BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS
type: channel
description: The Brazilian Electronic Journal of Mathematics (BEJOM) is a publication from the Mathematics Department of the Institute of Exact and Natural Sciences of Pontal (ICENP) at the Federal University of Uberlândia (UFU). It serves as a platform for scientific registration and dissemination, offering open access. The primary objectives of BEJOM are to publish results, whether final or partial, of scientific research; reviews of scientific or academic productions; reports of experiences; and educational products obtained in professional master's programs. These contributions should fall within the scope of education, probability and statistics, pure and applied mathematics, demonstrating consistency and rigor in their approach. All submissions must be original and unpublished. Hosted on the Portal de Periódicos da UFU, , the journal holds the eISSN 2675-1313, and each article is identified with an individual DOI (Direct Object Identifier). From 2020 to 2022, the journal followed an annual publication format with two issues (Jan/Jun and Jul/Dec), published semiannually. Starting in 2023, BEJOM transitioned to continuous flow publication in annual volumes. With the adoption of this model, there is no longer a need to wait for the final composition of the volume before publishing each article. The publication timeline now depends solely on the anonymous peer review process, ensuring agility in the communication and dissemination of research.
publisher: Portal de Periódicos UFU
language: pt-BR
publication name: BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS
issn: 2675-1313
copyright: Articles published from 2025 onwards are licensed under the CC BY 4.0 license. By submitting material for publication, authors automatically agree to the journal’s editorial guidelines and affirm that the text has been properly reviewed. Simultaneous submission of articles to other journals is prohibited, as is the translation of articles published in this journal into another language without proper authorization. Articles published prior to 2025 are licensed under the CC BY-NC 4.0 license.
items: Modeling and simulations of pollutants dispersion in the Lagoa dos Patos
items: Relationships between creating digital games and mathematics learning in education
items: Preface
items: Summary
items: Some results on periodic orbits of functions
items: Mathematical modeling with the SIR model applied to epidemiology: a bibliographic study
items: Mapping and analysis of the presence of Mathematics [Education] in Pedagogy Courses in Minas Gerais
items: A note on the generalized bi-periodic Lucas-balancing numbers
items: Singularities as generators of signal constellations and hyperbolic triangles
items: Practical applications of matrices and linear transformations with GeoGebra
items: PIBID mathematical literacy and reflective writing:
items: Use of didactic sequence for teaching functions in high school: a study atthe Colégio Militar de Brasília
items: On repunit polynomials sequence
items: Numerical verification of the singularity of Newtonian flow in a 4:1 contraction via the streamfunction-vorticity formulation
items: https://seer.ufu.br/index.php/BEJOM/article/view/74670
items: Binary numbers, finite fields and polynomial division, making a QR Code
items: One an alternative method for solving fourth degree polynomial equations
items: Pythagoras’ Theorem
items: The Hermite normal form
items: Presentation
items: The becoming of the teacher who teaches mathematics in multi-grade schools in the countryside: affects and subjectivities at play
items: Complex Structures on Real Vector Spaces
items: The use of the Vicmeter as an instrument for the study of trigonometric concepts in the rectangle triangle
items: A note on the Tetrarrin sequence
items: Fractals in nature and Mathematical Modelling
items: Mapping of published productions on the presence of Digital Technologies and Mathematics Education in teacher training (2012-2021)
items: Didactic guide for teaching practice for teaching mathematics
items: The perceptions of undergraduate students and teachers who teach Mathematics about Dyscalculia
items: Narrative mobilizations and teacher training (Mathematics): potential of diaries and portfolios

Modeling and simulations of pollutants dispersion in the Lagoa dos Patos
type: item
description: The survival of life on planet Earth depends on essential natural resources, such as water. The growth of industrialization and urbanization has had a major impact on ecosystems and biodiversity, which, like people, need water bodies. This article presents a study on the dispersion of pollutants in aquatic environments, using mathematical modeling and computer simulations. The model used was built based on the diffusion-advection equation, an equation that deals with both the movement and dispersion of the pollutant. The numerical solutions were obtained via computational implementation of the finite difference method, in Python language. To apply the proposed model, Lagoa dos Patos, the largest lagoon in Brazil, located in the southern region of the country, was chosen as the domain. The simulations presented in this work mainly sought to explore different situations and, for this, some scenarios were created, considering different values for the diffusion coefficient and wind regime. The results allow us to observe how the pollutant behaves in the lagoon, explaining its movement, dispersion and concentration rate over time. Once results like these are obtained, it becomes possible to develop strategies to contain and clean the pollutant, contributing to minimizing damage caused to the aquatic environment.
subject: Applied Mathematics
  topic: section
subject: Advection-diffusion equation
  topic: keywords
subject: finite difference method
  topic: keywords
subject: Lagoa dos Patos
  topic: keywords
subject: pollutants
  topic: keywords
creator: Ludmila Vitória Ribeiro Rocumba
creator: Graciele Paraguaia Silveira
rights: Copyright (c) 2024 Ludmila Vitória Ribeiro Rocumba, Graciele Paraguaia Silveira https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-03
publication date: 2024-07-03
starting page: 1
ending page: 20
doi: 10.14393/BEJOM-v5-2024-72489

