Browsing by Author "Breda, Adriana"

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Análise de relatos de prácticas de professores utilizando o modelo de competencias e conhecimentos didático matemáticos. (CCDM)
(Editora UNIVATES, 2020) Hummes, Viviane Beatriz
Análise de uma tarefa de medida de tendência central com a ferramenta adequação didática: um olhar desde a formação inicial de professores
(Universidad de Vale do Taquari, 2022) Calle Palomeque, Carmen Eulalia; Oyervide Pesantez, Mari Carmen; Alvarez Calle, Nelly Guadalupe; Breda, Adriana
O objetivo deste trabalho é apresentar a análise didática de uma tarefa sobre Medidas de Tendência Central, proposta por uma futura professora de matemática a alunos da educação básica do Equador. Para isso, aplicou-se à futura professora um questionário de nove perguntas que foram analisadas, qualitativamente, por meio da ferramenta Critérios de Adequação Didática. A análise didática contempla, de maneira geral, alguns dos componentes dos Critérios de Adequação Didática, em particular: os diferentes significados do objeto matemático; o uso de recursos materiais e tecnológicos; a interação entre o professor e o aluno; a adaptação ao currículo; a inovação didática; a análise dos erros e dificuldades dos alunos e; as motivações, interesses e necessidades dos alunos. Como conclusão, evidencia-se que a tarefa apresenta uma alta adequação cognitiva, epistêmica, interacional e de meios e, em menor medida, uma adequação afetiva e ecológica.
Conhecimento de futuros professores sobre os diferentes significados do objeto matemático media aritmética
(Federal University of Mato Grosso do Sul, 2020) Calle Palomeque, Carmen Eulalia
Conocimientos del futuro profesor de matemáticas sobre los diferentes significados de la media aritmética
(2022) Font Moll, Vicenc
This study characterizes the knowledge of future mathematics teachers at the University of Cuenca about the mathematical object of arithmetic mean. The exploratory-interpretive qualitative approach study indicates that, out of a total of twenty-two future participating teachers, twenty-one show little knowledge about the complexity of the object arithmetic mean (understood as a plurality of meanings), presenting difficulties to justify what kind of meaning of arithmetic mean they must use to solve a specific problem.
La complejidad de los objetos matemáticos en la formación inicial de docentes
(Universidad de los Lagos, 2022) Font, Vicenc
The objective is the development of competence in the analysis of didactic suitability, corresponding to the representative sample component of the complexity of the mathematical object, in training programs for mathematics teachers in Ecuador. It is a qualitative research that describes the competent use of said component and, on the other hand, it has a development component when developing didactic resources to achieve it. Tasks were designed and the productions of the participants were analyzed from a priori categories (the different meanings of the mathematical object involved) through a content analysis to infer the partial meaning used. The main result is that participants assume the importance of considering the multiple meaning of mathematical objects in the instructional process; nevertheless, they have difficulty designing tasks that involve the use of a variety of meanings.
La enseñanza de las matemáticas en un curso de formación en contexto de pandemia: la percepción de futuros profesores de matemáticas de Ecuador
(2021) Calle Palomeque, Carmen Eulalia; Mora Naranjo, Blanca Maribel; Jácome Guzmán, Marco Vinicio; Breda, Adriana
The World has gone through a forced transformation process brought about by the sanitary emergency that the Covid-19 pandemic caused. This situation trigged abrupt changes in all aspects of life, particularly, in education, where both teachers and students have not been equipped to face these conditions, as, suddenly, classrooms became improvised virtual learning environments. Under these circumstances, it has become significant to examine the perceptions that teacher-trainees at the Exact Sciences (Math and Physics) Pedagogy Major of Universidad de Cuenca have regarding the Math virtual classes that took place in their major during March and April, 2020. To attain this goal, a multiple-choice online questionnaire was administered. The findings suggest that, although the major’s instructors apply some of the modern Math teaching and learning tendencies, several of them simply develop their traditional classes though a computer screen, without a significant methodological or strategical shift; this situation reveals a lack of training regarding the instrumental use of technological tools that support this new learning modality. Moreover, one can conclude that these virtual practices ought to be improved by means of new methodologies that prompt greater interaction among teachers and students.
Partial meanings of the Pythagorean theorem used by teachers in the creation of tasks within the framework of a continuing education program
(2023) Calle Palomeque, Carmen Eulalia
[Objective] This article presents the results of research on the teaching and learning of the criterion “implement a representative sample of the complexity of the mathematical object to be taught,” which was carried out with high school mathematics teachers from Ecuador in a master’s degree program in continuing education. [Methodology] After a discussion of the instructional process which was used when teaching this criterion, a qualitative analysis of the responses to one of the tasks proposed for the students in this master’s degree program is presented: creating tasks for whose resolution the students had to apply a certain partial meaning of the Pythagorean theorem (geometric or arithmetic-algebraic), as a demonstration of the learning that they had achieved. [Results] The results show that some students in the master’s degree program proposed tasks to work on the Pythagorean theorem, but did not specify or justify whether the tasks they designed were related to arithmetic-algebraic meaning, to geometric meaning or to both; other students did not propose any task to work on arithmetic-algebraic meaning; and one participant in the master’s program did not propose any task to work on geometric meaning. It was also observed that some students created tasks that did not correspond to either of these meanings. [Conclusions] It was concluded that teachers have difficulties in creating a task and indicating the type of meaning of the Pythagorean theorem that should be used to solve it, and that geometric meaning was most related to the tasks that they proposed.
