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The 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. [ABSTRACT FROM AUTHOR]

This paper fits the area of Mathematics Education at Higher Education, especially the area of studies concerning the teaching and learning of Differential Calculus. We present, in this study, theoretical elements and teaching approaches concerning the concept of Calculus proposed by David Tall and others, gathered from the development of a panorama including papers written by these researchers. In an introductory way, we present elements about the constitution of this area of Mathematics Education, as well as questions which enhance it. With this paper, the authors hope to have contributed to the consolidation of the area of Mathematics Education at Higher Education in general, and to the GT -- No. 04, because not only do they broaden the diffusion of one theorist but also try to summarize the results of researches. [ABSTRACT FROM AUTHOR]

This Article presents results of a Survey of the Professional Master's Degree in the Teaching of the Sciences and Mathematics PUCMinas and studies of the Research Group in Informatics and Methodologies in teaching of Mathematics - GRUPIMEM. It was created an Object of Learning - OA, from Resolution of Problems of Physical Phenomena with Related Rates. The theoretical basis is made by the parameters of the Resolution of Problems and with the use of ICTs, working with problem the teaching and learning of Calculation. The OA was structured containing a set of activities that have been constituted by problems of thermodynamics, variation in the intensity of current in an electrical circuit, circular wave, and dilatation of a balloon, among others. In this Article are presented 4 (four) OA activities, performed by students of graduate courses in Mathematics and Engineering from PUCMinas who had already attended the discipline of Calculation with the contents of related fees. It was noted that the handling of the OA, brought the dynamics inherent in the studied phenomena, facilitating the conceptual understanding of the rate of change related, despite the students have already had this content, but without the domain of the concept. This observation was made by the testimonials of students on the observation of the application of OA. [ABSTRACT FROM AUTHOR]