Abstract
This research proposes a didactic strategy to enrich the assimilation processes of the change of variable theorem in solving the definite integral. The theoretical foundations that support it are based on the contributions of social constructivism, problem solving, and treatment of theorems. The practical validation of the strategy is carried out with students of the Higher Technical Level in Applied Mathematics at the Autonomous University of Guerrero.
Highlights
The origin of integration undoubtedly comes from several problems of geometric order posed by the Ancient Greeks, such as, for instance, calculation of areas, volumes, lengths, or centers of gravity
Based on the aforementioned information, we propose to focus this research on the study of the variable change theorem for the resolution of the definite integral and contribute to favor its assimilation within the teaching–learning process of Integral
We propose a set of theoretical–practical knowledge based on methods, strategies, principles, and procedures that the teacher must consider to guide the student during the teaching–learning process of mathematical content
Summary
The origin of integration undoubtedly comes from several problems of geometric order posed by the Ancient Greeks, such as, for instance, calculation of areas (or squares), volumes, lengths, or centers of gravity. Ponce and Rivera [4] established that it is common to see the study of the primitives of functions in books concerning calculus; most authors pay little attention to the domains over which the primitives are valid, which might lead to mistakes while evaluating definite integrals The authors highlight this situation by using the universal trigonometric substitution to calculate the area under a given curve. Sci. 2021, 11, 357 one through the definite integral, students use the change of variable to solve the definite integral without attending to the necessary conditions that allow this change to be made In this regard, they present insufficiencies to argue the geometric meaning of the change of variable, as well as they do not see the relationship between the Variable Change Theorem with the Fundamental Theorem of Calculus. The objective was to develop and apply a didactic strategy to promote the assimilation of the variable change theorem through problem-solving in students of the Higher Technical University level in Applied Mathematics of the Faculty of Mathematics of the Autonomous University of Guerrero, Mexico
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