Doutorado em Educação em Ciências e Matemática (PRPG)
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Item Quando os estudantes não são mais os mesmos: o processo de apropriação de conhecimentos geométricos nos anos iniciais e a teoria histórico-cultural(Universidade Federal de Goiás, 2022-05-12) Oliveira, Daniela Cristina de; Cedro, Wellington Lima; http://lattes.cnpq.br/1123884255260078; Cedro, Wellington Lima; Damazio, Ademir; Longarezi, Andrea Maturano; Sousa, Maria do Carmo de; Silva, Sandra Aparecida Fraga daAssuming the historical-dialectical materialist method as a conception of the world, a research method and as a praxis, this research was developed in a public school in Goiânia, with children from the early years, in an attempt not only to understand the educational reality, but to transform it to a new quality. This work is materialized in an investigation into the process of appropriation of geometric knowledge, in the early years of elementary school, based on Historical-Cultural Theory, Activity Theory and theoretical and methodological assumptions of Teaching Guiding Activity. To this end, a didactic-formative experiment was organized, composed of a set of Tasks, developed in the years 2018 and 2019, in the municipal education network of Goiânia, with children in the fourth year and, later, in the fifth year of Elementary School. The guiding question of the investigation was: What are the formative movements of transformation of students, from the early years, in the process of appropriation of the concept of form, in a teaching organization supported by the Historical-Cultural Theory? Associated with this, we aimed to investigate the formative movements of qualitative transformation in students in the process of appropriation of the concept of form, based on Historical-Cultural Theory, Activity Theory and the theoretical-methodological assumptions of Teaching Guiding Activity. Therefore, the analysis by units was the chosen path to apprehend the object of study in its movement, materializing in two units of analysis, namely: Formative movements revealing the development of collective activity; and The process of appropriation of the concept of form: the formative movements of qualitative transformations in the students. Relating the stages of development of geometric knowledge, the students showed greater ease in the appropriation process when the nexuses involved aspects of practical and sensorial geometry, however, in manifesting the attributions of meaning referring to formal geometry, the subjects explained difficulty in the abstraction process and generalization, operating with general representations of the object or verbalizing conceptual mistakes. Conclusively, this research allows us to defend the following thesis: in a proposal for the organization of geometry teaching for the early years, supported by Historical-Cultural Theory, the transformation of subjects takes place through their collective experiences in the process of conceptual appropriation.Item A formação coletiva de licenciandas em Matemática: contribuições da atividade orientadora de ensino(Universidade Federal de Goiás, 2022-12-16) Santos, Wérica Pricylla de Oliveira Valeriano; Cedro, Wellington Lima; http://lattes.cnpq.br/1123884255260078; Cedro, Wellington Lima; Côco, Dilza; Araujo, Elaine Sampaio; Panossian, Maria Lucia; Pozebon, SimoneThis doctoral research takes as theoretical reference the Historical-Cultural Theory, the Activity Theory and the theoretical-methodological assumptions of Teaching Guiding Activity. From this perspective, it is assumed that human development is mediated by social relations, that work is the main activity of man and that the teacher in the development of his work – the teaching activity – must organize teaching in an intentional way. Assuming that the object of research in education is the Pedagogical Activity, understood as a unit between teaching activity and learning activity, the object of this research is the collective movement of training for teaching. By intentionally organizing teaching, seeking to enable students to learn concepts, the teacher triggers processes of reflection, analysis and synthesis. This movement may bring new quality to the way the teacher organizes the Pedagogical Activity, putting him/her in a learning movement. Thus, the importance of carrying out the Pedagogical Activity in the collective is understood, because when carrying out the activity in the collective, there is a division of actions and initial operations among individuals, exchange of modes of action, mutual understanding, communication, action planning individuals and reflection. Here, collective work is understood as a set of coordinated actions that are carried out by a group of people who have common needs and goals and who work together to satisfy these needs. In this sense, the research question is: How do formative movements favor the understanding of Pedagogical Activity by Mathematics graduates taking the Teaching Guiding Activity as a principle and practice in a process of collective formation? The main objective is to analyze the training movements for teaching learning developed in the study group, seeking to understand them as a possibility for the process of collective training. Formative movements are understood as the processes that mobilize knowledge, actions and reflections, enabling the individual to add new qualities to teaching learning, and in this research the study, planning, production of tasks, the development of pedagogical actions, reflection and evaluation. The research participants were three Mathematics undergraduates from a federal educational institution in Goiás. For the investigation process, a formative experiment was organized that took place in the study group composed of the teacher/researcher and the undergraduates. In the study group, the participants carried out readings and theoretical discussions, prepared tasks and developed them in weekly meetings with high school students. Data collection took place through audio and video recordings, field diary, undergraduate students' reading diaries, memorial and photographic records. The analysis was organized with the aim of apprehending the movement of the investigated object and is presented in the following units: Guiding Dimension, Executing Dimension, Reflection and evaluation processes. It was observed that the study group taken as a learning space for teaching enabled the development of a collective training process, in which the undergraduates could understand the Pedagogical Activity from the principles and practices of the Teaching Guiding Activity.Item A apropriação dos aspectos constituintes da atividade pedagógica por professores de matemática em formação inicial(Universidade Federal de Goiás, 2018-10-08) Silva, Maria Marta da; Cedro, Wellington Lima; http://lattes.cnpq.br/1123884255260078; Cedro, Wellington Lima; Moura, Manoel Oriosvaldo de; Echeverría, Agustina Rosa; Souza, Neusa Maria Marques de; Serrão, Maria Isabel BatistaThe present research is inserted in a reality marked by the lack of pedagogical clarity on 'how to organize' the processes of initial formation of Mathematics teachers and the teaching of Mathematics at schools. The purpose of this study was to investigate the actions of Mathematics teachers in formation to understand the process of