Relationships between creating digital games and mathematics learning in education
type: item
description: This research investigates the interaction of elementary school students with the technological and educational resource Scratch, with the aim of instructing them about block programming and exploring mathematical knowledge. The study is conducted through a qualitative approach, using the ethnographic case study method. The participants are eight 6th year students from a public school in Catalão-GO, and the project is carried out in the school’s IT Laboratory, during after-school hours, in 2019. Students play digital games as a way of familiarizing themselves with the technology and computational language, promoting the development of cognitive and creative skills. The main objective of the research is to answer the question: “What are the contributions of Scratch to the teaching and learning of Mathematics in Elementary School?”. The data was found through interviews, observations and photographic records of the students’ activities, being analyzed along two axes: “Learning about and with Scratch” and “Producing with Scratch”. The results revealed that the participants acquired mathematical concepts and basic notions of programming, highlighting Computational Logic, the Cartesian Plane and Fractions as prominent areas.
subject: Dossiê - SiTAPEM
  topic: section
subject: Mathematics
  topic: keywords
subject: programming
  topic: keywords
subject: Scratch
  topic: keywords
subject: digital games
  topic: keywords
creator: Taynara Derci Babugem Mesquita
creator: Crhistiane da Fonseca Souza
creator: Fernando da Costa Barbosa
rights: Copyright (c) 2024 Taynara Derci Babugem Mesquita, Crhistiane da Fonseca Souza, Fernando da Costa Barbosa https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-12
publication date: 2024-07-12
starting page: 133
ending page: 150
doi: 10.14393/BEJOM-v5-2024-71832

Preface
type: item
subject: Expediente
  topic: section
creator: Tânia Maria Machado de Carvalho
creator: Milena Almeida Leite Brandão
creator: Vlademir Marim
creator: Vinícius Sanches Tizzo
rights: Copyright (c) 2025 Vlademir Marim, Milena Almeida Leite Brandão, Tânia Maria Machado de Carvalho https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 6
doi: 10.14393/BEJOM-v6-2025-78033

Summary
type: item
description: Volume 5 of the Brazilian Electronic Journal of Mathematics (BEJOM), published in 2024, presents a diverse set of contributions in both mathematical research and mathematics education. The articles address topics ranging from teacher training and the use of digital technologies in education to theoretical and applied studies in pure and applied mathematics. Highlights include analyses of teaching in multigrade classrooms, the use of the Vicmetro in trigonometry education, and investigations into complex structures in real vector spaces. The volume also features papers on many-valued logic, polynomial sequences (such as Repunit and Tetrarrin sequences), alternative solutions to fourth-degree equations, and applied studies such as modeling pollutant dispersion in the Patos Lagoon and numerical verification of Newtonian flow. This edition reinforces BEJOM's commitment to a plurality of mathematical approaches, connecting pedagogy, academic research, and real-world problem solving.
subject: Summary
  topic: section
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-04-30
publication date: 2025-04-30
starting page: 1
ending page: 2
doi: 10.14393/BEJOM-v5-2024-77936

Preface
type: item
subject: Expediente
  topic: section
creator: Edward Luis de Araújo
creator: Evaneide Alves Carneiro
creator: Milena Almeida Leite Brandão
creator: Patrícia Borges dos Santos
creator: Tânia Maria Machado Carvalho
rights: Copyright (c) 2025 Edward Luis de Araújo, Evaneide Alves Carneiro, Milena Almeida Leite Brandão, Patrícia Borges dos Santos, Tânia Maria Machado Carvalho https://creativecommons.org/licenses/by/4.0
date: 2025-04-30
publication date: 2025-04-30
doi: 10.14393/BEJOM-v6-2025-77930

