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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1955: o saber matemático escolar na subjetivação de trabalhadores
(Universidade Federal do Pará, 2014-09-11) SGROTT-RODRIGUES, Ana Maria; MANCINO, Emanuela; https://orcid.org/ 0000-0002-6736-5931; CHAVES, Sílvia Nogueira; http://lattes.cnpq.br/9353964127402937; https://orcid.org/ 0000-0002-9771-4610
In this research context we conduct ourselves building a "history of today", about ways of subjectivity of workers from different labor areas, in the relationships they establish with the knowledge-power practices and with the truth games in the field of School Mathematics Education, space in which occupies a place of relevance in the socioeducational context, due to the dissemination and value assigned to it. We take on the challenge of talking about the variation of the subjectivity ways produced by statements and enunciations of the mathematical discourse, exploring the sayings of workers that enable to see: Which subjectivities are produced in the relations established by the individuals with school mathematics? How is the production of subjectivities from these relationships? We start from the narratives of workers to broader cultural narratives, searching the threads that weave and sustain the discursive network that enables to say and see the mathematical knowledge in the constitution of the subject. To analyze how the discourses reverberate in the ways of being, seeing and telling in relation to school mathematical knowledge, we will use the theoretical tools designed by Michel Foucault, considering from his teachings that workers are historical subjects, forged in history, as well as in the cultural context that runs through them, once subjectivity is not innate, but fabricated and imposed by the discourses that produce us historical and culturally. With this understanding and the intricacies of the provocation arising from Foucault, we brought to our thinking in relation to how the workers place themselves in the struggle between their labor mathematical knowledge and erudite knowledge of mathematical science, the mechanisms they use and the effects of this fight, or the acceptance of the erudite in what they do. We emphasize that the mesh of discursive and non-discursive practices produces mathematics as knowledge that qualifies a person, a people, a nation, producing at the same time the "good"student, the successful worker, and also the disabled, the unsuccessful worker. However, if there are subjections, there is also resistance, refusal, insurrections. From them are born other ways of being, other knowledges, other mathematics that make new truths appear, new skills that dispute and pluralize spaces of power in the broad discursive symphony. This encourages us to say that if life is a friend of art, it is possible with art to invent, incessantly, mathematical knowledge which mean the opening of this big prison closures that are the boundaries.
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1978: Licenciatura intercultural indígena da UEPA: saberes matemáticos e prática pedagógica
(Universidade Federal do Pará, 2017-05-02) LIMA, Aline da Silva; SOUZA FILHO, Erasmo Borges de; http://lattes.cnpq.br/5387951750537371; https://orcid.org/ 0000-0002-4092-7973
This work brings the study and analysis between the training of indigenous teachers and educational practice effective of these teachers in indigenous schools, considering the intersection of knowledge about traditional indigenous knowledge and emphasizes the need for dialogue between their traditional knowledge in math education practices, contributing to the improvement of indigenous teachers in the process of academic training. Being the research of qualitative nature approved in the case study, having as a starting point the following question: how was accomplished the pedagogical practice of indigenous teachers in training in Intercultural Indigenous Degree UEPA, considering the intersection of school knowledge and indigenous knowledge? In order to make a comparative study between the formation of indigenous teachers and their pedagogical practices in mathematics, considering the intersection of school and indigenous knowledge in school Parkatêjê and Kýikatêjê, of the indigenous land Mother Mary. For research were considered the views of the students and teachers/trainers of the intercultural indigenous university degree course. The interview was the basic procedure of research, whose analysis procedure sought to highlight paths to achieving more productive education to develop their scientific knowledge learned in the academic, confirming the idea that there is only one way to systematize the teaching, but relate to traditional indigenous wisdom with scientific wisdom. With reference to surveys, discussions and the monitoring of indigenous scholars in their trajectories in the institution of higher education, through the Intercultural Indigenous University degree course at Universidade do Estado do Pará-UEPA and supported by such authors as Candau (2006) defends the position that the differences are intrinsic, constitutive to educational practices, Knijinik (2012) addressing the thought etnomatemático interested in examining the practices outside school , Ferreira (2001) where the recent sociocultural determinations indicate a ressignification of education, Luciano (2006) discusses the indigenous question for various aspects of your social organization, D'ambrosio (2011) pedagogical practices related to Ethnomathematics enable to overcome the walls of the classroom and RCNEI/National Curricular Reference for Indigenous School (1998), which discusses the development of a proposal for intercultural education giving a new meaning to curricular content.
