Tendências Internacionais para o Pensamento Algébrico nos Anos Iniciais

RESUMO: Na história da Matemática o acaso vem retratado em diversos momentos. Os jogos de azar serviram de base para se entender o acaso e as ideias de Cardano, Pascal e Fermat sobre decisões e regularidades trouxeram reflexões e indagações acerca da probabilidade. Bernoulli e Laplace confrontaram o acaso com o determinismo e Cornout imprimiu ao acaso a sua origem a partir de causas independentes, sendo as causas também o foco do estudo do acaso por Poincaré, como descreve Coutinho. E se ao longo da história a compreensão do acaso e da probabilidade geraram diversas concepções e formas de compreendê-los, ensiná-los nos anos iniciais do Ensino Fundamental mostra-se desafiador, sob o ponto de vista conceitual e procedimental e das metodologias a serem adotadas para sua abordagem. Assim, neste trabalho apresentamos os resultados parciais de uma pesquisa sobre material didático para o ensino de probabilidade nos anos iniciais do Ensino Fundamental. A Base Nacional Comum Curricular recomenda o ensino de noções de probabilidade anos inicias do Ensino Fundamental e estudos realizados por Piaget e Inhelder já constatavam que as crianças compreendem as noções de acaso e probabilidade de uma maneira particular, e sendo assim, abordagens adequadas com material potencialmente significativo contribuem para a aprendizagem dos conceitos. Por meio de uma revisão sistemática de literatura, selecionamos dois trabalhos que explanam sobre materiais didáticos para o ensino de probabilidade nos anos iniciais do Ensino Fundamental, na categoria jogos, sendo um manipulável concreto e o outro digital, e apresentamos uma análise das potencialidades desses materiais. Seja por meio de um caráter problematizador ou por meio de um viés mais ligado diretamente aos conceitos de probabilidade, os jogos analisados possibilitam auxiliar na compreensão dos conceitos de forma lúdica e interativa nos anos iniciais do Ensino Fundamental, além de estimular o interesse dos alunos pela aprendizagem e maior participação nas aulas de Matemática. PALAVRAS-CHAVE: Recursos didáticos, Probabilidade, Ensino Fundamental.

This article aims to analyze the specificities of the construction of algebraic thinking by deaf students in the early and final years of elementary school through a Systematic Review. The specific objectives are: to identify the curricular recommendations - National Common Curricular Base (2017) and Pernambuco Curriculum (2019) related to the construction of algebraic thinking by elementary school students; to retrieve from the CAPES Periodicals Portal, Brazilian Digital Library of Theses (BDTD) and Google Scholar research that deals with the construction of algebraic thinking or the learning of mathematical knowledge by deaf students; to point out the recommendations of the literature on the development of algebraic thinking by deaf elementary school students. The study was guided by a systematic literature review methodology based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), which started with searches for articles and dissertations in the CAPES Periodicals Portal, BDTD and Google Scholar databases. A total of 2 727 studies were identified. After applying the inclusion or exclusion criteria, nine studies were selected for review. The results indicated that deaf students, like hearing students, present particularities in the construction of mathematical knowledge, especially in the Algebraic Unit Theme.

RESUMO: O domínio das operações aritméticas básicas pelos alunos dos anos iniciais do Ensino Fundamental seja conceitual ou procedimental ainda configura-se como aquém do esperado nas macroavaliações. Para atingir níveis de proficiência satisfatórios é fundamental que se promova o desenvolvimento das habilidades e competências necessárias à compreensão das operações e suas aplicações no cotidiano. A simples operacionalização dos métodos de resolução dessas operações por procedimentos práticos e o descaso com a compreensão dos algoritmos podem afetar consideravelmente a aprendizagem de outros conteúdos nos quais as operações são utilizadas. Além do mais, as dificuldades que se formam pela falta do domínio dessas operações nos anos iniciais se arrastam ao longo dos anos finais do Ensino Fundamental até o Ensino Médio, evidenciando que é importante que os professores revejam suas práticas docentes. No entanto, os professores dos anos iniciais do Ensino Fundamental, etapa de escolarização onde as operações aritméticas são desenvolvidas primordialmente, também encontram dificuldades nas compreensões dessas operações e ensiná-las pode se constituir um desafio, ao mesmo tempo que pode implicar em adoção de abordagens equivocadas que levam à incompreensão sem ter de fato ocorrido a aprendizagem. Dentre as operações aritméticas, a operação divisão, seja exata ou inexata, ainda é uma das operações nas quais tanto professores dos anos iniciais do Ensino fundamental quanto alunos apresentam dificuldades, assim como a operação subtração. No sentido de melhorar a compreensão do algoritmo da divisão exata e inexata nos anos iniciais do Ensino Fundamental, uma oficina foi ofertada em 2019 para professores e futuros professores. Os resultados apontam que as dificuldades se concentram nos casos especiais de divisão e na divisão inexata. PALAVRAS-CHAVE: Aritmética; Divisão Exata e Inexata; Material Dourado; TDICs; Ensino de Matemática.

