Programa de Pós-Graduação em Educação em Ciências e Matemáticas - PPGECM/IEMCI
URI Permanente desta comunidadehttps://repositorio.ufpa.br/handle/2011/2290
O Programa de Pós-Graduação em Educação em Ciências e Matemáticas (PPGECM) faz parte das atividades do Instituto de Educação Matemática e Científica (IEMCI), antigo Núcleo de Pesquisa e Desenvolvimento da Educação Matemática e Científica (NPADC) da Universidade Federal do Pará (UFPA). O PPGECM visa oferecer aos graduados e formadores de professores das áreas de Ciências (Física, Química e Biologia), Matemática, Educação Ambiental e áreas afins, oportunidade de estudos e pesquisas sobre os fundamentos atuais do ensino e pesquisa na área de Ensino de Ciências e Matemáticas (Área 46 da CAPES).
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Item Acesso aberto (Open Access) Comunicação matemática: concepções e práticas letivas de futuras professoras dos anos iniciais(Universidade Federal do Pará, 2019-02-28) ARAÚJO, Angélica Francisca de; BORRALHO, António Manuel Águas; http://lattes.cnpq.br/3404547486428285; https://orcid.org/ 0000-0001-6278-2958This is the report of a research with a qualitative approach of interpretative character, developed through a design of collective instrumental case study, with the collaboration of a group of Integrated Degree in Education in Mathematical Sciences and Languages of the Institute of Mathematical Education and The study, a formative experience on the theme "mathematical communication" that developed through the thematic axis "language and knowledge" (compulsory curricular component), started from the assumption that the conceptions about mathematical communication of future teachers of the initial years are formed during all their school experience (elementary, middle and undergraduate) and manifest themselves in their classroom practices during the initial training, while in internship activities. The research took place in two interconnected moments: the first one in the university classroom, in which the researcher also assumed the role of teacher of the class, and the second through the observation, by the researcher, of the teaching practices of three participants, during the classes that they taught in the compulsory internship. The objectives of the research are described as follows:a) general objective: understand the concepts and practices of mathematical communication of future teachers in the early years and their relationse b) specific objectives: (i) to identify and understand the conceptions about mathematical communication of future teachers in the initial years; (ii) analyze and discuss how the conceptions about mathematical communication of future teachers of the early years are manifested in the learner practices during the initial formation; and (iii) relate learner conceptions and practices about mathematical communication during initial training and internship activities. Mathematical communication was treated as an aspect of the teaching practices of future teachers, trying to analyze if their conceptions are related to their classroom practices. Data emerged from reflective journals, questionnaires, interviews and observations, instruments used to collect data in the two moments in which the research developed. The analysis of the data was done through a triangulation based on a table organized in objects of analysis and instruments of data collection. The study evidenced that the conceptions about mathematical communication identified refer to effective and favorable communication to social interactions in mathematics classes, but the relation between these conceptions and learner practices during initial formation and in stage activities is not linear, in communication practices, from the point of view of the interactions and the arguments of their students, the communication is less effective than the one expressed in their conceptions.Item Acesso aberto (Open Access) Concepções de matemática e se seu ensino: experiências e reflexões de professores formadores de professores em um curso de licenciatura de proposta integrada e interdisciplinar(Universidade Federal do Pará, 2018-05-02) MATOS, Mônica Gonçalves; GONÇALVES, Tadeu Oliver; http://lattes.cnpq.br/6789250569319668; https://orcid.org/ 0000-0002-2704-5853In this research, we aim to understand the relations of direction and meaning between conceptions of Mathematics and teaching of Mathematics manifested by teachers that train others teachers, involved in an interdisciplinary proposal to train future teachers for the initial years of Elementary Education and Youth and Adult Education, as they reflect on their training, research and teaching practices. We built the question that orientates the investigation: In what terms, teacher-training teachers, involved in an integrated and interdisciplinary training proposal, express conceptions about Mathematics and its teaching, when reporting on their training experiences and when performing their teaching practices? The trajectory we followed was oriented from the qualitative research, whose option