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1984: Organizações didáticas nos livros didáticos nos anos iniciais do ensino fundamental: o caso da noção de raciocínio combinatório
(Universidade Federal do Pará, 2016-12-20) MORAES, Guilherme Motta; NUNES, José Messildo Viana; http://lattes.cnpq.br/5188612973174798; https://orcid.org/0000-0001-9492-4914
The aim of the research was to analyze praxeological (PO) organizations around the mathematical object Notion of Combinatory Reasoning in two collections of textbooks from 1st to 5th year of EF, used in schools in the city of Belém / PA. This made it possible to highlight and characterize the didactic organization of mathematical knowledge, based on the didactic books approved by the National Textbook Plan, 2013 and 2016, as well as the National Curriculum Parameters, the Book Review Guidebook National Curriculum Reference Matrix for this year of schooling (1st to 5th year of EF). In this sense, to study this object, the Anthropological Theory of Didactics, proposed by Yves Chevallard is adopted as theoretical reference, and a methodological approach is made based on qualitative research, carried out through the bibliographic study. The results of this research highlight some important issues, such as: the focus of the two collections of textbooks based on the resolution of activities, in a purely classical approach. We observe a change in the technique to calculate the proposed activities, from a point organization to a local organization, and also that the tasks and techniques related to the calculations of possibilities and numbers of combinations have not changed. Over the years in both collections of textbooks. Thus, the praxeological organization around these two collections of didactic books analyzed according to Gascon are classic.
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Ações avaliativas em ambiente de ensino e aprendizagem gerado pela modelagem matemática
(Universidade Federal do Pará, 2015-06-25) SANTOS JÚNIOR, Augusto Fergusson dos; CHAVES, Maria Isaura de Albuquerque; http://lattes.cnpq.br/1914620696226334; ESPÍRITO SANTO, Adilson Oliveira do; http://lattes.cnpq.br/5870609258842071
This study aims to point evaluative actions evidenced in teaching and learning environment generated by mathematical modeling and consolidate them as argument for the use of modeling in educational contexts whether in Elementary School, Secondary School or University. To this end, we used a qualitative research of bibliographic nature consisting in the Experience Reports analysis of teachers who developed Modeling activities in the classroom and whose experiences were published in the VIII National Conference on Modelling in Mathematics Education – VIII CNMEM held in 2013. Since the documents considered dealing with experiences in Mathematical Modelling and not specifically the learning evaluation, we conducted a literature search of the meta-analysis type in order to extract and interpret evidence other than weren’t in the original research focus. For the conduct of the documental analysis, the methodology of the Discursive Textual Analysis was used, as Moraes and Galiazzi (2007), according to which it was possible to fragment and categorize relevant aspects regarding the phenomenon investigated. Data analysis according to the theoretical references of Mathematical Modelling and researchers in the field of learning evaluation pointed out that the teacher whose practices are systematized in teaching and learning environment generated by Mathematical Modelling shows interactive and retrospectives evaluative actions.Interactive evaluative actions indicate that during execution of the Mathematical Modelling activity, the teacher is willing to evaluate the student's knowledge construction, having the opportunity to verify the learning or intervene starting from the need revealed in the students demonstrations. Retrospective evaluative actions reveal that, after the completion of Mathematical Modeling activity, the teacher is willing to evaluate their own practice, in order to judge whether their objectives have been achieved and consider adjustments in their didatic choices to guide future practice. In that way, the Mathematical Modelling process provides teacher actions characterized by the link between teaching actions, evaluation and learning.
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Adaptação transcultural e validação do Metacognitive Knowledge in Mathematics Questionnaire (MKMQ) para o contexto brasileiro.
