Differential and Integral Calculus in a Variable in the Training of Teachers of Mathematics in Costa Rica - Fonseca Castro, Jennifer Liseth (2018)
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 mathematics teachers training 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, university-mathematics teachers of such institutions with experience in teaching calculus in one variable, and advanced students of the career of Mathematics Education of the Universidad Nacional (UNA) de Costa Rica, 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 teachers of mathematics. The data were obtained by applying interviews, questionnaires, and workshops to administrative authorities and teachers of mathematics of the School of Mathematics at public universities and advanced students of the career of Teaching Mathematics of the UNA. Regarding the main results, the subjects with greater difficulty in the teaching-learning of the differential and integral calculus were detected those in which there were greater conceptual requirements and mathematical reasoning, for example, the problems of optimization and related reasons for change; as well as the proof of theorems. With regard to the use of problem solving, teachers consider it important in the construction of mathematical concepts; however, they focus on practice routinely, at the end of a topic. It is expected that this research undelies for curricular reforms in teacher education of mathematics.