The present study makes a reflection and analysis of the speeches of eight teachers that work in the early years of elementary school in two public schools at the city hall of Uberlândia, on technologies in the teaching and learning of Mathematics. The proposed goals were to identify the design of teachers in the early years of elementary school about what they understand by technology. Know the challenges/barriers encountered by teachers in relation to the use of technology in their educational practices in teaching mathematics. Discover whether teachers consider technology as an effective tool in the teaching and learning of mathematics in the early years of elementary school. Moreover to reflect about the use of technology in the educational practices of teachers working in the early years of elementary school. The methodological way adopted to address the problem of this study was a qualitative study. Two data collection instruments were used: the questionnaire and the interview recorded. The questionnaires were applied in order to characterize the subjects and interviews were used in order to understand the discourse of teachers regarding technology in teaching and learning. To select the teachers who were interviewed we have established two criteria. In the first criterion of the interview, it was required that the teachers had completed their undergraduate degree in the last five years, from 2006. In the second criterion of the interview, the selected teachers had little work experience in the profession. To analyze the interviews, we have used the content analysis method. Because this technique allows us to understand and interpret the speech of the individual participating on this interview. The results of this study show that teachers have the idea that technology is strictly a machine. The technological device has also demonstrated a lack of knowledge of them to integrate technology in their educational practices. For teachers, technology is a mean in itself that cause changes in the processes of teaching and learning. Besides, the results also demonstrate that the teachers resist to the use of technology in their educational practices. Which is a consequence of the difficulties encountered by them to articulate their pedagogical proposals with the technologies.

http://dx.doi.org/10.5007/2175-7941.2016v33n2p579 Os avanços da Ciência e da Tecnologia são de grande importância para a modernização da sociedade e se faz necessário a introdução dos primeiros conceitos científicos desde os anos iniciais de escolarização, visando fomentar na criança o interesse por assuntos relacionados à Ciência. Nesse sentido, no presente trabalho investigamos a inserção do ensino de Física junto aos anos iniciais do ensino fundamental, bem como avaliamos os resultados da introdução de módulos de Física em um programa formativo para professores dos anos iniciais sobre suas práticas docentes. Nos módulos de Física foram empregadas diferentes metodologias que consistiram em realização de atividades experimentais, debates e grupos de discussão. Participaram deste estudo 41 docentes, que foram sujeitos às técnicas para avaliação; questionário, grupo focal, fotografias e observação participante. Depois da análise dos dados, constatamos a ausência de temas relativos à Física durante as aulas de Ciências, com o predomínio do ensino da Língua Portuguesa e Matemática em detrimento do ensino de Ciências. Após a participação dos docentes no programa formativo, verificamos mudanças profícuas na prática dos mesmos, que em massa passaram a introduzir o ensino de Ciências/Física nas suas aulas. Ademais, seus alunos foram motivados intrinsecamente, despertando assim o interesse dessas crianças por assuntos relativos ao ensino da Física. Por fim, este trabalho nos possibilitou desconstruir as concepções dos professores acerca da impossibilidade de se ensinar Física para a criança, bem como apontou para a necessidade de ampliação na oferta de programas formativos nas áreas de Ciências para os anos iniciais da formação básica.