(Universidade Federal do Pará, 2023-09-11) BRAUN, Layane Caroline Silva Lima; GONÇALVES, Tadeu Oliver; SILVA, Marcos Guilherme Moura
Mathematical metacognition is a variable associated with high mathematical performance and is also an important predictor of self-regulation of learning. In the Brazilian context, to date there is no validated instrument that measures students' metacognitive knowledge of mathematical learning. The present study aims to cross-culturally adapt and validate the Metacognitive Knowledge In Mathematics Questionaire (MKMQ) for the Brazilian context. The guidelines for the instrument's cross-cultural adaptation process followed five Stages proposed by Beaton et al. (2000), as follows: Translation, Synthesis of Translations, Back Translation, Committee of Experts and Pre-test. The psychometric analyzes were evaluated using a sample of 434 participants of Elementary School II students. Validity Evidence occurred through Descriptive Analysis, Confirmatory Factor Analysis, Internal Consistency, Content Validity, Criterion Validity, Invariance Test and Evidence of Known Groups (gender, age, school year and school). The study population consisted predominantly of females, representing 56.68% of the total participants, aged between 11 and 18 years enrolled in the sixth (n = 109), seventh (n = 95), eighth (n = 163) and ninth (n = 67) school years of two different schools (School 1: 196 and School 2: 238), both public/state. The Metacognitive Knowledge In Mathematics Questionaire (MKMQ) by Efklides and Vlachopoulos (2012) was validated for the Brazilian version, in seven factors and 44 items, showing adequate psychometric properties in the cultural context of the Brazilian population. While Multivariate Analysis of Variance showed a significant difference in the mean scores of the MKMQ scale factors between males and females (F (7, 426) = 3530.409, p ≤ 0.001; Pillai Screening = 0.983; 2p = 0.98), also among schools (F (7, 426) = 3563.776, p ≤ 0.001; Pillai Screening = 0.983; 2p = 0.98). Research shows that there is a positive relationship between Metacognition, Mathematics and the educational environment. Being a great ally when used correctly by teachers, to know and measure the metacognitive skills of students.
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Alfabetização matemática no contexto ribeirinho: um olhar sobre as classes multisseriadas da realidade amazônica
(Universidade Federal do Pará, 2012-04-30) OLIVEIRA, José Sávio Bicho de; LUCENA, Isabel Cristina Rodrigues de; http://lattes.cnpq.br/3255121871351967
This dissertation, entitled "Mathematical literacy in the river context: a look at the multigrade classes of reality Amazon", aimed to investigate theoretical and methodological approaches to teaching and learning of mathematics within the mathematics literacy, able to be established in classes multigrade schools riverside reality Amazon. In this research, the vision of mathematics literacy was constructed taking into account not only the first skills of reading and writing early language school mathematics by the child (DANYLUK, 1997), but as a path to learning of man and woman in the world of relationships mathematics, from theoretical conceptions of D'Ambrosio (2002), Domite and Mosque (2003), Sebastiani Ferreira (1997), I. Mendes (2009) and Freire (2002). The survey was conducted in São Domingos do Capim, Para State, Brazil, between October 2010 and August 2011. In research on literacy in math classes multigrade schools riverside, interactions were held with representatives of the Municipal Education riverside multigrade school visits, interviews with teachers of this county. As instruments of construction data were utilized field diary, interviews and observations. The analysis of field research was organized in the following items: a) the multigrade classes in mathematics and literacy riverside b) Teaching tools and mathematical literacy, and c) Culture and mathematics education in Amazonia: between scientific knowledge and knowledge of tradition . It can be argued that the mathematical literacy expressed within coastal still restricted to the strictly mathematical experiences related to school curriculum without considering the wealth of possibilities knowledge of students' experiences in their daily context as spatial displacement in the rivers, in Mathematical elements involved in marketing fruit and fish, for example.
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Análise da fala-em-interação professor-alunos na Aula de Matemática: um enfoque na Psicologia Discursiva
(Universidade Federal do Pará, 2021-05-06) MACÊDO, Laécio Nobre de; SOUZA, Elizabeth Gomes
Investigating the phenomenon of talk-in-interaction is a practice that has been expanding in research in the social sciences, linguistics, communication, psychology and education. In this scenario, Discursive Psychology (DP) emerges as a theoreticalmethodological perspective in the conception of the discursive phenomenon capable of contributing to the development of research in Mathematics Education. Interpretative repertoires and the Discursive Action Model (DAM) are concepts proposed by DP theorists that can connect different particularities that are present in the speeches of the participants in a systematic way, emphasizing the activities carried out by such particularities in the subjects' social practices. This research arose from the need to investigate the speeches-in-interaction that occur in the mathematics classroom taught by teachers without qualification to teach this discipline at school. The study aims to analyze the talk-in-interaction between teacher-students related to the interpretative repertoires and linguistic processes of action, fact and interest and responsibility that occur in the mathematics classroom. This is a study with 30 students from the 6th grade of middle school in a public school in the city of Imperatriz - MA and a pre-service teacher in the Natural Sciences Degree course at the Federal University of Maranhão (UFMA). The production of data was carried out in three stages: audiovisual recordings of mathematics classes, transcription of dialogues, coding and analysis of the talk-ininteraction. The results indicated the occurrence of didactic, pedagogical and arithmetic interpretative repertoires in the speeches of the teacher and students. Throughout the mathematics class, the teacher used the following discursive resources: attribution of advantage, technique of questions, inoculation of interests and role-play. Such resources represent an advance for the field of DP and Mathematics Education because they help to understand how teaching and learning situations related to arithmetic concepts are developed through the analysis of talk-in-interaction in the classroom.
