Predominance of Teaching Models Used by Math Teachers in Secondary Education

This research examines the teaching models used by secondary math teachers when teaching logarithmic, quadratic and exponential functions. For this, descriptive case studies have been carried out on 5 secondary teachers. These teachers have been chosen from 3 scientific-humanistic and technical schools, in Chile. Data have been obtained through non-participant class observation and the application of a questionnaire and a rubric to teachers. According to the results, the didactic model that prevails is the one that starts with an interactive strategy, moves to a more content-based structure, and ends with a reinforcement stage. Nonetheless, there is always influence from teachers, their methods, and the group of students.

Authors:

• Verónica Diaz Quezada

Keywords:

• Teaching models
• math teachers
• functions
• secondary education.

References:

[1] Z. Kurnik, “The scientific approach to teaching math,” Metodika, vol. 17, no. 2, pp. 421-432, 2008.
[2] L. Del Pino, “The teaching and learning process of mathematics in the primary education stage: A constructivist proposal within the framework of key competences,” IEJME-Mathematics Education, vol. 12, no.7, pp. 709-713, 2017.
[3] M. Bhowmik, “Constructivism approach in mathematics teaching and assessment of mathematical understanding,” Basic Research Journal of Education Research and Review, vol. 4, no.1, pp. 8-12, 2015.
[4] A. Jazim, and D. Rahmawati, “The use of mathematical module based on constructivism approach as media to implant the concept of algebra operation,” IEJME-Mathematics Education, vol. 12, no. 6, pp. 579-583, 2017.
[5] N. Martínez, Los modelos de enseñanza y la práctica en aula. Universidad de Murcia, 2004. Available online from: https://educar.ec/jornada/doc-clases/modelos.pdf
[6] Agencia de Calidad de la Educación, Resultados Educativos 2016. Santiago: Impresos Universitaria, 2016.
[7] OCDE Organización para la Cooperación y el Desarrollo Económico. PISA 2012 Results: What students know and can do (Volume I, Revised edition, February 2014): Student performance in mathematics, reading and science. Paris: OCDE Publishing, 2014.
[8] G. Harel, and K. L. Lim, “Mathematics teachers' knowledge base: preliminary result.(Published Conference Proceedings stile), “ in Proc. 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen University College, 2004, pp. 25-32.
[9] P. Sureda, M.R. Otero and A. Donvito, A, Secuencia didáctica para enseñar las funciones exponenciales en la escuela secundaria. Una propuesta diseñada en el marco de la teoría de los campos conceptuales. Argentina: Universidad Nacional del Centro de la Provincia de Buenos Aires, 2017.
[10] A. Monge, and R. Vallejos, El uso del juego como mediador del conocimiento matemático a partir de las experiencias docentes. 2012. Available online from: http://www. cientec.or.cr/matematica/2012/ponenciasVIII/Adolfo-Monge.pdf
[11] A. Jiménez, “La naturaleza de la matemática, sus concepciones y su influencia en el salón de clase, Educación y Ciencia,” vol. 13, pp. 135-150, 2010.
[12] J. F Leguizamón, O.Y. Patiño, and P. Suárez, “ Tendencias didácticas de los docentes de matemáticas y sus concepciones sobre el papel de los medios educativos en el aula,” Educación Matemática, vol. 27, no.3, pp. 151-174, 2015.
[13] A. Murillo, and L. Ceballos, “Las prácticas de enseñanza empleadas por docentes de matemáticas y su relación con la resolución de problemas, mediados por fracciones”, Revista Científica, Edición Especial, pp. 244-248, 2013.
[14] J. Gascón, “Incidencia del modelo epistemológico de las matemáticas sobre las prácticas docentes,” Revista Latinoamericana de Investigación en Matemática Educativa, vol. 4, no.2, pp.129-159, 2001.
[15] J. Villota, A. Pereira, and H. González, “What mathematic teachers say about the teaching strategies in the implementation of tasks,” English Language Teaching, vol. 11, no.1, pp. 65-79, 2018.