was by a collective study of cases in a theoretical multirefencial approach. We selected 05 (five) teacher-training teachers who teach in a degree course offered by the Institute of Mathematical and Scientific Education, belonging to the Federal University of Pará, whose beginning of the teaching activities occurred in 2010, characterizing itself as a new and unique course in Brazil, of an interdisciplinary proposal and integrated in the training of teachers for the initial educational years and Youth and Adult Education, denominated Integrated Degree in Education in Sciences, Mathematics and Languages. The instruments used to collect the information were: interviews, video recordings of classes and theses and / or dissertations written by the participants of this research. For an analysis of the information, we used Textual Discursive and chose to execute a mixed categorization. Practices and the reports of the teacher-training teachers configure as important elements to understand their conceptions of Mathematics and its teaching, as well as these conceptions are related with new pedagogical modes of action. The manifested conceptions are relative to Mathematics as a knowledge of human construction and, therefore, changeable and fallible. As for teaching, they show that for teaching, knowledge of Mathematics content is indispensable, and articulation with others areas of knowledge can be possible through dialogue, partnership and collaboration. Teachers give indications on which they move in the direction of changes of conceptions and practices, demonstrating that they are in the process of constructing the understanding of the proposal of the Integrated Licentiate course, in terms of the development of interdisciplinary practices and the restlessness that moves them to beyond the boundaries of its field of knowledge. Thus, indicating that they are in the process of overcoming the paradigms from which they were formed.Item Acesso aberto (Open Access) Ensino e aprendizagem de matemática na síndrome de Williams-Beuren: uma abordagem a partir de pesquisas em neurociência cognitiva(Universidade Federal do Pará, 2020-02-28) SILVA, Fabio Colins da; GONÇALVES, Tadeu Oliver; http://lattes.cnpq.br/6789250569319668; https://orcid.org/ 0000-0002-2704-5853Research on Cognitive Neuroscience points to evidence that may contribute to didactpedagogical practices related to the teaching of mathematics for students with dyscalculia (KAUFMANN; VON ASTER, 2012; LENT, 2018; HAASE, DORNELES, 2018). It is in this context that this research aims to investigate the effect of Computerized Mathematical Training on the development of Numerical Cognition (numerical sense, numerical processing and calculus) in an adult student with Williams-Beuren Syndrome. This syndrome causes specific disorder of mathematical learning and compromises skills related to the domains of Numerical Cognition, according to the triple code model proposed by Dehaene (1995; 1999; 2001). This was a qualitative approach research of the case study type. The participant was evaluated in the three domains of Numerical Cognition at two different times (pretest and posttest) using a dyscalculia screening protocol, PROMAT. To improve performance in mathematical skills, the Dybuster Calcularis digital intervention was used, a systematic and consecutive training performed for a period of 12 weeks. The reports generated by the intervention pointed to significant benefits in several skills, such as the estimation of symbolic and non-symbolic magnitude; the sudden estimate of numerosity; the estimation of adding sets of points without counting them; the development of increasing and decreasing oral counting; production and numerical understanding; the number line; the positional value and addition and subtraction calculation with up to two digits. However, the results were not expressive in skills related to knowledge of multiplication and division calculation procedures with up to two digits and the evocation of arithmetic facts. Finally, the research allowed us to reflect on the importance of organizing an Individualized Educational Care Designer based on evidence from studies in Cognitive Neuroscience.Item Acesso aberto (Open Access) EPAEM: duas décadas de história e produções científicas(Universidade Federal do Pará, 2020-03-16) SALES, Flávia Helena Vasconcelos dos Passos; ROCHA, Maria Lúcia Pessoa Chaves; http://lattes.cnpq.br/4291670232604529; https://orcid.org/ 0000-0002-8022-2601This dissertation is a historical narrative of the EPAEM1 editions. Researching the theme was the way found to awaken the sleeping memories of the events and, thus, expose them, since it was not known where the documents of the regional meetings were kept. From the problematic raised, the following question was raised: how to write the history of SBEM-PA and the scientific productions of EPAEM? In order to answer the question, it was established as a general objective to investigate the creation process of the EPAEM and the production of the twelve meetings, carried out in the period from 1999 