A study on the pre-service elementary mathematics teachers’ knowledge on the convergence and divergence of series in the context of theory and application

espanolEl foco de esta investigacion es el examen del conocimiento teorico y practico sobre la convergencia y la divergencia de la serie. En linea con el enfoque de investigacion, los maestros pre-servicio de matematica sobre la convergencia y divergencia de la serie con la ayuda del problema de la vida real en el contexto de la teoria y la aplicacion utilizando el concepto de series armonicas. La investigacion se guio de un metodo cualitativo, estudio de caso. Los datos de la investigacion han consistido en dos preguntas escritas y un problema y cuatro preguntas de entrevista que fueron formadas por los investigadores y se aseguro su validez y confiabilidad. El estudio llego a la conclusion de que maestros de pre-servicio matematica tienen conocimientos teorico sobre la convergencia de series y series armonicas, su percepcion de las series, las series armonicas, los conceptos de convergencia y divergencia cambiaron en el proceso de solicitud y adoptaron diferentes enfoques en la resolucion de problemas. EnglishThe focus of this research is the examination of the theoretical and practical knowledge regarding the convergence and divergence of the series. In line with the research focus, it is aimed to reveal the approaches of pre-service elementary mathematics teachers on the convergence and divergence of the series with the help of the real-life problem in the context of theory and application by using the concept of harmonic series. The research carried out the qualitative research method is designed according to the case study. The data of the research have consisted of two written questions and one problem and four interview questions which were formed by the researchers and their validity and reliability were ensured. The study concluded that pre-service teachers have theoretical knowledge on the convergence of series and harmonic series. Also, their perception of series, harmonic series, convergence and divergence concepts changed in the application process and they performed different approaches in problem-solving