International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Locia-Espinoza E, Morales-Carballo A, Merino-Cruz H. Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training. INT ELECT J MATH ED. 2020;15(3), em0585. https://doi.org/10.29333/iejme/7852
APA 6th edition
In-text citation: (Locia-Espinoza et al., 2020)
Reference: Locia-Espinoza, E., Morales-Carballo, A., & Merino-Cruz, H. (2020). Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training. International Electronic Journal of Mathematics Education, 15(3), em0585. https://doi.org/10.29333/iejme/7852
Chicago
In-text citation: (Locia-Espinoza et al., 2020)
Reference: Locia-Espinoza, Edgardo, Armando Morales-Carballo, and Héctor Merino-Cruz. "Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0585. https://doi.org/10.29333/iejme/7852
Harvard
In-text citation: (Locia-Espinoza et al., 2020)
Reference: Locia-Espinoza, E., Morales-Carballo, A., and Merino-Cruz, H. (2020). Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training. International Electronic Journal of Mathematics Education, 15(3), em0585. https://doi.org/10.29333/iejme/7852
MLA
In-text citation: (Locia-Espinoza et al., 2020)
Reference: Locia-Espinoza, Edgardo et al. "Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0585. https://doi.org/10.29333/iejme/7852
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Locia-Espinoza E, Morales-Carballo A, Merino-Cruz H. Taylor’s Formula, Limited Development, and Development of Power Series: A Study of the Knowledge of University Professors in Training. INT ELECT J MATH ED. 2020;15(3):em0585. https://doi.org/10.29333/iejme/7852

Abstract

This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests on the Mathematics Teacher’s Specialised Knowledge (MTSK), specifically in the domain: Mathematical Knowledge (MK).
As a result of the analysis of the responses to the questionnaires, it was identified that the notion of development of power series played an important role as a means of justification and that, from the three notions addressed (Taylorʼs Formula, limited development, development of power series), this was the most prevalent in the mind of the students. These results will be used as the starting point for the development of proposals that improve the teaching and learning of the subject of study.

References

  • Abarca, N. (2007). La enseñanza del cálculo diferencial e integral mediante la resolución de problemas, una propuesta motivadora. Revista Tecnociencia Universitaria Bolivia, 5(5), 14-20. https://doi.org/10.15359/ru.32-2.3
  • Antibi, A. (1988). Etude sur l’enseignement de méthodes de démonstration. Enseignement de la notion de limite: reflexions, propositions (State thesis). Universidad Paul Sabatier.
  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes its special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Bottazzini, U. (1986). The higher Calculus: a history of real and complex analysis, from Euler to Weierstrass. Springer Verlag. https://doi.org/10.1007/978-1-4612-4944-3
  • Carrillo, J., Aguilar, A., Contreras, L, Climent, N., Carmona, E., Escudero-Avila, D., … Zakaryan, D. (2014). Un marco teórico para el conocimiento especializado del profesor de matemáticas. Huelva, Spain: Universidad de Huelva Publicaciones. https://doi.org/10.1080/14794802.2018.1479981
  • Duarte, A. (1993). Une introduction historique de la notion de convergence. Une étude sur la convergence simple de certains suites de fonctions. Memoria de D. E. A. Universidad Paul Sabatier.
  • Escudero-Ávila, D., Carrillo, J., Flores-Medrano, E., Climent, N., Contreras, L. C., & Montes, M. (2015). El conocimiento especializado del profesor de matemáticas detectado en la resolución del problema de las cuerdas. Revista de Investigación en Didáctica de la Matemática, 10(1), 53-77. https://doi.org/10.30827/pna.v13i1.7944
  • Godino, J. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. Unión, Revista Iberoamericana de Educación Matemática, 20, 13-31. https://doi.org/10.1590/1980-4415v31n57a05
  • Huchecorne, B. (1988). Les contre-exemples en mathématiques. Paris, France: Ellipses.
  • Pichon, J. (1986). Calcul des limites. Paris, France: Ellipses.
  • Polya, G. (1958). Les mathématiques et le raisonnement plausible. Paris, France: Gauthier Villars.
  • Robert, A. (1982). L’acquisition de la notion de convergence de suites numériques dans l’enseignement supérieur (State Thesis). Universidad Paris III.
  • Shulman, L. (1986). Those who understand. Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189x015002004
  • Shulman, L. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1-21. https://doi.org/10.17763/haer.57.1.j463w79r56455411

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