gonzales-García, A.; Muñiz-Rodríguez, L. y Rodríguez-Muñiz, L. (2018). Un estudio exploratorio sobre los errores y las dificultades del alumnado de Bachillerato respecto al concepto de derivada. Aula Abierta, v. 47(4), 449-462.
Haghjoo, S. y Reyhani, E. (2021). ndergraduate basic sciences and engineering students’ understanding of the concept of derivative. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(4), 277-298.
Hatisaru, V. (2022). Mathematical connections established in the teaching of functions. Teaching Mathematics and its Applications. An International Journal of the IMA, 1-21.
Kaur, B. y Lam, T. T. (2012). Reasoning, Communication and Connections in Mathematics: An Introduction. In: Kaur, B. y Lam, T. T. (ed). Reasoning, Communication and Connections in Mathematics (pp. 1-10). World Scientific Publishing.
Lakoff, G. y Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.
Mhlolo, M. (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 76-191.
Memòria Del Departament D' Ensenyament. (2017). Generalitat de Catalunya. Departament d'Ensenyament. Memòria Del Departament D' Ensenyament.
Ministerio de Educación Nacional. (2006). Estándares básicos de competencias en Lenguaje, Matemáticas, Ciencias y Ciudadanas. Bogotá: Ministerio de Educación Nacional.
Ministerio de Educación Nacional. (2017). Derechos Básicos de Apredizaje. Bogotá: Ministerio de Educación Nacional.
National Council of Teachers of Mathematics [NCTM]. [ (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics [NCTM].
Özgen, K. (2013). Problem cözme baglamida matematiksel iliskilenddirme becerisi: ögretmen adaylari örnegi. NWSA- Education Sciences, 8(3), 323-345.
Pino-Fan, L.; Godino, J. D. y Font, V. (2015). Una propuesta para el análisis de las prácticas matemáticas de futuros profesores sobre derivadas. Bolema - Mathematics Education Bulletin, v. 29(51), 60–89.
Pino-Fan, L.; Godino, J. D. y Font, V. (2018). Assessing key epistemic features of didactic mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education, 21, 63–94.
Pino-Fan, L.; Guzmán, I.; Font, V. y Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value function: Two theoretical perspectives. PNA 11(2), 97-124.
Reveles-Gamboa, S., Orta, M. D. L. L. N., & Villegas-Berumen, H. G. (2022). La relación entre el uso de tecnologías de la información, el aprendizaje del cálculo diferencial y el liderazgo. Un Análisis realizado en Jerez, Zacatecas. El cálculo y su enseñanza, Enseñanza de las ciencias y la matemática, 18(1), 1-12.
Rodríguez-Nieto, C.; Rodríguez-Vázquez, F. y García-García, J. (2021a). Exploring University Mexican Students' Quality of Intra-Mathematical Connections When Solving Tasks About Derivative Concept. Eurasia Journal of Mathematics, Science and Technology Education, v. 17(9).
Rodríguez-Nieto, C.; Rodríguez-Vázquez, F. y García-García, J. (2021b). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220.
Rodríguez-Nieto, C.; Rodríguez-Vázquez, F.; Font, V. y Morales-Carballo, A. (2021c). Una visión desde la red de teorías TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada / A view from the ETC-OSA networking of theories on the role of mathematical connections in understanding the derivative. Revemop, 3, 1-32.
Rodríguez-Nieto, C. y Alsina, A. (2022). Networking Between Ethnomathematics, STEAM Education, and the Globalized Approach to Analyze Mathematical Connections in Daily Practices. EURASIA Journal of Mathematics, Science and Technology Education, 18(3), 20-85.
Rodríguez-Nieto, C.; Rodríguez-Vázquez, F. y Font, V. (2022). A new view about connections: the mathematical connections established by a teacher when teaching the derivative / Una nueva visión acerca de las conexiones: las conexiones matemáticas establecidas por un profesor cuando enseña la derivada. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256.
Ruiz, A. y Barrantes, H. (1996). Elementos de cálculo diferencial. Volumen 1 límites y la derivada. Universidad de Costa Rica.
Sari, P.; Hadiyan, A. y Antari, D. (2018). Exploring derivatives by means of GeoGebra. International Journal on Emerging Mathematics Education, 2(1), 65-78.
Stewart, J. (1999). Cálculo. Conceptos y contextos. México: International Thomson Editores.
Selinski, N. E.; Rasmussen, C.; Wawro, M. y Zandieh, M. A. (2014). method for using adjacency matrices to analyze the connections students make within and between concepts: The case of linear algebra. Journal for Research in Mathematics Education, 45(5), 550-583.
Vanegas, Y.; Giménez, J. y Font, V. (2017). Conexiones matemáticas en la reflexión sobre prácticas escolares. Acta Latinoamericana de Matemática Educativa, 114-1124.
Vargas, M. F.; Fernández-Plaza, J. A. y Ruiz-Hidalgo, J. F. (2020). Significado de derivada en las tareas de los libros de 1° de Bachillerato. Bolema - Mathematics Education Bulletin, Rio Claro (SP), 34(68), 911-933.
Yavuz-Mumcu, H. (2018). Examining mathematics department students’ views on the use of mathematics in daily life. International Online Journal of Education and Teaching (IOJET), 5(1), 61-80.