Some results on periodic orbits of functions
type: item
description: In this work we will study several concepts related to real continuous functions in one variable, highlighting results related to fixed points, periodic orbits and the Li-Yorke Theorem. This last theorem establishes that if a real function applies the interval [a,b] to itself and has a point of period three, then it will have periodic points of any positive integer period. The results will be obtained mainly through applications of the Intermediate Value Theorem and Brouwer Fixed Point Theorem, two classic results in Mathematics, whose formulation and geometric interpretations are relatively simple and whose applications are quite relevant in several sciences.
subject: Pure Mathematics
  topic: section
subject: Periodic points
  topic: keywords
subject: periodic orbits
  topic: keywords
subject: Intermediate Value Theorem
  topic: keywords
subject: Li-Yorke Theorem
  topic: keywords
creator: Mayara Beatriz Ferreira Drumond
creator: Wenderson Marques Ferreira
creator: Eder Marinho Martins
rights: Copyright (c) 2025 Mayara Beatriz Ferreira Drumond , Wenderson Marques Ferreira, Eder Marinho Martins https://creativecommons.org/licenses/by/4.0
date: 2025-09-26
publication date: 2025-09-26
starting page: 1
ending page: 19
doi: 10.14393/BEJOM-v6-2025-76862

Mathematical modeling with the SIR model applied to epidemiology: a bibliographic study
type: item
description: The present research aimed to carry out a bibliographic study of applying the SIR model in some studies of epidemic or pandemic situations for some States in Brazil. The methodology was to review some works that address applications of differential equations using SIR from which three works were chosen for analysis: the first dealing with hepatitis A in the municipality of Juruti in Pará, the second dealing with dengue fever in Mossoró in Rio Grande do Norte; and the third dealing with the spread of COVID 19 in the State of Maranhao. The research results indicated that the use of modeling tools, such as the SIR model, can be fundamental in helping to understand how contagious diseases spread, this allows public authorities to make the most appropriate decisions to mitigate the disease and the collateral problems that it causes to the population.
subject: Applied Mathematics
  topic: section
subject: Epidemiology
  topic: keywords
subject: spread of disease
  topic: keywords
subject: SIR model
  topic: keywords
creator: Marcio Costa Araújo Filho
creator: Reginaldo Tudeia dos Santos
creator: Letícia Alencar Mendes Martinho
rights: Copyright (c) 2025 Marcio Costa Araújo Filho, Reginaldo Tudeia dos Santos, Letícia Alencar Mendes Martinho https://creativecommons.org/licenses/by/4.0
date: 2025-11-28
publication date: 2025-11-28
starting page: 1
ending page: 18
doi: 10.14393/BEJOM-v6-2025-77209

Mapping and analysis of the presence of Mathematics [Education] in Pedagogy Courses in Minas Gerais
type: item
description: In this article, we present the results of mapping Pedagogy courses in the State of Minas Gerais, Brazil, and analyzing how they have incorporated mathematics [education]. To this end, a survey was carried out on the e-MEC website for Pedagogy courses in Minas Gerais. Data was crossed from the websites of institutions that offer these courses, which also served as a basis for collecting qualitative data (pedagogical projects, among others). Quantitative data were organized and described using Descriptive Statistics tools. Their analysis and the titles of compulsory disciplines involving mathematics [education] (qualitative data) were carried out based on the assumptions of the Model of Semantic Fields and the study of bibliographies on training in Pedagogy. As results, we point out the lack of data on Pedagogy courses offered by private institutions, low workload allocated to compulsory disciplines that involve mathematics [education], offering of these disciplines, predominantly, from the second half of the course, titles that they privilege methodologies that distinguish Early Childhood Education from the early years of Elementary School and that incorporate theorizations of Mathematics Education. We conclude that there is a need for in-depth analyzes relating the titles with the programs of the disciplines and research involving teacher trainers working in Pedagogy courses.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Mapping
  topic: keywords
subject: pedagogy
  topic: keywords
subject: initial training of teachers who teach mathematics
  topic: keywords
subject: Mathematics Education
  topic: keywords
creator: Rejane Siqueira Julio
creator: Vanessa Nogueira Oliveira
creator: Guilherme Henrique Gomes da Silva
creator: Denismar Alves Nogueira
rights: Copyright (c) 2025 Rejane Siqueira Julio, Vanessa Nogueira Oliveira, Guilherme Henrique Gomes da Silva, Denismar Alves Nogueira https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 21
doi: 10.14393/BEJOM-v6-2025-74304