to 2019. The theoretical-methodological basis that guided the construction of the research and composed the study is based a qualitative research, which allowed greater familiarity, since the subject is still little known and explored. We sought to conduct an exploratory survey process, which allowed the visualization of the procedures adopted, with a view to improving ideas, discovering intuitions and formulating hypotheses. Thus, it was observed, during the survey of the documents and reports of the organizers, that the number of works presented more than doubled, considering the 3rd to 12th edition of the event, as well as the thematic axis that stood out most was the of teaching-learning of Mathematics. This allowed us to conclude that, if the meeting is related to Mathematics Education, the greatest strength was conferences, lectures, short courses, scientific communications and posters, which dealt with the profile of Mathematical Education.Item Acesso aberto (Open Access) Um estudo do liber quadratorum (1225) de Leonardo Fibonacci (1180 – 1250) e suas potencialidades para o ensino de matemática(Universidade Federal do Pará, 2018-03-15) GUIMARÃES FILHO, José dos Santos; QUARESMA, João Cláudio Brandemberg; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550In this research report we show the Italian mathematician Leonardo de Pisa, better known as Fibonacci, who we refer to as Leonardo Fibonacci, who contributed significantly to the mathematical community of his time, attracting attention from important people of this period such as King Frederick II, and to his invitation Leonardo Fibonacci participates of a mathematical tournament, which, as a follow up the construction of his fourth work (that we have known) the Liber Quadratorum. In this way the following question occurs to us: what are the didactic / pedagogical potentialities that can be evidenced from these propositions and their demonstrations that can be used in the classroom to effect the teaching / learning of mathematical contents? In order to answer this question, we aim in this research report to analyze the problems contained in Leonardo Fibonacci 's Liber Quadratorum, in which we aim at a better understanding of the concepts, providing a material in Portuguese and searching for possible didactic / pedagogical potentials. To do so, we searched for materials that subsidized the study and a basic text for the construction of the material in Portuguese referring to twelve propositions contained in the Liber Quadratorum, which deal with the sequence of consecutive odd numbers and square numbers. The book of squares of LE Sigler of 1987, as our main reference and BR McClenon in his work titled Leonardo of Pisa his Liber Quadratorum of 1919 as our secondary reference. We took a tour of the period experienced by this important character, who was a teacher and wrote about mathematics, so we highlight its influence for the development and dissemination of algorithmic methods of Arab mathematics in Europe in the early thirteenth century, from a proposed model diagram by Chaquiam (2015, 2016), thus, a basis was built so that we could point out the didactic / pedagogical potentialities of this book by Leonardo Fibonacci, especially considering the reinforcing arguments of Miguel (1997) and Miguel and Miorim (2004). After the analysis, it was possible to respond to our questioning and we could point out potentialities such as: construction of several ways to find the Pythagorean triples, potentiation activities, mainly squares, activities with square root, among others described in this report. In this way, to maintain the Liber Quadratorum for explicitly pedagogical purposes, by vectorizing the teaching, can greatly assist the mathematical educator who wants to trace paths that meet the needs of the student.Item Acesso aberto (Open Access) Experiência estética com formas geométricas nos anos iniciais(Universidade Federal do Pará, 2019-10-16) CAVALCANTE, Larissa Gabrielle Mendes; SILVA, Carlos Aldemir Farias da; http://lattes.cnpq.br/7226908910873590; https://orcid.org/0000-0001-5463-1316The present study reflects on the integration of knowledge between the Visual Arts and Geometry, in an inter-transdisciplinary attitude, based on the concept of aesthetic experience according to John Dewey. The main object is to investigate how the teaching-learning process of geometric shapes can, when lived as an aesthetic experience, help to consolidate the geometric thought of primary school children. In order to achieve that, we planned and implemented “Aesthetic Experience with Geometric Shapes”, an atelier in which fifty-two students of the third year of primary school took part, in a public school in Belém, Pará. We chose to approach Geometry contents with the students through the works of three modern artists, namely, Pablo Picasso, Paul Klee and Almada Negreiros, with activities that stimulated the development of visual perception, spatial relations and the ability to abstract geometric shapes from the elements of daily life and nature. These activities resulted