Design and implementation of an educational experience on linear variation for prospective mathematics teachers
DOI:
https://doi.org/10.15359/ru.37-1.16Keywords:
Didactic-mathematical skill, research design, prospective teachers training, linear variation, mathematics education, higher education, teaching and learningAbstract
[Objective] This paper discusses the design, implementation, and analysis of an educational experience focused on linear variation, aimed at prospective secondary school mathematics teachers. The objective of this experience is to improve the prospective teachers’ didactic-mathematical knowledge and to contribute to the development of their onto-semiotic analytical skills. Linear variation is an important topic because it is present in different educational moments through multiple approaches and meanings – arithmetic, algebraic, and functional. As a complex mathematical object, it can generate teaching and learning conflicts, which can be studied to provide useful information about improvement of educational activities. [Methodology] This is a qualitative investigation, based on the preliminary study, design, implementation, and analysis of 5 didactic activities according to the theoretical principles of the Onto-semiotic Approach. The data gathered for the investigation included video recordings of classes, field notes and written answers provided by nine prospective teachers in the eighth semester of a Licentiate’s Degree in Secondary Education program, specializing in Mathematics. [Results] The results indicate that linear variation is indeed a complex issue, and deficiencies were found in the didactic-mathematical knowledge of prospective teachers. Likewise, difficulties in terms of knowledge and skills were found when participants were asked to analyze hypothetical responses to tasks related to the concept of linear variation. [Conclusions] The results of this investigation indicate that experiences such as these can be a valuable resource in educational programs for teachers to acquire knowledge and skills for the appropriate treatment of mathematical content.
References
Alsina, Á.; Planas, N. y Calabuig, M. (2009). El aprendizaje reflexivo en la formación del profesorado de matemáticas. Actas de las VII Jornadas de redes de investigación en docencia universitaria: la calidad del proceso de enseñanza/aprendizaje universitario desde la perspectiva del cambio (pp. 252-257). Universidad de Alicante, Alicante.
Badillo, E.; Climent, N. y Fernández-Verdú, C. (Eds.). (2020). Investigación sobre el profesor de matemáticas. Ediciones Universidad de Salamanca.
Bojórquez A.; Castillo, J. M. y Jiménez J. R. (2016). Development of the variational thought in secondary students. Actas del Congreso Internacional en Tecnología y su Integración en la Educación Matemática (TIME) 2016. 29 de junio al 2 de julio de 2016. Austrian Center for Didactics of Computer Algebra (ACDCA) y Facultad de Ciencias de la UNAM. Ciudad de México. http://www.acdca.ac.at/fileadmin/Mathematik_Uploads/ACDCA/TIME2016/Garcia_ao.pdf
Breda, A.; Pino-Fan, L. y Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflections and assessment on teaching practice. Eurasia Journal of Mathematics, Science & Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
Burgos, M. y D. Godino, J. (2020). Modelo ontosemiótico de referencia de la proporcionalidad. Implicaciones para la planificación curricular en primaria y secundaria. Avances de Investigación en Educación Matemática, (18), 1–20. https://doi.org/10.35763/aiem.v0i18.255
Chapman, O. y An, S. (2017). A survey of university-based programs that support in- service and pre-service mathematics teachers’ change. ZDM, Mathematics Education, 49(2), 171-185. https://doi.org/10.1007/s11858-017-0852-x
English, L. (2008). Setting an agenda for international research in mathematics education. En L. English (Ed.), Handbook of international research in mathematics education (pp. 3-19). New York, NY: Routledge. https://doi.org/10.4324/9780203930236.ch1
Giacomone, B. (2018). Desarrollo de competencias y conocimientos didáctico-matemáticos de futuros profesores de educación secundaria en el marco del enfoque ontosemiótico. Doctorado tesis, Universidad de Granada.
Godino, J. D.; Aké, L.; Gonzato, M. y Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 32(1), 199-219. https://doi.org/10.5565/rev/ensciencias.965
Godino, J. D.; Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J. D.; Batanero, C. y Font, V. (2019). The Onto-Semiotic Approach: Implications for the Prescriptive Character of Didactics. For the Learning of Mathematics, 39(1), 38-43.
Godino, J. D.; Beltrán-Pellicer, P.; Burgos, M. y Giacomone, B. (2017). Significados pragmáticos y configuraciones ontosemióticas en el estudio de la proporcionalidad. In Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos (pp. 1-13). Granada: CIVEOS.