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Análise de um processo de estudo de semelhança
(Universidade Federal do Pará, 2007-05-11) SILVA, Reginaldo da; GUERRA, Renato Borges; http://lattes.cnpq.br/3199659904537033
This is about an investigation of a study procedure between similar images made by a research community, in a high school class from the public state branch in the outskirts of the city of Belém, seeking to answer if the activities developed by students in classroom characterize a mathematical activity in view of the didactic transposition theory by Yves Chevallard. This is accomplished through collaborative activities that try to identify the flow of mathematical knowledge evoked by students while building a concept of similarity. The research is of a qualitative nature with an ethnographic approach, adapted to education according to Lüdke and André. Analysis show that accomplished activities promote a mathematical action, therefore mathematical activity through the knowledge raised and the links established upon construction of comprehensive models of the concept of similarity by students. Difficulties are outlined as important elements identifying knowledge and their links, such as the research community collaboration eases the studying process.
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Análise praxeológica de conexões entre aritmética e álgebra no contexto do desenvolvimento profissional do professor de matemática
(Universidade Federal do Pará, 2012-11-16) PEREIRA, José Carlos de Souza; NUNES, José Messildo Viana; http://lattes.cnpq.br/5188612973174798
This study is an autobiographical narrative research that demonstrates the analysis of my praxeologies, in the context of my professional development, as a mathematics teacher. The focus of the analysis falls on the various praxeological conflicts I have faced in the classroom during the elaboration and application of an educational proposal for teaching polynomial operations to students in the 7th grade (1st year of junior high school). In this study my intention was to answer the following question: Which connections between arithmetic and algebra determined my praxeologies during the educational amplification I developed, to teach the addition, subtraction, multiplication and division of polynomials, in the 7th grade of fundamental education? In order to analyze my own praxeologies through the educational proposal I elaborated, I used the Anthropological Theory of the Didactic (ATD) of Yves Chevallard as the main theoretical reference. The analysis I made of my own praxeologies involved the system of decimal numeration, fundamental arithmetic operations, polynomial operations, types of tasks and techniques, the cognitive universe and praxeological equipment. The results show that my personal relations with types of ostensive and non ostensive object sand the types of tasks and techniques present or not in the educational proposal I elaborated, reveal which past and present praxeologies made up the different moments in my professional development as a mathematics teacher. In this sense, before graduation I lived the praxeologies of a lay teacher, during and after my specialization my cognitive universe went through praxeological conflicts, revealing that the institutional subjections shaped my praxeologies for teaching polynomial operations.
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O aprendizado de regras matemáticas: uma pesquisa de inspiração wittgensteiniana com crianças da 4ª série no estudo da divisão
(Universidade Federal do Pará, 2011-03-01) SILVA, Paulo Vilhena da; SILVEIRA, Marisa Rosâni Abreu da; http://lattes.cnpq.br/3588315106445865
In this study, we investigated the learning of mathematical rules in the context of the classroom, emphasizing, primarily, the discussions about language. Our main goal was to investigate the linguistic difficulties, faced by students during the learning of mathematical rules, in particular, the concept / division algorithm. To this end, we discuss, among other things, the theme "following rules" proposed by the Austrian philosopher Ludwig Wittgenstein in his Philosophical Investigations. Our work and our analysis were based primarily on this author, who discusses, among other themes, language and their meaning and foundations of mathematics, as well as the reflections of philosopher Gilles-Gaston Granger who analyzes the formal languages. We conducted a field survey that was developed at the “school of pedagogical application” of the Federal University of Pará, in a class of fourth grade. The lessons taught by the classroom teacher was observed and later the students were asked to solve division problems, verbal and nonverbal, followed by a brief interview in which we ask, among other issues, how students solve problems involving the division. In our analysis we highlight some students' difficulties, perceived in observations and in their written records or oral: some students, in its resolution strategies, invent new “mathematical rules". There are still those who "confuse" the contexts in solving verbal mathematical problems as well as the difficulty of understanding the problems that bring implicit information.
