This work presents an alternative method for teaching the concept of Arithmetic Mean using musical data such as the sound frequency of notes emitted by students while singing. Its main objective is to answer the following question: is the perception that, in any musical performance, the audience seems to sing in tune even if there are out-oftune individuals within it true or illusory? The research also aimed to verify if this interdisciplinary Physical-Mathematical-Musical method contributed to student learning. To this end, two classes were taught. Before the classes, a questionnaire was used to assess students' knowledge of music and statistics. During the classes, two introductory exercises on statistical concepts were proposed: mean, mode, median, and standard deviation; a musical practice in which students sang some notes in chorus from the song "Twist and Shout" by The Beatles; and at the end of the second class, a final questionnaire, identical to the first, was suggested. This experiment was conducted with a class of 9th-grade students in the municipality of Canoas, Rio Grande do Sul. The teaching approach used online tuners to measure the frequencies of the students' voices and Google Sheets to calculate the arithmetic mean. This dissertation shows that the Arithmetic Mean of the frequencies emitted by the students' (audience's) voices approximates the original frequency of the music and, in this way, gives meaning to this important statistical concept. The final questionnaire revealed that a large portion of the students significantly understood the concept of the average. 

Over the years, with each new edition of the OBMEP (Brazilian Educational Standards) administered to the classes I worked with, the perception grew that the questions that most intrigued students were those involving pure logical reasoning, without the need for specific mathematical knowledge. Incredulous, students questioned whether they would need to do any "additives" for these questions. This perception sparked the idea of bringing logic problems, like those found in puzzle magazines, into the classroom as a tool to sharpen students' reasoning. The BNCC (Brazilian National Curricular Framework) identifies logical reasoning as a skill to be developed in elementary and high school students, although it maintains its connection to mathematical content. This view can reinforce the idea that finding patterns, formulating problem-solving strategies, and investigating hypotheses are less mathematical. However, entire fields of mathematical knowledge, such as graph theory, emerged from mere speculation about puzzles that piqued curious minds. This dissertation seeks to create a space for logical questions to take center stage, with a view to implementing the teaching of propositional and predicate logic. These logic questions, which are excluded from the curriculum but are essential for equipping students with tools that help guide their reasoning, are used as a reference. To this end, the OBMEP logic questions are used as a reference, offering an interesting starting point for working with problem-solving methodology.

This study researches the mathematical concepts mobilized and the procedures employed by 2nd-year high school students in the construction of three-dimensional miniatures representing parts of their school environment based on a pedagogical approach grounded in Critical Mathematics Education and the Maker Culture. This is a qualitative research, with a descriptive objective,conducted during Mathematics and Problem-Solving classes, where the mathematical content was not taught in isolation but required and applied by students throughout the development of the miniature construction project. The didactic proposal was structured with collective moments and small groups, each group was responsible for reproducing a different school building at a reduced scale based on its architectural features and a scale reduction defined by the class. The dynamics encouraged the mobilization of various mathematical concepts, which were discussed by the class and shared during the project and a final seminar. The project development required collaborative strategies to obtain real measurements of the buildings, record data and critically analyze them, allowing the flat modeling of three-dimensional structures through softwares such as MakerCase and RDWorks. Thus, the activity demanded practical application of concepts such as proportion, similarity, trigonometry, plane and solid geometry, besides skills in organization, planning, technology use, critical investigation and group decision-making. A key moment of the project was the visit to the LabMaker at IFRS – Canoas campus, where the models were materialized through laser cutting and engraving on MDF boards. This visit expanded the students’ educational and professional horizons by exposing them to the resources available at the institution. The data collection involved questionnaires, written records, observations and digital files produced by students and the researcher, with the teacher's interventions limited to guidance and clarification of doubts, so fostering students’ autonomy and confidence during the project. The proposal enhanced students’ understanding of their active role in the learning process and their perception of mathematics as a tangible and ubiquitous tool for solving real-world problems. Student feedback also highlighted that activities involving exploration and practical application of concepts beyond the classroom walls, along with collaborative work, made learning and knowledge consolidation more meaningful.

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This study presents the development, implementation, and analysis of a didactic
sequence designed to teach fundamental concepts of statistical sampling in Basic
Education. The proposal was structured with the aim of bringing students closer to real
processes of producing and interpreting statistical information, promoting the
understanding of population, sample, representativeness, sample size, and different
probabilistic sampling methods. To this end, low-cost concrete materials, such as
bottle caps and simulated urns, were employed, enabling the practical and easily
replicable execution of statistical procedures that are often addressed only at an
abstract level. Grounded in theoretical references on Statistics Education, the

sequence sought to foster active knowledge construction through hands-on activities,
guided investigations, and the analysis of real and simulated data. The classroom
implementation revealed high levels of student engagement, as well as significant
progress in understanding key sampling concepts and in interpreting statistical results
in everyday contexts. The findings indicate that didactic strategies based on the use of
physical materials, simulation, and contextualization are effective pathways for
developing statistical thinking in high school, reinforcing the importance of
pedagogical approaches that integrate theory, practice, and active student
participation.

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.