in the production of drawings, paintings and collages which have been gathered in a visuality notebook, which can be found in the second part of this study. The students’ production highlights that they absorbed the proposed contents, so as to recognize geometric shapes as part of their daily experience, finding creative and flexible ways of systematizing geometric knowledge. Thus, the atelier’s results allow us to consider the integration with the Visual Arts as a possible pathway to turn the teaching of geometric shapes in primary school into a teaching-learning process that is attuned to the potentialities of the child. The data obtained from this pedagogical action were recorded in photographs, audio recordings and a teacher logbook. The proposal of living an aesthetic experience in the teaching of geometric shapes constituted a starting point for a reflection about the necessity of integrating knowledge amid the state of fragmentation in which school education finds itself.Item Acesso aberto (Open Access) A geometria na província do Grão-Pará: a inserção nos currículos e em outros discursos(Universidade Federal do Pará, 2019-04-22) SANTOS, Everaldo Roberto Monteiro dos; ALVES, José Jerônimo de Alencar; http://lattes.cnpq.br/9586790409626243The objective of this work is to provide an analytical description of the aspects that favored the modification of Mathematics teaching in the Grao-Pará Province during the 19th century. This research was initiated from a preliminary survey in documents that dealt with the History of teaching in the Amazon in this period, in order to reach the purpose of the work, started with the following questions: What is the social context in the Province of Grão-Pará, favored the emergence of these knowledge? What are the discourses about mathematics teaching at the time? What is the relation of Mathematics teachers to the structures of political power? Seeking to answer such questions, he focused mainly on primary sources such as: laws, decrees and government reports concerning the public education of the Province, regulations of the institution Liceu Paraense, books and newspapers of the time and also in secondary sources that dealt with this subject or correlates. The documentary analysis extended from 1838, year of the resumption of the activities of the Provincial Assembly, an organ that legislated on the education of the Province until 1851, the year of a reform that modified the teaching of Geometry in the Liceu Paraense. Some conclusions were reached, such as the following ones: in 1838 favorable discourses emerged for the insertion of Geometric knowledge in the Province. The purpose of these discourses had been realized in 1840, with the creation of the Geometry School that functioned in the Episcopal Seminary in the years 1840 and 1841 and whose main purpose was to train skilled workers to play the infrastructure works of the city. With the reform of 1841, which included, among other things, the establishment of the Liceu Paraense, an institution that had the purpose of providing secondary education in the Province of Grão-Pará; the Geometry school became part of the Chair of this institution, and this knowledge became part of the Chair "Arithmetic, Algebra and Geometry" and that the presence of Geometry since the first curriculum of the Liceu Paraense, was part of a process modernization of education in the Empire Province. That the teachers who taught the discipline of Geometry, besides professors were influential citizens in the social and political life of the society of the Province, occupying positions as judge of Right and provincial Deputies.Item Acesso aberto (Open Access) Memória didática na perspectiva narrativa : a história de vida de um professor pesquisador da área de educação matemática(Universidade Federal do Pará, 2019-10-10) SOUSA, Gilvana Bezerra de; NUNES, José Messildo Viana; http://lattes.cnpq.br/5188612973174798; https://orcid.org/0000-0001-9492-4914Considering that in recent years the researches that analyze the history of the teaching life in diverse social spaces, mainly in the perspective of studies that improve the didactic comprehension, in any area of the school knowledge, the present work investigated theoretical reflections inserted in the didactic memory in the narrative perspective. In this aspect, it included the clipping of professional life, where I proposed to investigate the associated teaching practice seeking to answer the question that guides the investigation as follows: The didactic memory in the narrative perspective is configured as a tool for analysis of academic experiences lived by a research teacher? From this question, it focused on the objective of instituting didactic memory as an analytical tool of academic experiences in the narrative perspective. The trajectory that has been taken is qualitative in an approach, whose option was to use descriptive and explanatory purposes of life history. The instruments used to collect the information were: works, video recording of lectures, interviews and a memorial that involved