Objective: The purpose of this study is to identify how the topic of English Language Inclusion in the Early Years of Elementary School is addressed in research conducted between 2018 and 2023 on the CAPES Portal. Theoretical Framework: The theoretical framework used underpins discussions on the topic of English language inclusion in the Early Years of Elementary School: an analysis of research conducted between 2018 and 2023 proposed in these materials. First, a theoretical framework is provided on children in the Early Years, who they are and how they develop, and then a deeper look is taken at the legal basis for teaching foreign languages ​​in Elementary School. Finally, a chapter is presented on the importance of introducing English language teaching to students in the Early Years of Elementary School. Method: This study was conducted based on the theoretical assumptions of bibliographic research, with the analysis of 5 articles whose research was directly directed to the Early Years of Elementary School. As a data collection instrument, we chose to prepare a form in which relevant elements for the theme of this study were identified in the works analyzed. Results and Discussion: Based on the development of the research presented here, it was found that early learning of a second language not only expands future academic and professional opportunities, but also enriches the cognitive and cultural development of students. Implications of the Research: The practical and theoretical implications identified in this study are considered to be the reflections resulting from a discussion on the contributions arising from the inclusion of the English language in the Early Years of Elementary School. Originality/Value: The relevance of this study is justified by the fact that it is considered that the inclusion of the English language in the initial years of elementary school is of utmost importance, as it provides children with a solid foundation in a globally dominant language from an early age. This early learning facilitates the acquisition of linguistic skills in a more natural and intuitive way, taking advantage of the cognitive plasticity characteristic of children in this age group. In addition, mastery of English opens doors to future academic and professional opportunities, promotes access to a vast amount of information and resources available in English, and facilitates communication in an increasingly globalized world.

This article addresses reading from the perspective of the reading process in teaching and learning in elementary school, encompassing: reading and teaching and learning, reading in the early years of elementary school, reading in the later years of elementary school, and intervention proposals. The main objective was to discuss how the teaching and learning of reading takes place within the early and later years of elementary school. Reading has been a concern for teachers, due to the fact that many students are unaware of the importance of this practice not only in school, but, above all, in society. The methodological process for producing this work is a qualitative bibliographic research approach, considering the thoughts of various authors who address the topic. It highlights the relevance of critical reading to understand the world, seeking to clarify the meaning of the different languages ​​around us, in the desire to clarify the meaning of the languages ​​that surround us. Thus, reading is a specific activity of enormous importance for the teaching-learning process in school, especially in elementary school.

This paper aims to present results of research conducted with graduates of the Pedagogy course, with training in early childhood education and early years of elementary school and its role in school management. Highlights that the training required to act in school management was a long time given to the course of Pedagogy. This training was the restructuring of the curriculum of the course, from the opinion of CFE 252/69, which printed the license administration, supervision, orientation and inspection giving the school the title of graduate education specialist. This model was subjected to considerable criticism by polarizing the training of teachers and pedagogue and fragment the pedagogical work. Such criticisms have contributed to the course Pedagogy to take over the training of teachers for early childhood education and early years of elementary school. Locally the graduates of this training in school management act, this suggests that discuss the implications of training, focused on the teaching of early childhood education and early years of elementary school, to act in school management. To this end, the discussion focuses on building a common national base for training of teachers and how they drive the configuration of the of the Pedagogy course. So, evidence that the unfolding of this process alters the landscape of the work of the pedagogue in school, especially in schools of the state of Parana, whose job as a teacher pedagogue is occupied by public tender by the licensee in Pedagogy.

This research was based on the following question: what teaching methodologies can contribute to the learning of mathematics by students with Autism Spectrum Disorder (ASD) in the early years of elementary school? Based on the guiding question, the aim was to study, identify and analyze the methodological possibilities for the learning of mathematics by students with Autism Spectrum Disorder (ASD) in the early years of elementary school. To answer the suggested problem and achieve the defined objectives, the investigation was carried out using qualitative bibliographical research, specifically meta-analysis. By contextualizing the teaching of mathematics in the early years of elementary school, it was discussed the guidelines, conceptions, and practices of teaching mathematics, analyzing how students' learning is constituted in the current context, based on research into the results of the tests of the Basic Education Evaluation System (SAEB) and the Minas Gerais Public Education Evaluation and Equity System (SIMAVE). Were presented some reflections as well on the causes that influence school failure in the learning of mathematical content. It presented an analysis of the historical, cognitive and diagnostic aspects of Autism Spectrum Disorder (ASD) and the history of inclusive education in Brazil. It also presented some methodological alternatives that can help in the learning of mathematical concepts, seeking to establish whether these methodologies are appropriate for students with ASD. In this way, the methodological possibilities for the development of teaching practice in mathematics presented were Problem-solving, Games and Information and Communication Technologies, always seeking to establish an interrelationship between the teaching methodologies presented and their viability for students with ASD.