A note on the generalized bi-periodic Lucas-balancing numbers
type: item
description: In this study, we introduce a new class of integers called the sequence of generalized bi-periodic Lucas-balancing numbers, which extends the well-known sequence of Lucas-balancing numbers. We present several fundamental properties, including the deduction of the corresponding generating function, as well as homogeneous and non-homogeneous recurrence relations associated with this new sequence. We also formulate generalized versions of Binet's formulas for these numbers. In addition, we investigated the validity of several classical identities within this new context, such as the Tagiuri-Vajda, d'Ocagne, Catalan, and Cassini identities, considering the two different cases of the discriminant value of the equation polynomial associated with the recurrence relation. These extensions contribute to a structural and algebraic deepening of the properties of Lucas-balancing numbers.
subject: Pure Mathematics
  topic: section
subject: Lucas-balancing sequence
  topic: keywords
subject: bi-periodic sequence
  topic: keywords
subject: identities
  topic: keywords
subject: analytic representations
  topic: keywords
creator: Eudes Antonio Costa
creator: Elen Viviani Pereira Spreafico
creator: Paula Maria Machado Cruz Catarino
rights: Copyright (c) 2025 Eudes Antonio Costa, Elen Viviani Pereira Spreafico, Paula Maria Machado Cruz Catarino https://creativecommons.org/licenses/by/4.0
date: 2025-06-16
publication date: 2025-06-16
starting page: 1
ending page: 15
doi: 10.14393/BEJOM-v6-2025-75273

Singularities as generators of signal constellations and hyperbolic triangles
type: item
description: In this work, three regular singularities of fuchsian differential equations will be considered, one of them being infinity, as generators of signal constellations and as vertices of a hyperbolic polygon, in order to establish a connection with error analysis in a discrete memoryless channel and in a geometrically uniform code. The procedure is based on the following steps: given two complex points and the infinite: (1) consider these points as singularities of a fuchsian differential equation; (2) generate constellations of signals on the complex plane from the obtained singularities; (3) consider the existence of a perfect or quasi-perfect code on the signals constellation and their ability to correct errors; (4) analyze these singularities as vertices of a hyperbolic triangle to identify the genus of the associated surface, through the pairings of the sides of this triangle; (5) verify which channel is associated with the same genus, and thus represent the vertices of the hyperbolic triangle as channel inputs and outputs; (6) analyze the channel associated with the codewords to verify the error probability of the transmitted singularity. Through the results obtained, it can be concluded that singularities with the opposite real part generate perfect and/ or quasi-perfect codes with the same ability to correct errors. It was possible to represent the codewords as inputs and outputs of a discrete memoryless channel, showing that the probability of error, p, is related to the number of codewords on the constellation. When considering singularities as vertices of a hyperbolic triangle, a connection was established with the symmetric binary channel C2.2, whose inputs and outputs represent pairs of opposite singularities relative to the imaginary axis. The established connections can be applied to error analysis in an information transmission process.
subject: Applied Mathematics
  topic: section
subject: Geometrically uniform codes
  topic: keywords
subject: Fuchsian equations
  topic: keywords
subject: communication channels
  topic: keywords
creator: Mariana Gabriela Gusmão
creator: Anderson José de Oliveira
rights: Copyright (c) 2025 Mariana Gabriela Gusmão, Anderson José de Oliveira https://creativecommons.org/licenses/by/4.0
date: 2025-04-30
publication date: 2025-04-30
starting page: 1
ending page: 20
doi: 10.14393/BEJOM-v6-2025-73876

Practical applications of matrices and linear transformations with GeoGebra
type: item
description: In this paper we present linear algebra concepts used in computer graphics. The content related to matrices and linear transformations often raises doubts in high school and college students because it is very theoretical. One way of strengthening the learning of this content is by presenting its applications. The dynamic geometry \textit{software} GeoGebra was used to demonstrate two practical applications that allow users to interact dynamically to learn concepts of linear transformations such as shear, contraction, dilation and reflections. In addition, two applications of the Fundamental Theorem of Linear Algebra were demonstrated.
subject: Applied Mathematics
  topic: section
subject: Linear algebra
  topic: keywords
subject: graph computing
  topic: keywords
subject: GeoGebra
  topic: keywords
subject: matrices
  topic: keywords
subject: Linear transformations
  topic: keywords
creator: Clésio Rodrigues da Silva Júnior
creator: Vania de Fátima Lemes de Miranda
creator: Giselle Moraes Resende Pereira
creator: Eduardo dos Santos Rocha
creator: Luis Florial Espinoza Sánchez
creator: Danilo Elias de Oliveira
rights: Copyright (c) 2025 Clésio Rodrigues da Silva Júnior, Vania de Fátima Lemes de Miranda, Giselle Moraes Resende Pereira, Eduardo dos Santos Rocha, Luis Florial Espinoza Sánchez, Danilo Elias de Oliveira https://creativecommons.org/licenses/by/4.0
date: 2025-04-30
publication date: 2025-04-30
starting page: 1
ending page: 19
doi: 10.14393/BEJOM-v6-2025-74190