Godino, J. D.; Giacomone, B.; Batanero, C. y Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema: Boletim de Educação Matemática, 31, 90-113. https://doi.org/10.1590/1980-4415v31n57a05
Godino, J. D.; Rivas, H.; Arteaga, P.; Lasa, A. y Wilhelmi, M. R. (2014). Ingeniería didáctica basada en el enfoque ontológico-semiótico del conocimiento y la instrucción matemáticos. Recherches en Didactique des Mathématiques, 34(2/3), 167-200.
Godino, J.; Batanero, C.; Font, V. y Giacomone, B. (2016). Articulando conocimientos y competencias del profesor de matemáticas: el modelo CCDM. En A. Berciano; C. Fernández; T. Fernández; J. L. González; P. Hernández; A. Jiménez; J. A. Macías; F. J. Ruiz y M. T. Sánchez (Eds.), Investigación en Educación Matemática XX (pp. 285-294). Málaga, España: Universidad de Málaga.
Goldsmith, L. T.; Doerr, H. M. y Lewis, C. C. (2014). Mathematics teachers’ learning: a conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17, 5-36. https://doi.org/10.1007/s10857-013-9245-4
Hernández, S.; Fernández, C. y Baptista, L. (2010). Metodología de la investigación. México: Mc Graw Hill.
Herrera-García, K.; Dávila-Araiza, M. T.; Giacomone, B. y Beltrán-Pellicer, P. (2021). Una propuesta de secuencia didáctica sobre variación lineal para la formación inicial de profesores de matemáticas de secundaria. Números. Revista de Didáctica de las Matemáticas, 108, pp. 263-289.
Hummes, V. B.; Font, V. y Breda, A. (2019). Combined use of the Lesson Study and the Didactic Suitability for the development of the reflection on the own practice in the training of mathematics teachers. Acta Scientiae, 21(1), 64-82. https://doi.org/10.17648/acta.scientiae.v21iss1id4968
Martínez-Juste, S.; Muñoz-Escolano, J. M.; Oller-Marcén, A. M. y Ortega, T. (2017). Análisis de problemas de proporcionalidad compuesta en libros de texto de 2.º de ESO. Revista Latinoamericana de Investigación en Matemática Educativa, 20(1), 95-122. https://doi.org/10.12802/relime.17.2014
Panorkou, N.; Maloney, A. y Confrey, J. (2016). Expressing Covariation and Correspondence relationships in elementary schooling. https://nctm.confex.com/nctm/2014RP/webprogram/ExtendedAbstract/Paper1940/EQX_NCTM_040314%20.pdf
Pino-Fan, L. y Godino, J. D. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor. PARADIGMA, 36(1), 87-109.
Ponte, J. P. y Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in Mathematics, 93, 51-66. https://doi.org/10.1007/s10649-016-9681-z
Potari, D. y da Ponte, J. P. (2017). Current research on prospective secondary mathematics teachers’ knowledge. En The mathematics education of prospective secondary teachers around the world (pp. 3-15). Springer, Cham. https://doi.org/10.1007/978-3-319-38965-3_2
Rivas, H.; Godino, J. D. y Arteaga, P. (2018). Desarrollo de conocimientos estadísticos en futuros profesores de educación primaria a través de un proyecto de análisis de datos: posibilidades y limitaciones. Educación matemática, 30(3), 83-100. https://doi.org/10.24844/EM3003.04
SEP. Secretaría de Educación Pública. (2017). Planes de estudio de referencia del marco curricular común de la educación media superior. Ciudad de México, SEP. http://www.sems.gob.mx/work/models/sems/Resource/12491/4/images/libro.pdf
SEP. Secretaría de Educación y cultura. (2017). Aprendizajes Clave para la Educación Integral. Ciudad de México. SEP. https://www.gob.mx/cms/uploads/attachment/file/198738/Modelo_Educativo_para_ la_Educacio_n_Obligatoria.pdf
Sousa, J. R.; Silva Gusmão, T. C. R.; Font, V. y Lando, J. C. (2020). Task (re)design to enhance the didactic-mathematical knowledge of teachers. Acta Scientiae, 22(4), 98-120 https://doi.org/10.17648/acta.scientiae.5711
Thompson, P. W. y Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. En J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.
Vasco, C. E. (2003). El pensamiento variacional y la modelación matemática. En Anais eletrônicos do CIAEM–Conferência Interamericana de Educação Matemática, Blumenau.
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