intentional samples about a researcher professor of Mathematical Education of the Institute of Mathematical and Scientific Education of the Federal University of Pará. understanding of the didactic gestures established in professional acting. The analyzes were developed based on the teachings of an analytical model of didactic memory, which was nourished by an important element of the Anthropological Theory of Didactics and information from social areas such as sociology, anthropology and others, which conform the subject teacher milieu. of the research that presented interactions of particular memories in the constructions of didactic memory, which substantiated the thesis in the perceptions of new praxeologies that made it possible to answer the research question in the information spectrum of the teacher's life from the narratives explaining didactic memories inserted in experiential for the strengthening of professional gestures in teacher education.Item Acesso aberto (Open Access) Modelagem Matemática escolar: uma organização praxeológica complexa(Universidade Federal do Pará, 2019-02-28) SODRÉ, Gleison de Jesus Marinho; GUERRA, Renato Borges; http://lattes.cnpq.br/3199659904537033; https://orcid.org/0000-0002-9228-2337; http://lattes.cnpq.br/3199659904537033; https://orcid.org/0000-0002-9228-2337This work questions the mathematical modeling cycle like a technique of the task of mathematically modeling problems at concrete contexts from the notion of complex praxeological organization conceived in the light of the Didactic Anthropological Theory. The work proposes new modeling techniques that preserve the cyclical character and from empirical experimentation, it proposes the investigative cycle of mathematical modeling.Item Acesso aberto (Open Access) Potencialidades da tecnologia para avaliação em matemática(Universidade Federal do Pará, 2021-06-30) SILVA, Bárbara Chagas da; BORRALHO, António Manuel Águas; http://lattes.cnpq.br/3404547486428285; https://orcid.org/ 0000-0001-6278-2958This investigation aims to identify the possibilities of using technology to assess learning in mathematics in order to contribute to studies on the subject considering the role of the educator in the teaching, assessment and learning process. In addition, it was intended to specify which technological tools can be used to assess mathematics and describe the benefits and risks of such tools. The investigation was carried out through an intrinsic case study with a qualitative approach of an interpretative character, taking the classroom as a unit of analysis. The case investigated is centered on the evaluative practice of a mathematics teacher who teaches at a state public school in the city of Belém / PA, carrying out evaluations with formative characteristics and with the aid of technological resources. As a result, it was observed that the technologies contribute to formative assessment practices and assist the teacher in delivering personalized feedbacks, as well as optimizing the task correction process and identifying the students' pedagogical needs, providing more time for dedication in the development of strategies education.Item Acesso aberto (Open Access) A prática de ensino como uma trajetória de formação docente do professor de matemática(Universidade Federal do Pará, 2017-04-04) MESQUITA, Flávio Nazareno Araújo; GUERRA, Renato Borges; http://lattes.cnpq.br/3199659904537033; https://orcid.org/0000-0002-9228-2337This research tries to problematize the practice of teaching with an given object of internal didactic transcription of execution of this practice by the teacher. Thus, there is questioning if this process leads to the construction of a trajectory of teacher training on a given school mathematician. An affirmative answer is constructed from a course of studies and research on the theoretical support of the anthropological theory of education, considering the teaching of resolutions of equations of the second degree. The construction of this trajectory is the methodology of the research that is embodied in a course of study and personal investigation of the teacher who seeks in the confrontation of his training problem to build or access the necessary mathematical school infrastructure that answers his questions. This infrastructure is given by the understanding of a epistemological model of reference by the teacher that is translated into his personal epistemological model of reference for the study of the resolution of equations of the second degree embodied in task systems that articulate several objects of school mathematics.Item Acesso aberto (Open Access) Signwriting da linguagem matemática para o ensino de geometria plana(Universidade Federal do Pará, 2018-08-30) GONÇALVES FILHO, José Sinésio; SALES, Elielson Ribeiro de; http://lattes.cnpq.br/5467537517169068; https://orcid.org/0000-0001-6242-582XSignWriting, also known as writing signs, brings to our society a new technique of writing spacevisual languages. This system becomes important to the Deaf communities, whereas before the signs were passed from