Programa de Pós-graduação em Educação em Ciências e Matemática
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Navegando Programa de Pós-graduação em Educação em Ciências e Matemática por Por Orientador "Alvarenga, Karly Barbosa"
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Item Análise de processos de construções de modelos: o movimento de translação(Universidade Federal de Goiás, 2021-07-19) Costa Junior, Edson Ferreira da; Alvarenga, Karly Barbosa; http://lattes.cnpq.br/8950541327384418; Alvarenga, Karly Barbosa; Silva, Jhone Caldeira da; Villa-Ochoa, Jhony AlexanderThis work aims to analyze the construction processes of mathematical models carried out by first-year high school students, to represent the changes in the plane, specifically the horizontal movement. Geometric transformations, isometries, rigid movements and symmetries are common, either formally or in a simple way. With the purpose of mediating the work between these two extremes, a workshop was carried out, with the students developing the mutual teaching of algebra, geometry and arithmetic so that they could make use of creativity and mathematical language to descrive the actions observed. The workshop was supported by ideas about mathematical modeling, with the intention of mathematically interpreting and describing the horizontal translation movement through the manipulation of the concrete material, then providing a better visualization of the situation investigated by the participants. Therefore, two workshops were held with students during the 1st year of high school (14 – 15 years) in a public school in Goiás. It is important to emphasize that the objective was not to find the correct solution, the ideal answer, but to create a space of construction of significant knowledge where students, with the help of the teacher, were instructed to discover, criticize and question their decisions and the creation of a model based on the concrete world. To gather data, activity forms, questionnaires and audio recordings were used. Regarding the results, the arithmetic, algebraic and geometric approaches were analyzed when representing the phenomenon, and students showed difficulties related to the elementary operations and the use of symbology. It was noticed that students used one of the languages, the mathematics or the written mother tongue, or both, to solve problems by choosing the one that is more convenient for them to understand. It is possible to conclude that these difficulties are reflections of a mechanical teaching without meaning production in the previous grades. In addition, the research results can contribute to the interdisciplinary treatment of this topic and boost the development of mathematics, in addition to highlighting its applicability in everyday life.Item Panorama sobre etnomatemática em eventos brasileiros(Universidade Federal de Goiás, 2019-01-25) Lima, Luara Laressa Ferreira dos Santos; Alvarenga, Karly Barbosa; http://lattes.cnpq.br/8950541327384418; Alvarenga, Karly Barbosa; Gonçalves Junior, Marcos Antônio; Lemos, Glen CezarThis research is established along the lines of the Ethnomathematics Program and its main objective is to map and analyze the work of this program of three Brazilian congresses and in particular to analyze those related to Africanism in four events. Therefore, this research is of the State of the Art type. The data were collected in the annals of the National Meeting of Mathematical Education, International Seminar on Research in Mathematical Education and the Brazilian Meeting of Postgraduate Students in Mathematical Education. For those related to Africanity, the Brazilian Meeting on Ethnomathematics is added. The analyzes were made through the abstracts, using Content Analysis and Depth Hermeneutics. With the data mapped, it is inferred that the number of publications in this line tends to growth. Indications of possible paths to the research line in Ethnomathematics are pointed out at the end.Item Discalculia: estado da arte em congressos de educação matemática(Universidade Federal de Goiás, 2023-08-29) Ribeiro, Hellen Marques Pinto; Alvarenga, Karly Barbosa; http://lattes.cnpq.br/8950541327384418; Alvarenga, Karly Barbosa; Lara, Isabel Cristina Machado de; Nery, Érica Santana SilveiraThis study has the main objective of mapping and analyzing articles related to Developmental Dyscalculia in national and international Mathematics Education events from 2006 to 2021. It is a qualitative study with numerical subsidies, bibliography of type of State of the Art. The mapping was carried out electronically in the databases of: Encontro Nacional de Educação Matemática, Seminário Internacional de Pesquisa em Educação Matemática, Associação Nacional de