Other transgressive learning about sustainability needs to be part of the lives of students in the early years of elementary school, as they are responsible for seeking and achieving a sustainable future. However, the focus on socio-ecological sustainability does not seem to be present at this level of education as the literature has addressed. Therefore, the objective is to review articles from journals that address the relationships on socio-ecological sustainability and school garden in the early years of elementary school, published from 2016 to 2021. Based on the ideas of Okoli and Schabram (2010), they used if, in the research, the SciELO and Google Scholar databases and 10 papers were chosen, which were read in full for analysis and discussion. The results show a limited focus on how the teaching of socio-ecological sustainability and school garden has been carried out in elementary school, that is, interdisciplinarity is not widespread and the approach to this sustainability, through the use of the school garden, is non-existent in classroom. It was noticed in the articles that the school garden is insufficiently used in teaching, despite its relevance in teaching-learning, as well as the sustainability addressed in schools involves only the economic dimension when it is essential to connect the social and ecological approach.

The introduction of neuroscience needs to be considered in all teaching modalities. Among these, Distance Education (EAD) in the early years of elementary school, which was the focus of this study. Neurosciences contribute to distance education, as current knowledge about neurodevelopment and the functioning of the brain-mind complex helps in understanding how to learn. The acquisition of neuroscience knowledge enables the teacher to motivate, teach and evaluate students in a format compatible with brain functioning. The objective is to investigate teaching practices in the early years of Elementary School in the face of the information society, for autonomous and meaningful learning; through the case study. As well as highlighting the importance of neurosciences in the Distance Education (EAD) system in the early years of Elementary School. In this study, we opted for scientific bibliographical research, for using theoretical sources; qualitative for appropriating the subjectivities of the authors used and exploratory, for investigating the phenomenon “Distance Education (EAD) in the initial years of Elementary School in relation to pedagogical practices” approaching the scientific community, aimed at a teacher in the early years of Elementary School of private network in Campos dos Goytacazes/ RJ. From this study, it can be concluded that: learning is a result of neuroplasticity; the human brain does not complete its development, but is constantly restructured and reorganized; new ideas about cognition and development can provide new directions for education; neuroeducation is a proposal that has been growing and constituting a field and intersection between education and neuroscience.

In the contemporary educational scenario, Religious Education in the Early Years of Elementary School emerges as an essential component for the comprehensive education of students. This article aims to promote a reflection on the training of Religious Education teachers in the early years of elementary school, since the school plays a crucial role in critically exploring religious dimensions, promoting a reflective and contextualized understanding. Addressing topics such as the function and values ​​of religious traditions and the relationship between multiple religious cultures enriches learning and ethical formation. The motivation for choosing this theme is driven by the pressing need to rethink Religious Education practices in the Early Years, based on the premises of the National Common Curricular Base (BNCC) and in light of the perspective of continuing education and teaching knowledge of Tardif (2000 and 2014) and Gauthier (1998). Thus, we sought to analyze the training of teachers in the early years of Elementary School to teach the curricular component of Religious Education. The study is based on bibliographic and documentary research in this area of ​​knowledge, aiming to understand the path of educators' training from undergraduate studies to continuing education programs offered by the municipal education system. This study aims to broaden the debate on the importance of consistent teacher training, since the legislation establishes that the integration of this knowledge into School Knowledge, as an object of study of the Religious Education Curricular Component (CCER), occurs from the 1st year of the initial years of Elementary School. The results indicate that, although there are indications in the documents about the objects of knowledge of RE to be addressed in the initial grades, there is no prevalence of records on teacher training, as occurs in the other curricular components.