one deaf to another throughout history. In order to do so, the objective of the present work was to record SignWriting of the Geometry-terms signs from the survey of these signs in institutional sites, multimedia and books. It was a documentary research with a qualitative approach, presenting a comparative study of the scientific and intellectual productions Capovilla; Raphael (2001a, 2001b, 2001c), Brandão (2002), Calculibras website, youtube channels Instituto Phala and Zanúbia Brandão, which constituted the corpus of the signs-terms of Mathematics. It was detected that there is a variety of signs of the area of Mathematics, however, they are scattered in several documents, not having a specific one. The need for a signal of the area will enable teachers, students and interpreters to interact with the mathematical language in Pounds in the written mode. In this way we present a glossary model of Signal-terms of the Flat Geometry in SignWriting, from a list of Geometry signs-terms, which are accompanied by their respective concepts and examples where we chose to organize these signs-terms in alphabetical order.Item Acesso aberto (Open Access) O sistema de numeração decimal na formação de professores dos anos iniciais(Universidade Federal do Pará, 2020-11-30) FERREIRA, Raquel Soares do Rêgo; GUERRA, Renato Borges; http://lattes.cnpq.br/3199659904537033; https://orcid.org/0000-0002-9228-2337This work deals with the problem of initial teacher training related to decimal numerals, considering the difficulties in their teaching and learning. Observed by different researches and which point to strong indications of the cause being the naturalization of decimal numerals within society. This problem was faced from the validation of the thesis that the quantification processes of units of concrete quantities allow the denaturalization of decimal numerals, with the help of the theoretical and methodological resources of the didactic anthropological theory, we consider the hypothesis that factors external to the room of the classroom act by making it difficult to teach part of the objects of interest in this theoretical field. This problem was addressed through a course of studies and research with the main role of teachers in training that was developed with the help of a study and research advisor. This journey was carried out under the guidance of the researcher with the help of a praxeological reference model on the quantification process from a generating situation, both taken as hypotheses to be validated, and with that the thesis, of providing a study path and research that would take teachers in training to meet the denaturalization of decimal numerals. The results demonstrate that the teachers in formation saw and assumed the occurrence of changes in their relations with the decimal numerals and point favorably towards the validation of this path forwarded from the proposed generating situation and praxeological reference model. The results encourage the development of future research, among them, on what impact of the design of numerals forwarded here on the curriculum of the early years, since they go beyond the mathematical discipline and, perhaps more urgently, on the design and construction of praxeological organizations on the decimal numerals for teaching the early years of elementary, under the understanding developed here, for the purpose of experimental validation in the classroom.Item Acesso aberto (Open Access) Teorias cognitivas do Pensamento Matemático Avançado e o processo de construção do conhecimento: um estudo envolvendo os conceitos de limite e continuidade(Universidade Federal do Pará, 2018-12-18) MESSIAS, Maria Alice De Vasconcelos Feio; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550The aim of this thesis was to conjecture about which mental structures and mechanisms need to be built by an individual in order to lead one to comprehend the concepts of limit and continuity of a function. For that, the research was organized in two stages. In the first stage, based on the theory of concept image and concept definition (VINNER, 1991), a preliminary study was developed, by which it was possible to analyze the elements that composed the concept image of mathematics students about such concepts. In the second stage, it was presented a genetic decomposition to limit and continuity, having as reference these mathematical objects, their historical-conceptual development, teaching experiences in the field of Calculus, multiple representations of such concepts and, specially, some assumptions of the APOS theory (DUBINSKY et al., 1984; ARNOON et al., 2014). As principle results, it was observed that various comprehensions about limit and continuity were evoked in the first stage, which led to reflections about the parts of the genetic decomposition that was elaborated from different mathematical objects, such as function, limit‟s definition, relation, relation between lateral and bilateral limits, limit properties, limits involving infinity, continuity at a point and along an interval, among others.