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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Agora exibindo 1 - 7 de 7

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Desvendando mitos na educação matemática: como pseudo-histórias afetam o ensino
(Universidade Federal do Pará, 2024-02-22) ARAUJO, Demetrius Gonçalves de; BRANDEMBERG, João Cláudio
This research aimed to investigate the origins and emergence of Pseudo-stories in mathematics teaching. The study highlights three of the main Pseudo-histories of mathematics and analyzes how they are transmitted and perpetuated, including their dissemination in books and media. Furthermore, the work proposes measures to correct or minimize the impact of Pseudo-histories on the perception of the history of mathematics. The research covers the Pseudo-histories of mathematics that emerged from the 19th century to the present day. Secondary sources will be used, such as books, articles and published research, as well as primary sources, such as historical documents. The study will adopt a bibliographic approach, with critical analysis of the sources. The analysis method proposed by Martins (2000) will be applied to verify the veracity of Pseudo-stories, with adaptations for the cases of Archimedes' Crown, Newton's Apple and Bhaskara's Formula. In this way, the research seeks to expand knowledge about the impact of Pseudo-stories on mathematics teaching and contribute with proposals for a more accurate perception of mathematical history.
Acesso aberto (Open Access)
Um estudo acerca da inserção de aspectos históricos dos conceitos de dependência e independência linear em cursos de álgebra linear
(Universidade Federal do Pará, 2022-02-22) DIAS, Renan Marcelo da Costa; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
The present study aimed to investigate how the historical development of the concepts of Linear Dependence and Independence can be approached in Linear Algebra courses to enable a better understanding of these concepts by Mathematics undergraduates. To this end, we developed a Bibliographic Research with a qualitative approach for data analysis consisting of two moments. In the first moment, based on Dorier (1995b; 2000) and Moore (1995), we discuss the historical constitution of Linear Algebra, in which we identify four different preceding notions of the current concepts of Linear Dependence and Independence, whether they are inclusive dependence (Euler), unified dependence for equations and n-tuples (Frobenius), generalization of dependence to n-dimensional space (Grassmann) and axiomatization of dependence and linear independence (Peano). In the second moment, we present didactic suggestions, based on Mendes (2006; 2015; 2016) and Brandemberg (2018; 2021), on how to approach these different notions in Linear Algebra courses. Such suggestions aim to give students the opportunity to have contact with different aspects that allow them to broaden their understanding of linearity as a relationship between vectors, as well as to visualize the current definitions of Linear Dependence and Independence as a language that does not discard the notions given by Euler, Frobenius, Grassmann or Peano, but keep them in a unifying and generalizing character.
Acesso aberto (Open Access)
Um estudo exploratório sobre a imagem conceitual de estudantes universitários acerca do conceito de limite de função
(Universidade Federal do Pará, 2013-02-28) MESSIAS, Maria Alice de Vasconcelos Feio; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176
This is an exploratory research that aimed to investigate the elements that compose university students’ concept image related to the concept of limit of a function of one real variable. It was investigated the knowledge of 25 students of mathematics’ course in two public universities in the state of Pará (Brazil). The data collection was made, at first, through a questionnaire that contained tasks involving limit of one real variable function’s conceptual aspects. The second stage consisted in interviews with six students that were selected because of their evoked concept images in the previous stage, since they were related to the four Discussion Themes (DT) that leaded those interviews. The data analysis was based on the theory of Tall&Vinner (1981) and Vinner (1991), besides the studies of Cottril et al (1996), Jordaan (2005), Juter (2006), Nair (2009), above others, which composed the theoretical framework of this study. Above the results obtained in this research, we emphasize that the students relate the concept of limit of a function of one real variable with static and/or dynamic interpretations that, in some moments, constituted themselves as potential conflict factors, such as described by Vinner (1991). Besides, we’ve also noticed that some evoked concept images weren’t coherent, which influenced them to construct a personal concept definition different from the formal concept definition of limit of a function of one real variable.