[16] D. Mora, Evaluación de los aprendizajes. Un modelo para su aplicación en el aula, especialmente en matemáticas. La Paz: Instituto Normal Superior Simón Bolívar, 2003.
[17] M.J. Mayorga, and D. Madrid, “Modelos didácticos y estrategias de enseñanza en el Espacio Europeo de Educación Superior,” Tendencias Pedagógicas, vol.15, no.1, pp.91-111, 2010.
[18] A. Lira, and G. Corona-Corona, “Usefulness of didactic strategies in teaching high school mathematics,” American Scientific Research Journal for Engineering, Technology, and Sciences, vol. 33, no.1, pp.162-168, 2017.
[19] M. Feo, “Orientaciones básicas para el diseño de estrategias didácticas,” Tendencias Pedagógicas, vol. 16, pp. 221-236, 2015..
[20] L. M. Córmack, “Estrategias de aprendizaje y de enseñanza en la educación del menor de 6 años,” Acción Pedagógica, vol. 13, no. 2, pp. 154-161, 2014.
[21] O. Chen, S. Kalyuga, and J. Sweller, “Relations between the worked example and generation effects on immediate and delayed tests”, Learning and Instruction, vol.45, pp. 20–30, 2016.
[22] R. Anijovich, and S. Mora, Estrategias de enseñanza: Otra mirada al quehacer en el aula. Buenos Aires: AIQUE, 2009.
[23] S. Norton, “The relationship between mathematical content knowledge and mathematical pedagogical content knowledge of prospective primary teachers,” Journal of Mathematics Teacher Education, 2018. Available online from: https://doi.org/10.1007/s10857-018-9401-y
[24] H. C. Hill, “The nature and predictors of elementary teachers’ mathematical knowledge for teaching,” Journal for Research in Mathematics Education, vol.41, pp.513–545, 2010.
[25] J. E. Tarr, R.E. Reys, B.J. Reys, O. Chavez, J. Shih, and S.J. Osterlind, “The impact of middlegrades mathematics curricula and the classroom learning environment on student achievement,” Journal for Research in Mathematics Education, vol.39, pp.247–280, 2008.
[26] D. L. Ball, and F.M. Forzani, “What does it take to make a teacher?,” Phi Delta Kappan, vol.92, pp.8–12, 2010.
[27] D. Ball, M. Thames, and G. Phelps, “Content knowledge for teaching: What makes it special?,” Journal of Teacher Education, vol.59, pp.389–407, 2008.
[28] L.S. Shulman, “Knowledge and teaching: Foundations of the new reform,” Harvard Educational Review, vol.57, no.1, pp.1-22, 1987.
[29] MINEDUC Ministerio de Educación de Chile. Bases Curriculares 2013. Matemática 7° Básico a 2° medio. Santiago: Impresos Universitaria, 2013.
[30] MINEDUC Ministerio de Educación de Chile. Matemática: guiones didácticos y guías para el/la estudiante de 2º año de educación media. Santiago: Impresos Universitaria, 2015.
[31] R. Hernández, C. Fernández, and P. Baptista. Metodología de la investigación. México, D. F.: McGraw-Hill, 2006.
[32] R.E. Stake, Multiple case study analysis. New York: The Guilford Press, 2006.
[33] W. Li, and A. Castro, “Mathematics teacher educators’ perspectives on their design of content courses for elementary preservice teachers,” Journal of Mathematics Teachers Education, vol. 21, no.2, pp. 179–201, 2018.
[34] M.W. Brown, The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, and G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction, New York, NY: Routledge, 2009, pp.17-36.
[35] S. Zarate, Estrategias de enseñanza para desarrollar habilidades del pensamiento en la escuela básica estadual caura, Dissertação Mestrado em Ciencias de la Educación, 2009.
[36] D. Mora, Probleme des mathematikunterrichts in lateinamerikanischen ländern -explorative empirische studie zur entwicklung didaktischer und curricularer innovationsansätze im kontext der educación popular am Beispiel, Nicaragua und Venezuela. Alemania: Universidad de Hamburgo, 1998. Available online from: http://www.sub.uni-hamburg.de/disse/05
[37] L. Contreras, “Concepciones, creencias y conocimiento. Referentes de la prác¬tica profesional,” Revista Electrónica Iberoamericana de Educación en Ciencia y Tecnología, vol.1, no.1, pp.11-36, 2009.