The present proposal aims to integrate the teaching of Real Functions of real variables with Geometry and Trigonometry, articulating different representations of functional relations based on the resolution of geometric problems. The choice of this theme arose from the observation of significant gaps in the geometric knowledge of students entering integrated technical courses at the Federal Institute of Education, Science and Technology of Rio Grande do Sul (IFRS) – Campus Feliz.  To address this difficulty, we propose to bring forward the teaching of geometric content from the first year of the course, allowing enough time for the development and consolidation of this knowledge. In this context, we developed a didactic proposal aimed at integrated high school students, with the support of GeoGebra software as a pedagogical resource.  The main objective is to provide students with learning situations that favor the construction of knowledge about Functions based on the study of areas of plane figures. We also intend to stimulate the perception of the pedagogical potential in the integration of Geometry and Function content through an unconventional approach that values intuition and experimentation.  Using GeoGebra allows the creation of dynamic graphs, promoting a new way of understanding and relating graphic and algebraic representations. By observing these representations in motion, students have the opportunity to visualize transformations and identify invariant properties in geometric constructions. Instead of analyzing a single static figure, they come into contact with a family of infinite figures generated by successive positions throughout the movement, which can favor the formulation of conjectures and the construction of deductive arguments. 

This is a work on abstraction. It is divided into two parts. The first part is theoretical: we want to understand abstraction from a biological, psychological, and metaphysical perspective, as we are interested in providing as complete an answer as possible to the questions related to the topic of abstraction. We aim to answer the questions: "What is the definition of the concept 'abstraction'?", "What is the metaphysical nature of an abstract concept?", "What is abstraction?", "What are the types of abstraction and what types of concepts do they generate?", "How does the process of abstraction occur?", "What are the levels of abstract thought?", and "What are the human conditions for the process of abstraction to occur?" To answer these questions, we draw particularly on the studies of Aristotle, Steven Pinker, and Jean Piaget.

The second part investigates, with a didactic interest, the processes of mathematics, specifically algebra, related to the teaching and learning of abstraction. We applied the knowledge gained in the theoretical part to the study of algebraic abstraction. We conducted research to determine whether it is possible to develop the concepts of algebraic abstraction through problem-solving methodology. To this end, we organized four classes, where students will be asked to solve arithmetic and algebraic problems, as well as a fifth class for assessment. Data will be collected through this assessment and through observations made in the four classes. These observations will be conducted using action research elements.

A educação financeira exerce papel significativo na vida das pessoas, contribuindo para a gestão eficiente de recursos, prevenção do endividamento e melhoria da qualidade de vida. Diante das dificuldades que muitos enfrentam na organização de suas finanças pessoais, torna-se essencial a integração do tema ao currículo escolar da educação básica. Frente a esse contexto, esta pesquisa buscou abordar o tema por meio do uso de planilhas eletrônicas, favorecendo a aprendizagem e a aplicação prática de conceitos financeiros em uma turma da Educação de Jovens e Adultos (EJA). Foi elaborada e implementada uma proposta didática que integrou a educação financeira às situações cotidianas vivenciadas pelos estudantes, abordando desde cálculos de porcentagem e juros presentes em compras e financiamentos, até a análise de tabelas de amortização e diferentes tipos de investimentos, conectando cada conteúdo à realidade econômica e às necessidades práticas do dia a dia. O objetivo principal foi estabelecer uma relação direta entre conteúdos de matemática financeira, ensinados em sala de aula, e sua aplicação prática no dia a dia, utilizando planilhas eletrônicas. A coleta de dados envolveu registros de atividades impressas, respostas inseridas pelos alunos em planilhas eletrônicas com a resolução das situações propostas, anotações no diário de bordo da pesquisadora e aplicação de um questionário final. Como atividade inicial, cada estudante definiu um bem, objeto ou experiência a ser adquirida, denominado “sonho”, que foi trabalhado ao longo das atividades em situações envolvendo juros, financiamentos e investimentos, buscando sua possibilidade de realização. Os resultados evidenciaram que as aulas sobre juros foram relevantes, possibilitando que os alunos estabelecessem relações diretas entre teoria e prática, e repensassem suas perspectivas financeiras e desenvolvessem maior consciência sobre planejamento e tomada de decisões. Além disso, a proposta despertou interesse dos alunos sobre a possibilidade de sonhar, e sobre como realizar ou avaliar possibilidades para realizar ou alcançar o sonho. Assim, conclui-se que a integração da educação financeira à EJA, aliada ao uso de planilhas eletrônicas, contribui para a formação de uma postura crítica e responsável na gestão dos recursos de ordem financeira.