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Aprendizagem baseada em problemas e o raciocínio hipotético-dedutivo no ensino de ciências: análise do padrão de raciocínio de Lawson em um curso de férias em Castanhal (PA)
(Universidade Federal do Pará, 2013-09-10) NEVES, Moisés David das; MALHEIRO, João Manoel da Silva; http://lattes.cnpq.br/7502225344402729
Aiming to study and offer methodological tools that further the development of logical reasoning and the learner autonomy, this research assesses whether and how the participants in a summer school biology develop the pattern If / and / then / and or but / therfore described by Anton Lawson. The author postulates that this pattern of hypothetical-deductive reasoning is common in the way humankind acquires knowledge and scientific research. The pedagogical approach of the course where the research was conducted adopt the principles of Problem Based Learning (PBL) and aims to encourage participants to produce their own knowledge from problems investigated by experiments with scientific methodology. The audience of course were high school students and teachers of physics, chemistry, biology and mathematics. The seminars for socialization the activities and results achieved by them were videotaped. The analysis of these discourses revealed that Lawson`s pattern is developed, but not consciously and not clearly expressed in a few steps. The expected results for the tests is confused with the hypothesis, confirming a universal tendency pointed out by Lawson. In light of cognitivism of Piaget and Ausubel, is shown the importance of making predictions, because these can drive prior knowledge, creating opportunities for construction and/or discovery new knowledge. Some participant teachers showed discomfort in question what seems obvious. The students showed difficulty in formulating problem issues related to their daily lives. But, as they explored the animal collection, began to make puzzling observations and new questions, suggesting predominant thoughts of concrete cognitive functioning and pointing to the need for actions to stimulate hypothetical-deductive thought. With the evolution of the activities, it was noted advances in reasoning and argumentation of participants in general. It is conclude that adopt patterns like Lawson`s one is useful in the task of promoting thinking skills, as it provides a tool for observing and assessing how students are thinking, giving to the teacher an opportunity to plan pedagogical actions and interventions. It is also conclude that the experimental activity can be rich in stimulating situations of logical reasoning, since it is accompanied by moments of reflection. The results also speak in favor of the Problem-Based Learning as stimulatory of intrinsic motivation and higher cognitive skills. It is measured that to know how to seek the answer is more important than knowing the answer, which require curriculum changes in order that really teaching thinking skills is a priority in relation to the transfer of large amount of theoretical knowledge.
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Aprendizagem em modelagem matemática pelas interações dos elementos de um sistema de atividade na perspectiva da teoria da atividade de Engestrom
(Universidade Federal do Pará, 2015-10-23) BRAGA, Roberta Modesto; ESPÍRITO SANTO, Adilson Oliveira do; http://lattes.cnpq.br/5870609258842071
This thesis entitled "Learning Mathematical Modelling the interactions of the elements of an activity system from the perspective of the Engeström activity theory" aimed at understanding effects on learning by interactions evidenced in Mathematical Modeling environment, from the perspective of Engeström activity theory. To accomplish this, I developed in the Mathematical Modeling Experimental Laboratory (LEMM), at the University Campus of Castanhal (UFPA), modeling activities with groups of Math Course students in graduating, graduate or post graduate students to obtain data through observation and interview. Based on the principles of the Engeström activity theory, Mathematical Modeling developed by the students were understood as an activity system that involves the elements (subject, object and community artifacts mediators, rules and division of labor) that relate to a result, that are mediated by interactions for achieving a result. Research has shown that the collective work, the historicity and multivocality of subjects acting in overcoming contradictions to reach expansive transformations have repercussions on learning in Mathematical Modeling, configured as an activity system, the interactions of the elements of the system itself.
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Aprendizagem geométrica em torno das ideias presentes na simulação de um motor a dois tempos no GeoGebra: um estudo de caso
(Universidade Federal do Pará, 2020-02-20) SÁNCHEZ SÁNCHEZ, Ivonne Coromoto; QUARESMA, João Cláudio Brandemberg; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
This research focuses on the geometric learning manifested by a group of future teachers from the Integrated Degree in Science, Mathematics and Languages of the Institute of Mathematical and Scientific Education (IEMCI) and three mathematics teachers who participate in the activities of Simulators with GeoGebra (ESG). Specifically, in the construction of a circular sector in GeoGebra to represent the crankshaft part of a two-stroke engine. From the historicalcultural point of view of the Objectification Theory, this learning is analyzed with attention to the objectification processes of geometric knowledge manifested during a series of activities carried out in the moments of mathematization and mathematical work, using a multisemiotic analysis. The results highlight some aspects of the objectification processes evidenced in the performance of teachers and students in relation to the activities carried out to represent the circular sector in GeoGebra and the semiotic means used by individuals.
