The infinitesimal concept in the learning of calculus
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Keywords
Mathematical thinking, Data analysis, Fractal geometry, Item response theory
Abstract
Introduction: The research follows a quantitative cross-sectional, explanatory and correlational approach framed in a multimethod approach. Objective: To apply a pedagogical strategy based on the study of fractal geometry to develop mathematical thinking and to achieve a better understanding and learning of differential and integral calculus. Materials and methods: explanatory, multivariate, correlational and quasi-experimental study. Sampling was performed probabilistically and randomly, starting with stratification by academic program and then selecting student clusters made up of those enrolled in calculus courses in each program. Results: the primary data for the research are obtained from the application of pre and posttests to the pedagogical intervention to assess the development of mathematical thinking and academic performance in calculus, results are compared and differences are evaluated to estimate the contribution that the study and understanding of the infinitesimal concept effectively contributes. Conclusion: it is found that there is a positive relationship between the understanding of the infinitesimal concept, the development of mathematical thinking and the academic performance of students in differential and integral calculus courses.
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Mawency Vergel Ortega, Francisco de Paula Santander University, Cucuta, Colombia
Postdoctoral Researcher in Social Sciences, Childhood and Youth, Teacher-Researcher. Francisco de Paula Santander University, Cúcuta – Colombia.
Henry de Jesús Gallardo Pérez, Francisco de Paula Santander University, Cucuta, Colombia
Doctor of Education, Research Professor. Francisco de Paula Santander University. Cucuta – Colombia.
Daniel Villamizar Jaimes, Francisco de Paula Santander University, Cucuta, Colombia
Master in Clinical Psychopedagogy, Research Professor. Francisco de Paula Santander University. Cucuta – Colombia.