Este artigo apresenta um estudo sobre os conhecimentos físicos presentes em documentos curriculares dos anos iniciais do Ensino Fundamental. O objetivo é abordar a questão da inserção da Física no âmbito do componente curricular referente às Ciências Naturais para esta etapa de ensino, tendo em vista as implicações para a organização didática docente e a formação inicial em Pedagogia. Trata-se de uma pesquisa do tipo documental, em que os documentos a serem analisados correspondem aos textos curriculares adotados pela rede municipal de ensino de Curitiba/PR nas últimas três décadas: o Currículo Básico para a Escola Pública do Estado do Paraná (1990), os Parâmetros Curriculares Nacionais – ensino de primeira à quarta série (1997) e o Currículo do Ensino Fundamental de Curitiba (2016). Para a constituição dos dados que viabilizaram a análise, utilizou-se a metodologia da análise textual discursiva e, a partir do processo de organização das informações, foram construídas as seguintes categorias de análise: 1) conteúdos de Física indicados para as séries iniciais; 2) conhecimentos das Ciências Naturais que remetem à Física, indicados para as séries iniciais e 3) temáticas amplas que podem ser vinculadas a conhecimentos de Física nas séries iniciais. Como resultados, percebeu-se que conhecimentos de Física estão presentes de maneira explicita em todos os documentos analisados, porém com o passar do tempo as orientações curriculares incorporaram vertentes metodológicas em que os conteúdos da Física são cada vez mais articulados com temáticas do ensino de Ciências, bem como temas atuais de caráter científico e tecnológico, e suas relações no contexto social. Estes resultados mostram que a Física constitui-se em uma importante dimensão para a introdução às Ciências da Natureza nas séries inicias, e precisa ser abordada em conjunto com os conhecimentos das demais áreas que pertencem a essa ciência. Isso implica que a formação inicial nos cursos de licenciatura em Pedagogia deve garantir que os futuros professores, que atuarão nos anos iniciais do Ensino Fundamental, tenham acesso a uma formação científica adequada durante a graduação, que permita a articulação da Física, Química e Biologia, sem privilegiar uma área de conhecimento em detrimento de outras, algo que pesquisas apontam ser realidade recorrente nos contextos escolares.

The central scope of this research addresses the Psychology of Mathematics Education for professionals with a degree in Pedagogy courses, focusing on teachers who exercise the teaching of mathematics teaching in the early years of elementary school I. This article analyzes and presents the potentialities and contributions of this theoretical field of knowledge in the teaching-learning process of Mathematics. Education aiming at improvements of the Brazilian student in the external evaluations of the Brazil Test published by the SAEB of 2017 and 2019, as well as the pedagogical practice between teacher-student-knowledge. It was justified the insufficient proficiency in mathematics of Brazilian students of about 70%, as well as the reduced number of scientific productions on the theme of this article. The objective of this study was to present contributions of the Psychology of Mathematics Education in the early years of elementary school I. On the methodological path, it was characterized within the qualitative approach and in the procedures of bibliographic research. Among the main results were the discourses of the interviewed subjects pointing out the potentiality of the theoretical basis of Psychology of Mathematics Education in their pedagogical knowledge/doing. It was found that the psychological, cognitive and affective-social dimension have implications for students' learning. It concludes an emergence of a further discussion of this field of knowledge in the degree of pedagogy courses in Brazil to increase the quality of pedagogical intervention of pedagogue teachers in mathematics classes, aiming to increase the quality teaching-learning process of mathematics in the early years and the results of institutional and large-scale evaluations.

Background: It is common the idea that the responsibility for learning mathematics worked in the first years of schooling rests solely with the teacher at this stage. This is a mistake since these contents run throughout basic education, and it is important that teachers at other levels understand the mathematics of the early years of elementary school. Objectives: The article aims to discuss the knowledge of mathematics undergraduate students about mathematics in the early years of elementary school. Design: The theoretical and methodological support is based on the assumptions of cultural-historical theory (CHT), which shows that the subject develops and impacts the reality where he/she lives by interactions with others through the acquired knowledge. Setting and participants: The study space consisted of workshops on the operations of addition, subtraction, multiplication, and division, carried out in the project “Knowing the mathematics taught in the early years” and the participants were seven undergraduates from the mathematics degree course. Data collection and analysis: The empirical data were systematised by the organization of the episode "Understanding the teaching of basic mathematics", composed of four scenes. Results: They reveal that when it comes to teaching mathematics in the early years, students show a weakness in relation to basic mathematical knowledge and didactic knowledge to teach them. Conclusions: Although the results come from a specific context, we concluded that it is important for mathematics undergraduates to be able to discuss mathematics teaching in all stages of basic education.