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Aprendizagens compartilhadas de formadores de professores: o caso da licenciatura integrada em educação em ciências, matemática e linguagens
(Universidade Federal do Pará, 2014-05-22) MACHADO JÚNIOR, Arthur Gonçalves; GONÇALVES, Tadeu Oliver; http://lattes.cnpq.br/6789250569319668; https://orcid.org/ 0000-0002-2704-5853
This work reports inquiry on practice of initial formation of teachers of the initial years of the Basic Teaching, developed by a community of teachers and formers of the Faculty of Mathematical Education and Scientific of the Institute of Mathematical and Scientific Education of the Federal University of the Pará. It is, therefore, an investigative journey of qualitative nature, in the modality of case studies, whose purpose is to identify, describe and understand how a community of trainers of teachers, in itself the seed stage, learn to develop professionally in their task of implementing a new course of teacher training Science, Mathematics and Languages for the initial years of elementary school, considering, in particular, the concept of community practice Lave and Wenger (1991), the perspective of social of learning Wenger (2001) and, professional development indicators presented by Imbérnon (2010). Defends the thesis that the mobilisation of knowledge and practices (re)constructed in interactions in the community produces professional knowledge of pedagogical practices and, in that process, participants will develop professionally in their tasks of training teachers for the early years of the elementary school. Over the twenty-six months we were in field, the practice of community, in focus, was accompanied through of registry audio and/or video and transcriptions of the narratives of the formers during the planning meetings, of study and evaluation of the training process, of interviews with trainers, through materials produced by the community and personal field notes, elaborated during the time we've been through "watching" the actions of the community. The captured material was treated and organized two axles, written in narrative episodes, which were mainly analyzed, not exclusively, from a rapprochement between the social theory of learning in communities of practice and the teachers learning communities and depth from the reflections on professional development. The narrative analysis of these materials reveal a practice produced in constant process of the negotiation of the concrete situations of work of the community.
Acesso aberto (Open Access)
Aprendizagens conceituais, procedimentais, atitudinais e o ensino por investigação em um clube de ciências
(Universidade Federal do Pará, 2024-02-29) RODRIGUES, Breno Dias; Malheiro, João Manoel da Silva; http://lattes.cnpq.br/7502225344402729; https://orcid.org/0000-0002-2495-7806
This investigation addressed the teaching and learning of conceptual content, procedural and attitudinal issues at the Prof. Science Club. Dr. Cristovam W. P. Diniz – which develops pedagogical practices with an Inquiry Teaching approach for Basic Education students – and we sought to analyze the learning expressions of the content in its three-dimensionality in the graphic records (writings and drawings) produced by club students during the Writing and Drawing stage in an Investigative Teaching Sequence entitled the “problem with the hydracor marker”. This didactic proposal addressed the Paper Chromatography experiment and the concepts of substances, mixtures and pigments, based on the problem “How to identify whether each marker has one or more colors in its ink?”. The process was conducted in two meetings with four stages. The participants were 25 club students from the 5º, 6º and 7º years of Elementary School, and 13 volunteer teacher-monitors, including the researcher. It was an applied and interventional research of an exploratory-explanatory nature, with a qualitative approach, characterized in two types: a) participant research – for planning and conducting an educational process at first; and b) documentary, since the 25 graphic records (corpus) treated by Content Analysis were analyzed, with the interpretation being based on the analytical model of Rodrigues and Malheiro (2023a). The analytical movement constitutes the categories that represent the procedural of students and learning: Manipulative descriptiveness and investigative fidelity in learning (a priori); conceptual, phenomenological and creative learning; and Subjective and socio-emotional aspects in investigative learning (both a posteriori). Some records were covered in full as representative, with 5, 3 and 2 corresponding to the categories. The results showed that the writings and drawings have particularities that are close to the characteristics of each dimension of the content, but that, in general, articulately contemplate all, whose tendency of the present aspects were the description of the experimental investigative stage, the manipulative and conceptual aspect, the indication of results and, in some cases, the expression of feelings and emotions in a collaborative process. As for the relationship between graphic records, the three-dimensionality of the content and teaching through investigation in the context of this science club, there is the (self)evaluative nature of these knowledge systematization instruments for procedural, creative, autonomous and evaluative learning for club members.