Acesso aberto (Open Access)
Potencialidades didáticas de textos e problemas históricos egípcios e babilônicos para o ensino de matemática na educação básica
(Universidade Federal do Pará, 2022-05-28) PEREIRA, Patricia Sheila Figueiredo; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
This research aimed to investigate which texts and historical problems present in the mathematics of Egypt and Babylon have didactic potentialities to be explored in the teaching of mathematics. For this, a bibliographical research was carried out in the literature of Boyer (1974) and Eves (2011), which provided the historical context of mathematics, as revealed several forms of solving ancient mathematical problems and that these are possible to be solved through the current notation. When studying the History of Mathematics, several potentialities that enable the development of mathematical skills were identified in the texts and historical problems that enable the development of mathematical skills, which were evidenced according to the arguments of Miguel (1997) and the studies of Mendes and Chaquiam (2016), Brandemberg (2020) and Brandemberg (2021), which corroborate the relevance of history in mathematics teaching. From this study, it was possible to select the texts of the Plimpton Table 322, the historical problems of the Rhind Papyrus and those of The BM Table 13901 as sources of/with potentialities, which are: to enable the conceptual development of the polynomial equation of the 1st degree; enable the development of the concept of the quadratic equation; to provide the student with new discourses on pythagoras' theorem and, with this, enable the development of skills foreseen in the National Common Curriculum Base (BNCC). In addition, it was suggested, through didactic activities, a way for the teacher to use the texts and historical problems in the teaching of school mathematics. Thus, it can be inferred that the selected texts and historical problems have potentialities that contribute to the construction of mathematical knowledge, as well as it was evidenced that they can be used in the process of teaching and learning mathematics in Basic Education.
Acesso aberto (Open Access)
Saberes docentes na licenciatura em matemática acerca do ensino de derivada
(Universidade Federal do Pará, 2016-03-28) PAULO, Stephany Glaucia de Oliveira; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
This work is developed from the qualitative research that aims to identify the Knowledge Teachers present in the Degree in Mathematics and teaching Derivative. The study involves five teachers who teach or have taught at the Calculus I course for the degree in Mathematics of the Pará State University and / or the Federal University of Pará, which seeks to answer the following question: what teaching knowledge present in the degree in Mathematics and teaching Derivative? This study is divided into two stages, the first is the application of a questionnaire containing eighteen questions about teacher training and performance in education derivative, the second is the interview which contains five questions concerning the professional career of the teacher since his graduation and six questions relating to teacher design in relation to the Derivative of education in degree in Mathematics. Later built a new interview script, which contains seven questions on teaching Derivative two about the difficulty of Derivative learning and four purpose of training, experience and the course curriculum. In the historical study of the development of derivative, we based the work of Haveroth (2013), Pires (2004), Bardi (2008), Carvalho (2007) and Baroni and Otero-Garcia (2014). In bibliographical study on the Derivative of education in the Degree in Mathematics, based in Dall'Anese (2000), Santos and Matos (2012) and Traldi Junior (2007) and on the teaching knowledge in Tardif (2014) and Pimenta (1996). Based on the analysis of the interviews, we made some considerations: we realize that this knowledge’s are closely linked to one another, knowledge that these are the training, the experience, discipline and curriculum.
Acesso aberto (Open Access)
Sistematização das técnicas aritméticas na Europa do século XIII
(Universidade Federal do Pará, 2024-02-28) GUIMARÃES FILHO, José dos Santos; BRANDEMBERG, João Cláudio
It is observed that, in the 13th century, Europeans used the abacus and Roman numerals. The abacus, to operationalize your problems, and the Roman numerals, to record them. In that same period, an Italian mathematician called Leonardo Fibonacci (1170 – 1240) came onto the scene who, after his travels in the East, brought an arithmetic that had not been widely disseminated in Europe, as well as Indian ciphers and their decimal positional number system, which were organized and systematized in Liber Abaci. In these circumstances, the question arises: what demands were met in the context of 13th century Europe by the systematization of arithmetic knowledge in the Liber Abaci, written by Leonardo Fibonacci? In the search for an answer to this question, the objective of this research is to identify demands met by the systematization of the set of arithmetic practices in Liber Abaci that were in production and use in Europe in the 13th century. To this end, a qualitative proposal was used, which allowed a reflective and analytical process of the historiographical aspects of the implementation of arithmetic methods and techniques in Europe in the 13th century, guided by the three spheres of analysis of updated historiography. These reflective processes showed that the set of arithmetic practices, arranged and organized in Liber Abaci, was reaching the clergy with the use of liturgical language and assistance in biblical exegesis and counting important dates for Christianity. The organization of this book, which is arranged from simple to complex, shows its interaction with more theoretical treatises, one of the signs that it was in the direction of reaching universities. Its systematization shows a feasible optimization in accounts with high values, so it could be used to move large quantities, whether of goods or monetary values, offering society a clear and reliable criterion in the accounts, which helped to solve commercial and agrarian problems. and taxable. In view of this, the systematization of arithmetic techniques in 13th century Europe contained in the Liber Abaci was meeting religious, academic, social and commercial, urban or mercantile demands.
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/0000-0001-8848-3550
The 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.

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