Pós-Graduação e Pesquisa em Educação, Encontro Nacional de Educação Matemática Inclusiva, Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática, Congresso Internacional de Educação Matemática and Reunión Latinoamericana de Matemática Educativa. The descriptors used were dyscalculia, disorder and learning difficulty in mathematics; as a result, a corpus with 22 articles was formed. A descriptive and interpretative analysis of the data was carried out, supported by Content Analysis, in order to learn about the mains concepts, ideas, gaps, trends and perspectives on the subject in question. Four emerging categories were established, which are: Research Methodology, Participants, Conceptualizations and Teaching. And from these, ten subcategories were elaborated namely: Theoretical Research, Practical Research, Teaching Perception, Tracking, Psychopedagogical Interventions, Conceptual Discussions, Inclusive Discourses, Cognitive Perceptions, Teaching Strategies and Diagnostic Strategies. For the theoretical basics Kosc’s work was used. The mapped publications are, for the most part, theoretical studies related to concepts and definitions inherent to the disorder itself, cognitive and inclusive perceptions, and the analysis of other scientific productions. Those of a practical nature refer to Field Research and Case Studies. The investigations showed that, after individual psychopedagogical interventions, students with this type of disorder showed advances in learning. The analysis showed that there is a need for more research, mainly empirical, as well as on brain functioning, diagnostic strategies and learning. Furthermore, the Developmental Dyscalculia can have consequences on the individual’s personal and professional life, and studies from this perspective are still incipient, requiring further in-depth and discernment. Thus, this State of the Art contributed to understanding aspects peculiar to this topic and made it possible to indicate directions and delimitations for future research.Item Um estudo sobre a abordagem de limite de funções em livros de cálculo diferencial e integral(Universidade Federal de Goiás, 2023-08-31) Santos, Leniedson Guedes dos; Silva, Geci José Pereira da; http://lattes.cnpq.br/9174074436425246; Alvarenga, Karly Barbosa; http://lattes.cnpq.br/8950541327384418; Alvarenga, Karly Barbosa; Ferreira, Joubert Lima; Rabelo, Mauro Luiz; Domingos, António Manuel Dias; Caicedo Roque, AlejandroBooks play a fundamental role as teaching instruments, which makes them important objects of study for researchers seeking to understand learning difficulties, especially with regard to Mathematics in higher education, a topic in which this type of research learning is still scarce. With a focus on teaching, this bibliographical work, of an explanatory and qualitative nature, aims to investigate the way in which the Differential and Integral Calculus books authored by Louis Leithold (1994), Hamilton Luiz Guidorizzi (2001) and James Stewart (2013) addresses the definition of the limit of functions of a variable. To achieve this objective, the methodological research framework of Depth Hermeneutics – HP, proposed by Jonh B. Thompson, was mobilized with the intention of answering the following questions: what types of semiotic representation records are it possible to identify these works and how Can they influence the teaching of function limits? What socio-historical aspects of the production of these books influenced the author in choosing a certain approach? Conceiving the book as a symbolic form, the phases that represent the HP were articulated: the socio-historical analysis, where this information was collected about the authors' biography, the evaluation of the preface and changes in the other editions, actions referenced by the Historical Analysis of Mathematics Books by Gert Schubring and the study of Editorial Paratexts by Gerrard Genette; formal analysis, in which the types of representations of limits and functions that appear in books were identified, as well as their transformations, through event activities, categorization and the construction of inventories, in the light of the Theory of Representation Records Semiotics - TRRS by Raymond Duval; and the interpretation/reinterpretation in which a creative synthesis of meanings on the works studied was constructed. The results demonstrated that, in the three books, there is a predominance of the algebraic register over the others and the absence of exercises proposed between registers, which, according to the TRRS, can make teaching the concept of limit difficult. Individually, influences from the Modern Mathematics Movement, the Bourbakist school and the Calculus Reforms were identified in the writing of these books.