Um percurso de estudo e pesquisa para o ensino de integral dupla: significados e praxeologias mobilizados por estudantes de engenharias e de licenciatura em matemática

Abstract

This thesis aimed to analyze the meanings and praxeologies mobilized by engineering and mathematics undergraduate students in the development of a Study and Research Pathway for teaching and learning the Double Integral. Two hypotheses were outlined: that the dimension of language involved in the teaching and learning processes of Double Integrals for calculating the measure of a Quadric Surface, when applied in a Path of Studies and Research, provides abductive reasoning capable of developing the autonomy of students in the construction of concepts inherent to the mathematical object and, the second, that there are differences in the meanings, interpretations and praxeologies mobilized by students of Engineering and Licentiate Degree in Mathematics in the development of a PEP. It was theoretically based on the assumptions of Charles Sanders Peirce's Semiotics and on the Anthropological Theory of Didactics. The research, with a qualitative approach, developed following the procedures of a Study and Research Course for the teaching of Double Integral in the calculation of the measure of the Quadric Surfaces, was characterized by five face-toface meetings, audio-recorded and filmed, which took place on Saturdays. , with the participation of twelve students enrolled in the Licentiate Degree in Mathematics courses at the State University of Southwest Bahia and Engineering (civil, electrical and environmental) courses at the Bahia Institute of Education, Science and Technology and who had attended the Differential Calculus and Full The results obtained showed that the students were able to apply the concepts of the chosen mathematical objects in a coherent and autonomous way when constructing and solving problem-situations involving knowledge of the courses from which they are alumni and of Differential and Integral Calculus. The shapes present in Gaudí's works enabled students to associate mathematical objects with an aesthetic language, pragmatism and the development of abductive reasoning that allowed them to align their use in different situations. The meanings, interpretations and praxeologies differed in terms of the use of mathematical knowledge in the two grades and in the interpretations of the proposed tasks, but they converged in the applied mathematical praxeologies