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Aproximações e distanciamentos entre as obras réflexions sur la métaphysique du calcul infinitésimal e théorie des fonctions analytiques a partir da análise de conteúdo
(Universidade Federal do Pará, 2022-03-31) LIRA, Alailson Silva de; QUARESMA, João Cláudio Brandemberg; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
In the 18th century period, several mathematicians contributed to the development of Infinitesimal Calculus (IC). Among the exponents of this context, Joseph-Louis Lagrange (1736 – 1813) and Lazare Nicolas Marguerite Carnot (1753 – 1823) stood out. Thus, as a research question, the present work raised the following problem: what points of closeness and distance do the works Réflexions sur la Métaphysique du Calcul Infinitésimal (RMCI), of 1813, by Lazare Carnot, and Théorie des Fonctions Analytiques (TFA), of 1813, by Lagrange, present, concerning the concepts of the Infinitesimal Calculus? To answer it, we used the methodological contributions of content analysis as well as the steps established in Bardin (2016), adapted for this research. Therefore, this thesis aimed to compare, based on content analysis, the approximations and detachments between the works RMCI and TFA. With this, we realized, as approximations, that both perform descriptions about their concepts and definitions and involve the same problems with the infinitesimals about the infinitely large and infinitely small quantities. As detachments, we observe that the central elements in Lagrange's work are functions and series and only the algebraic method is under discussion, while in Carnot's work infinitely small quantities and the theory of error compensation are present, and it conceives the use of infinitesimals without disregarding the other methods.
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Argumentação no ensino e aprendizagem de matemática básica: uma metapesquisa
(Universidade Federal do Pará, 2019-09-26) MELLO, Addelia Elizabeth Neyrão de; NUNES, José Messildo Viana; http://lattes.cnpq.br/5188612973174798; https://orcid.org/0000-0001-9492-4914
The objective of this research was to analyze researches at the level of dissertations and scientific articles published from 2014 to 2018 in Brazil that addressed the practice of argumentation in elementary school. In order to meet the research goal, data were collected from the catalog of theses and dissertations of the Higher Education Personnel Improvement Coordination in order to synthesize ideas, investigate contributions, classify and find similarities and point out possible divergences between researches. The research is qualitative in nature and followed the guidelines for reading, analysis and interpretation of texts and conducted on Academic Master's dissertations produced in Brazil, as a meta-analysis, whose research was raised and selected from the research summaries found. The research results presented according to our identification and classification criteria point to the need for more research on the theme related to the argumentation approach in the teaching and learning of mathematics, either in elementary school or higher education, especially doctoral research.
Acesso aberto (Open Access)
Avaliação das aprendizagens: uma possível articulação entre avaliação somativa e formativa em matemática
(Universidade Federal do Pará, 2022-11-16) BRAYNER, Conceição de Nazaré de Morais; BORRALHO, António Manuel Águas; http://lattes.cnpq.br/3404547486428285; https://orcid.org/0000-0001-6278-2958
This research emerged from the need to study pedagogical evaluation and also on how teachers use external evaluation to improve mathematics teaching in the early years. The investigation was developed with a qualitative approach of an interpretative nature, in the form of a collective instrumental case study. The general objective of the research is to analyze how teachers use external evaluation to improve their teaching practices in mathematics in the early years and the thesis presented is that the practice of evaluation in an articulated perspective can consolidate the relevance of pedagogical evaluation for the improvement of student learning and education management. Dimensions such as summative assessment, formative assessment, mathematics teaching and external assessment are analyzed, as well as an articulated perspective of assessment in the classroom. The empirical data were the object of a content analysis guided by a reference matrix, elaborated with the theme of evaluation, present in the dialogues with the researched teachers and in the theoretical framework adopted on internal and external evaluation. We considered in the research that external evaluation has subsidies that can be considered in the pedagogical evaluation process and that it should be at the service of improving students' learning. The data showed that teachers seek to know the results of external evaluation and are concerned with students' performance in mathematics and also, in a non-formal way, pedagogically analyze external data and make connections with the organization of teaching, learning and internal evaluation of the school. They commonly understand evaluation as a diagnostic function and recognize the need for theoretical deepening in Mathematics. They share with the school team the planning of teaching and assessment practices to improve student performance in external exams and point to the perspective of developing assessment practices that are at the service of improving student learnin.