Qué significado atribuyen a la media aritmética profesores de matemática en ejercicio?
(2020) Calle Palomeque, Carmen Eulalia; Breda, Adriana; Font Moll, Vicenc
The objective of this work is to study if professors in practice can identify the partial meaning of the arithmetic average mathematical object that allows solving a certain problem. For this, the answers of 95 teachers were analyzed to a task that consisted in relating the different meanings of this mathematical object with a list of proposed problems. It is concluded that the majority of teachers fail to correctly relate the meaning of the mean with the statement of the corresponding problem and, those who manage to relate, justify this relationship incorrectly.
Reflection on the complexity of mathematical objects in the initial training of teachers
(2021) Font, Vicenc
This work aims to know the perception of future mathematics teachers about the complexity of mathematical objects and their possible application in teaching practice, in order to improve the teaching and learning of mathematics in Basic General Education (GBS) and the Unified General Baccalaureate (BGU). For this, 19 future professors were asked about the different meanings of some mathematical objects, and they were proposed to raise contextualized problems in which a certain meaning had to be applied in their resolution. The results show that encouraging reflection on the complexity of mathematical objects in the initial training of teachers and their relationship with the design of contextualized problems affects their way of understanding mathematical competence.
Reflexión sobre la complejidad de los objetos matemáticos en formación inicial de profesores
(ASEFIE, 2019) Calle Palomeque, Carmen Eulalia
This work aims to know the perception of future mathematics teachers about the complexity of mathematical objects and their possible application in teaching practice, in order to improve the teaching and learning of mathematics in Basic General Education (GBS) and the Unified General Baccalaureate (BGU). For this, 19 future professors were asked about the different meanings of some mathematical objects, and they were proposed to raise contextualized problems in which a certain meaning had to be applied in their resolution. The results show that encouraging reflection on the complexity of mathematical objects in the initial training of teachers and their relationship with the design of contextualized problems affects their way of understanding mathematical competence
Significados de las medidas de tendencia central contemplados por profesores de matemática en sus trabajos de fin de máster
(Universidad del Atlántico, 2020) Calle Palomeque, Carmen Eulalia
This work aims to identify which meanings of the measure of central tendency are contemplated by practicing mathematics teachers. For this, three master thesis projects have been analyzed, with the study of said mathematical object as a central didactic proposal. It is concluded that teachers take into account the idea of working different meanings, but have difficulties designing tasks with application problems that respond to this plurality of meanings
Teaching and learning of mathematics and criteria for its improvement from the perspective of future teachers: a view from the ontosemiotic approach
(2021) Breda, Adriana; Seckel, María José; Farsani, Danyal; Fernandes da Silva, José; Calle Palomeque, Carmen Eulalia
The objective of this article is to identify the meaning attributed to the didactics of mathematics and what are the criteria with which an improvement in the teaching and learning process of mathematics is based, future teachers of mathematics, belonging to universities in three different countries (Brazil, Chile, and Ecuador). The qualitative analysis indicates that the majority of future teachers consider that the didactics of mathematics is a technical discipline that consists of providing strategies, resources, and procedures for teaching mathematics; few consider it as an art to teaching and almost none consider it as a scientific discipline that is concerned with studying the processes of teaching and learning mathematics. In addition, the results show that the criteria used by them, on how teaching and learning in this discipline can be improved, are focus, above all, in the cognitive, ecological, and emotional aspects and, to a lesser extent, to the interactional, mediational and epistemic. Finally, it is concluded that the improvement in teaching and learning is directly related to an improvement in the training programs of future mathematics teachers.
The complexity of the notion to teach in the assessment of the pre-professional practice of future ecuadorian mathematics teachers
(2022) Font Moll, Vicenc
Reflections on the complexity of mathematical objects, and the connection of the components of this complexity, are frequent in many of the theoretical approaches used in the area of Mathematics Education. As a consequence of these reflections, there is a tendency for mathematics teachers training to contemplate didactic sequences so that teachers consider the complexity of the mathematical object to be taught in the didactic sequences that they design and implement with their students. In this line, the first objective of this work is to determine the role of mathematics taught in the assessment guide of work practice used by the guidance teachers of the Mathematics Education Career at the University of Cuenca; while the second objective is to describe an instruction process whose objective is to incorporate in this guide the assessment of the mathematics taught, in particular the assessment of the incorporation of the complexity of the mathematical object to be taught. The results show that the guide does not value the mathematics taught and that in the didactic sequences implemented by future teachers according to it, they do not consider the complexity of the object to be taught.