.

The difficulties of thinking algebraically and understanding the concept of variable are recurrent, and can be evidenced in the students' lack of understanding of mathematical entities, such as the use of a letter to represent any number. As a result, failures occur from Basic Education to higher education. To alleviate this difficulty in Basic Education, this research seeks to contribute to improving the development of Algebraic Thinking based on teaching and learning experiences that explore Computational Thinking (CT) in Basic Education. In this sense, different didactic strategies for constructing algebraic language were used based on CT experimentation aimed at the development and consolidation of Algebraic Thinking. Such an exploratory CT approach to the development of Algebraic Thinking had the advantage of offering an intermediate step between the “concrete” and abstraction, as the concepts of variables and the need for symbolic representation for arbitrary or unknown quantities are introduced via algorithms to from concrete situations. The activities were applied to a seventh-year elementary school class in the municipal network of Cachoeirinha - Rio Grande do Sul. The class is made up of teenagers who, for the most part, have not yet had contact with the algebraic language. As results, it was observed that there is a relationship between activities that explore CT and the manifestation of Algebraic Thinking. Students who were able to develop the pillars of CT when solving a problem manifested elements that characterize Algebraic Thinking, therefore, this can be seen as an indication that the development of CT helps in the teaching and learning of Algebra in Basic Education, contrasting with what is described in the National Common Curricular Base. As indicated in the literature, it was found that the pillar of abstraction plays a fundamental role in the manifestation of Algebraic Thinking, and also that writing algorithms, even in natural language, allows checking whether the steps prior to writing them were carried out appropriately. . This approach also allowed us to verify which stage of Algebraic Thinking the student is at. A relationship was also observed between the capabilities of reading and interpreting text in problem solving and capabilities of decomposition, pattern recognition, abstraction and writing algorithms.

A escola na atualidade é um ambiente de estudo e socialização para crianças e
jovens. Por isso, é necessário ter em mente que a interação social é parte
fundamental do processo de aprendizagem escolar, como nos traz a teoria de
Vigotski (2007, 2009, 2020), conhecida como sócio-interacionista. Paralelamente,
por várias razões, são frequentes as queixas dos alunos sobre a (falta de)
aplicabilidade dos conteúdos vistos na escola nas situações do cotidiano fora do
ambiente escolar. Por esta razão, neste trabalho propõe-se uma sequência didática
para o 7º ano do Ensino Fundamental, buscando conectar o conteúdo de Razão e
Proporção com receitas das famílias dos alunos, partindo de algo afetivo e presente
na sua vida fora da escola – as receitas – e investigando nelas os conteúdos citados
através de atividades em trios, valorizando a interação entre os estudantes. Essa
sequência didática foi aplicada em uma turma na qual a pesquisadora é professora
titular, em uma escola pública de turno integral, no Rio Grande do Sul. A pesquisa
caracteriza-se como investigação qualitativa proposta por Bodgan e Biklen (1999), e
para a análise foram consideradas as atividades realizadas pelos alunos. Durante a
aplicação, percebeu-se um aumento no interesse dos alunos sobre o conteúdo
estudado e, analisando seus relatos e produções, foi possível verificar que os alunos
se dedicaram mais às tarefas nos grupos e que perceberam que a interação com
seus pares durante a realização das tarefas foi importante para sua aprendizagem.
Por fim, sugere-se adaptações nos tempos de duração das atividades e que a
sequência didática possa ser ajustada partindo das receitas de família dos alunos
que realizarão as atividades.

A inserir.

This dissertation presents a contextualized didactic proposal for teaching statistics in
the 9th grade of elementary school, focusing on conscious consumption, aligned with
the 12th Sustainable Development Goal (SDG) of the United Nations: "Ensure
sustainable consumption and production patterns." The main goal is to emphasize the
importance of statistical education to the students being able in reading, interpreting,
constructing tables and graphs, as well as producing written texts using data
communication, in a way to promote statistical literacy, an essential aspect of
statistical education. Aiming the goals, the didactic proposal was structured into two
teaching sequences: one about conscious water consumption and another on the
relationship between consumption and waste production. Based on the proposal of "Landscapes of Investigation," according to Critical Mathematics Education perspective, which encourages students to explore and reflect not only on numbers of a mathematical problem but also on the social, political, and economic issues related to it. The teaching sequences use data coming from the school community itself, which fosters student engagement, since they work with information to their own reality, which also enables the teacher to better understand the students' reality.