Abstract

FONSECA CASTRO, Jennifer Liseth1  and  ALFARO CARVAJAL 2, Cristian Roberto. Differential and Integral Calculus in a Variable in the Training of Teachers of Mathematics in Costa Rica. Educación [online]. 2018, vol.42, n.2, pp.289-305. ISSN 2215-2644.  http://dx.doi.org/10.15517/revedu.v42i2.25844.

The differential and integral calculus is present in most of the curricula of various university careers of the exact and natural sciences in Costa Rica. Reflections and discussions about the what, how, and what to teach of calculus have stimulated the study of it from different perspectives. In Costa Rica, academics and researchers from the state universities responsible of the formation of future teachers have been given the task to review and revise their mathematics courses, particularly those related to differential and integral calculus in one variable. In this sense, this article summarizes the perspectives of administrative authorities of the School of Mathematics at the aforementioned universities, mathematics professors from such institutions with experience in teaching calculus in one variable and advanced students of the Mathematics Teaching major at Universidad Nacional de Costa Rica (UNA) about the purposes, the approach, the methodology, and the most difficult issues in the process of teaching and learning differential and integral calculus in one variable in the training of mathematics teachers. Data was obtained from interviews and questionnaires applied as well as workshops for administrative authorities and mathematics professors from the School of Mathematics at public universities and advanced students pursuing the Mathematics Teaching major at UNA. Regarding the main results, the subjects with greater difficulty in the teaching-learning of differential and integral calculus were detected. Those in which there were greater conceptual requirements and mathematical reasoning; for example, optimization problems and related reasons for change as well as the proof of theorems. In regards to the use of problem solving, teachers consider it important in the construction of mathematical concepts; however, they focus on practicing it regularly at the end of a topic. It is expected that this research will provide a foundation for the curricular reforms in the formation of future mathematics teachers.

Keywords : differential and integral calculus in one variable; mathematics; problem solving; teacher training.

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