Obstáculos epistemológicos sobre los conceptos de límite y continuidad en cursos de cálculo diferencial en programas de ingeniería

Abstract

ResumenEl objetivo de este trabajo fue identificar los obstáculos epistemológicos sobre los conceptos de límite y continuidad que presentan los estudiantes de programas de la Facultad de Ingeniería al inicio del proceso de formación académica en una universidad pública. Se diseñó un instrumento que incorpora una serie de actividades que utilizan diversos registros de representación semiótica tendientes a determinar el nivel de apropiación que poseen los estudiantes alrededor de los conceptos de límite y continuidad. De los hallazgos se resalta que los estudiantes asumen como iguales los conceptos de límite y continuidad.Palabras claves: obstáculos epistemológicos, límite, continuidad. Epistemological obstacles on the concepts of limit and continuity in courses of differential calculus in engineering programsAbstractMany investigations have been carried out with the objective of identifying the difficulties that students have in the learning process of the different mathematical concepts. Some studies have highlighted that the process of teaching mathematical knowledge by teachers in secondary and secondary education in Colombia, has been limited to a minimalist expression of algebraic processes that in no way contribute to the understanding and appropriation of these concepts of origin abstract. Students who enter the various engineering programs in the university must immediately face a Differential Calculus course, which will demand from the student a whole series of competences around the numerical, variational and spatial thoughts. It is in this scenario where we seek to identify the epistemological obstacles presented by the students of the Faculty of Engineering programs at the beginning of the academic training process at the UFPS. An instrument was designed that incorporates a series of activities that use diverse registers of semiotic representation tending to determine the level of appropriation that the students have around the concepts of limit and continuity. From the findings it is highlighted that students assume the concepts of limit and continuity as equals.Keywords: epistemological obstacles, limit, continuity Obstáculos epistemológicos sobre os conceitos de limite e continuidade em cursos de cálculo diferencial em programas de engenhariaResumoMuitas investigações foram realizadas com o objetivo de identificar as dificuldades que os alunos têm no processo de aprendizagem dos diferentes conceitos matemáticos. Alguns estudos enfatizaram que o processo de ensino de conhecimento matemático por professores em educação secundária e secundária na Colômbia tem sido limitado a uma expressão minimalista de processos algébricos que de forma alguma contribuem para a compreensão e apropriação desses conceitos de origem resumo Os estudantes que entram nos vários programas de engenharia na universidade devem enfrentar imediatamente um curso de Cálculo Diferencial, que exigirá do aluno toda uma série de competências em torno dos pensamentos numéricos, variacionais e espaciais. É neste cenário que buscamos identificar os obstáculos epistemológicos apresentados pelos alunos dos programas de Faculdade de Engenharia no início do processo de treinamento acadêmico na UFPS. Foi desenhado um instrumento que incorpora uma série de atividades que utilizam diversos registros de representação semiótica que tendem a determinar o nível de apropriação que os alunos têm em torno dos conceitos de limite e continuidade. A partir dos achados, destaca-se que os alunos assumem os conceitos de limite e continuidade como iguais.Palavras-chave: obstáculos epistemológicos, limite, continuidade

Affective domain and mathematical processes in teaching practice. a review from mathematical education

“…They worked with a sample of 20 teachers from the math area of the Barranquilla District, 46 students from the sixth grade of the District Educational Institution for the development of Human Talent, from which the experimental group and the control group were chosen, with 23 students each, his age varies from 10 to 12 years. In their conclusions they established the importance of the development of mathematical competencies, when linked to communication and representation, as a starting point to understand, interpret and pose mathematical models that lead to solve problems, coinciding with the results mentioned in the research of Hernández-Suárez, Prada-Núñez and Ramírez-Leal (2017). On the other hand, research was found that sought to analyze the teaching work of teachers of the Bachelor of Mathematics at the Universidad Pedagógica y Tecnológica de Colombia (UPTC) as an initial step to improve classroom practices, as is the case of Leguizamón ( 2016), who worked with a sample of three teachers of the Bachelor of Mathematics under an Ontosemiotic Approach to Cognition and Mathematical Instruction.…”

Ability of engineering undergraduates to solve real function limit problems

“…Nevertheless, limits are never covered in any comprehensive, detailed way; instead, they are frequently introduced to move on to differentiation and then used when needed to introduce various other components of single or multivariable calculus, mostly using exercises but not problems. Along the same lines, [30] indicate that the activities carried out in the classroom influence how students understand and solve problems; added to this is the importance of registers of semiotic representation in the teaching of calculus, whose lack of various types of registers becomes an epistemological obstacle.…”

Concepciones epistemológicas de los docentes del área de matemáticas en educación básica

“…En cualquier área del conocimiento, las prácticas pedagógicas deben atender tres campos esenciales inherentes al proceso educativo. Al respecto, cabe destacar que se parte del conocimiento (dimensión epistemológica) que posee el docente en relación con el área de dominio (Hernández, Prada & Ramírez, 2017), de las prácticas que enfatizan los enfoques de aprendizaje (dimensión pedagógica) por medo de las cuales los docentes valoran la actuación del estudiante, y del desarrollo de estrategias (dimensión didáctica) para lograr la correspondencia entre los procesos de enseñanza y aprendizaje (Hernández, Prada & Gamboa, 2019).…”