Acesso aberto (Open Access)
Avaliação do uso de tecnologias digitais no apoio ao processo de modelagem matemática
(Universidade Federal do Pará, 2014-10-17) FURTADO, Alfredo Braga; ESPÍRITO SANTO, Adilson Oliveira do; http://lattes.cnpq.br/5870609258842071
In this research we investigate the utilization of Digital Technologies when mathematical modeling is used as a teaching strategy in mathematics, with the purpose to evaluate the learning that occurred in this environment. To achieve this goal, we studied the Mathematical Modeling and identified a modeling perspective to be employed in work; then, we studied the use of Digital Technologies (TD) in Education, focusing on the potential and the restrictions mentioned in the literature. As theoretical basis, we studied the theories of computerization of Tikhomirov, in particular the theory of reorganization of thought and activity theory of Leontiev and Engeström and Collective Thinking of Pierre Lévy. The purpose here was to formulate a methodology for teaching Mathematics with Modeling and Digital Technologies, which took into account the necessary conditions that would ensure effective improvements in learning. Thus, we proposed a methodology that explicitly incorporates a step in the process of modeling of utilization of TD, as well as gives emphasis on formative evaluation during the teaching process, so that the developed modeling projects achieve the expected learning objectives. Conditions for success of Digital Technologies in Education were identified. The proposed methodology has been implemented for a class of discipline "Mathematical Modeling", belonging to the Undergraduate Program in Mathematics and Science Education of Institute of Math and Science Education of Federal University of Pará (PPGECM/UFPA), which allowed us to evaluate its applicability, scope, results, relevance and assumptions that need to be addressed to ensure improved learning in the context of research. The results of qualitative research are identified: respecting the constraints identified, Digital Technologies effectively empower learning. Factors that demonstrate the aforementioned learning improvement have been identified.
Acesso aberto (Open Access)
Avaliação em matemática nos anos iniciais do ensino fundamental: práticas aceitas e movimentadas no cotidiano escolar
(Universidade Federal do Pará, 2018-07-06) BRITO, Maria Augusta Raposo de Barros; LUCENA, Isabel Cristina Rodrigues de; http://lattes.cnpq.br/3255121871351967; https://orcid.org/ 0000-0001-9515-101X
School evaluation is a complex process involving and considering the viewpoints of learning throughout students lifetime. This premise motivated the investigation performed to answer the question: “How is teacher rationality organized on the theoretical field of mathematical assessment in the early school years in order to promote learning?”. The research question gave rise to the general objective of the thesis, which consists in investigating, under the classroom context, imperative acts made clear during the evaluative practice in the scope of early years as a means of characterizing the teaching rationality concerning school evaluation in mathematics. This objective was divided into three other specific ones: to identify acts of understanding that constitute the teachers’ knowledge of the early years regarding evaluation in order to identify epistemological obstacles; to list dynamic evaluative procedures in terms of their purpose and the instruments used in the context of mathematics teaching in the early years; to classify evaluative tasks designed by the teachers of the early years in the teaching of mathematics. Three public school teachers from the early years of elementary school participated in this study, two in Belém/Pará and one in Évora/Portugal. For the study, a qualitative characteristic methodology was used, focusing particularly on the case study in light of the descriptive-interpretative character under which the data collection, consisting on non-participant observation and interviews, was based. Through the definition of objects and their corresponding dimensions, a Research Matrix or Guide was conducted, providing a look at didactic elements that constitute the pedagogical evaluative practice. Throughout the research process, it was necessary to develop a theoretical corpus to comprehend the phenomenon investigated in a broader way, anchored in the ideas of Hoffmann (1991), Perrenoud (1999), Buriasco (2002), Fernandes (2005, 2006, 2008), Afonso (2009) and Lukesi (2010) in the tangent to the school evaluation, as well as in Bachelard (1996) considering the possibility of identifying the epistemological obstacles present in the evaluation teaching practice. With the narratives in hand, it was possible to triangulate the data to answer the research question. From the results, I affirm that the evaluative practices accepted and implemented in the school context are cultural productions, that is, they are evaluative traditions that rest on a knowledge based on the teacher's own empiricism, from which the "scientific [spirit] starts with the class", classes that sometimes indicate beliefs that the repetitive demonstration (of teaching objects) is capable of teaching, and therefore, one cannot deny that this assumption can be reverberated in evaluative practices.