appropriation of the constituent aspects of their pedagogical activities. In order to achieve this goal, we started from the understanding that thinking about the problem of the organization of teaching learning in Mathematics implies understanding the aspects of the pedagogical activity of this teacher as an object of investigation. In connection with this objective and object of research, we organized ourselves to answer the following question: What teachers in formation`s actions give evidence of the development of the constituent aspects of the appropriation process of the Mathematics teacher`s pedagogical activity? In this sense, we sought to apprehend beyond the pseudoconcrete appearance and its singular and particular expressions, to identify the essential relations that constitute and define that peculiar social activity in which teachers and their students are engaged as agents of transformation of the surrounding reality. The empirical data for the analysis were obtained based on the development of a training experiment carried out with ten senior student teachers who were attending the Supervised Internship II course of their Mathematics Program in an IES (Higher Education Institution) in Goiás. The theoretical basis was the Cultural Historical Theory and the philosophical and methodological foundations that derive from Historical-Dialectical Materialism. The categories of movement, contradiction, qualitative change and totality, and the concept of consciousness were highlighted. From the data three units of analysis were build: 1st - The indications of appropriation of the lesson plan as an aspect of the pedagogical activity; 2nd - Contents: the understanding of its role; 3rd - Evaluation: integrating element of the pedagogical activity. In line with the units, episodes were build, consisting of scenes from which the flashes were taken. This analytical structure was able to develop the appreciation of the constitution of teaching learning through the Mathematics teaching of basic education. Therefore, the objective was to apprehend what the aspects that constitute the pedagogical activity of the Mathematics teacher would be. The results achieved stress three aspects: planning, content and evaluation, and they also highlighted the interface between them, being it understood as a system in which these elements mutually condition one another, making it a possible universal trait of pedagogical activity of the mathematics teacher in the totality of the capitalist society. The data also showed the formation of principles for the organization of the formative process of Mathematics teachers, connected to the teaching of Mathematics in basic education. They also highlighted that the relationship between the aspects of the pedagogical activity planning-content-assessment is not presented to the teacher in a pure way and can not be thought of in itself, but within the interdependences in reciprocal conditioning movement. In addition, data point that the relation of the aspects of pedagogical activity is manifested and accomplished in a unique way, the teacher has to organize it considering the classroom heterogeneity and recognizing the development as a singular-particular expression of universal laws inherent to the subject. Thus, the student teacher´s knowledge on the general laws and driving forces of the development of a universal-abstract character must articulate with the mathematical knowledge on the particular circumstances of the improvement of his/her students. Therefore, it reveals the particular-concrete expression of general laws, in a movement of ascension from the abstract to the concrete.Item Os motivos que sustentam escolhas dos futuros professores para organização do ensino de Matemática na formação inicial(Universidade Federal de Goiás, 2022-06-29) Silvestre, Bruno Silva; Cedro, Wellington Lima; http://lattes.cnpq.br/1123884255260078; Cedro, Wellington Lima; Araújo, Elaine Sampaio; Libâneo, osé Carlos; Moretti, Vanessa Dias; Moura, Manoel Oriosvaldo deThe research is part of the theme of initial training of mathematics teachers, considering the process of choices and decision-making in the organization of teaching. It is presented with the objective of understanding the motives (and meanings) related to the process of choices and decision-making about the methodological aspects inherent to the organization of mathematics teaching in the experiences provided in initial training. To achieve this goal, we started from the understanding that thinking about the problem of the organization of teaching implies understanding the meaning-generating motives that enable the choices that determine it. In this perspective, related to the objective, we tried to answer the question: in the context of the undergraduate course in mathematics, what are the motives (and meanings) that support the choices of future teachers for the organization of teaching? Highlighting the motives and meanings attributed by the subjects in initial formation, the research is based on the didactic and pedagogical aspects of the Cultural-Historical Theory. Within this context, relevant concepts are addressed, such as: Activity Theory, Pedagogical Activity, humanization process, organization of teaching from the perspective of Teaching Guiding Activity, constituent aspects of teaching, Study Activity in the initial training of mathematics teachers and processes of choices and decision making. The methodology is developed through a formative pedagogical intervention with subjects of the undergraduate course in mathematics of a private University Center in the city of Aparecida de Goiânia-Goiás. The participants of the research were two students of the undergraduate course in mathematics. The production of data occurred through the disciplines of Supervised Internship and Theoretical and Methodological Foundations of Mathematics Teaching, held in the year two thousand and nineteen and, also, during the orientation of the course conclusion work, materialized by means of an article and a memorial. The instruments that allowed the production of data were: audiovisual recordings and written records of several productions developed in the course of Foundations, portfolio of the Internships, recordings of the collective orientation of the final course work, memorial and interview. The data were analyzed from the perspective of the Vygotskian proposal, presented by means of units of analysis, episodes, scenes, and flashes. The results are shown in a triad of elements that support the process of choice and decision-making in the organization of mathematics teaching, highlighting: a) evidence in the theoretical and methodological orientations, as well as the awareness that subjects signal about processes that permeate the organization of teaching taking into account the specific and pedagogical knowledge; b) the experiences of subjects and c) needs, motives, interests and intentions when organizing the teaching, motives that are characterized in two: motives-stimuli and motives that generate meaning. The first is related to the propulsive motives, which direct the activity itself, and the second demonstrates the senses capable of overcoming individuality, stimulated by the universal vision of the teacher's work in developing his/her activity in a humanizing way for the transformation of future subjects.