PIBID mathematical literacy and reflective writing:
type: item
description: The present work aims to reflect on how reflective writings based on delight readings contribute to the tension of hegemonic teaching practices. The activities were developed in the Institutional Teaching Initiation Scholarship Program (PIBID) at Universidade of Minas Gerais, Unit Ibirité. The description of the experiences was based on the reflective writing of one of the Pibidians, based on her experiences in the context of a 2nd year elementary school class in the public school system in Ibirité. We believe that the opportunity to reflect on the experience was an important way for the student to identify points of conflict and concerns regarding ethnic-racial issues and her future teaching practice. This also gave us the opportunity to reflect on mathematics, its teaching and the relationship between this field of knowledge and the appreciation of different cultures.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Teacher training
  topic: keywords
subject: mathematics teaching
  topic: keywords
subject: reflective writing
  topic: keywords
creator: Janaina Silva
creator: Kemily Lopes da Silva
creator: Danielle Alves Martins
rights: Copyright (c) 2025 Janaina Silva, Kemily Lopes da Silva, Danielle Alves Martins https://creativecommons.org/licenses/by/4.0
date: 2025-11-12
publication date: 2025-11-12
starting page: 1
ending page: 15
doi: 10.14393/BEJOM-v6-2025-74615

Use of didactic sequence for teaching functions in high school: a study atthe Colégio Militar de Brasília
type: item
description: This article analyzes a didactic sequence applied to teaching functions in the 1st year of high school at the Colégio Militar de Brasília, covering concepts such as affine and quadratic functions. The methodology included an initial questionnaire, diagnostic assessments, structured interviews, lectures, guided study and activities with Geogebra. The results reveal that students face difficulties in recognizing mathematical notations in function theory and in contextualized problems. However, they demonstrate that the initial activities of the didactic sequence contributed to improving classes and facilitating understanding of the content about functions. The study highlights the importance of the applicability of diverse and adaptive methodologies to overcome gaps in knowledge that exist among students in the Mathematics discipline.
subject: Mathematics Education
  topic: section
subject: Functions
  topic: keywords
subject: methodology
  topic: keywords
subject: didactic sequence
  topic: keywords
subject: diagnostic assessments
  topic: keywords
creator: Michelle Ramos von Borries
creator: Luciana Maria Dias de Ávila Rodrigues
rights: Copyright (c) 2025 Michelle Ramos von Borries, Luciana Maria Dias de Ávila Rodrigues https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 19
doi: 10.14393/BEJOM-v6-2025-75670

On repunit polynomials sequence
type: item
description: In this paper, we define a sequence of polynomials associated with the repunit numerical sequence. This involves extending the concept of the repunit sequence, a sequence type Horadam, represented by the sequence of repunit numbers, where rₙ represents the n-th repunit, and the recurrence relation: rₙ₊₁ = 11rₙ-10rₙ₋₁, with r₀ = 0, r₁ = 1 for n ≥ 1. In this paper, we investigate this new polynomial sequence in detail and present some results and applications derived from this investigation. For instance, we study the characteristic equation and derive the corresponding generating function. Additionally, we analyze the recurrence relation associated with the sum of n repunit polynomials.
subject: Pure Mathematics
  topic: section
subject: Polynomial repunit
  topic: keywords
subject: repunit number
  topic: keywords
subject: sequence
  topic: keywords
creator: Eudes Antônio Costa
creator: Fernando Soares de Carvalho
rights: Copyright (c) 2024 Eudes Antonio Costa, Fernando Soares de Carvalho https://creativecommons.org/licenses/by-nc/4.0
date: 2024-11-28
publication date: 2024-11-28
starting page: 1
ending page: 15
doi: 10.14393/BEJOM-v5-2024-72280

Numerical verification of the singularity of Newtonian flow in a 4:1 contraction via the streamfunction-vorticity formulation
type: item
description: In this study, the asymptotic behavior of the velocity field and vorticity around a reentrant corner is investigated. The analysis is conducted through numerical simulations of Newtonian flow in a 4:1 contraction, using the streamfunction-vorticity formulation. The equations describing this flow were discretized using the finite difference method, and the numerical code was implemented in the C programming language. The robustness of the asymptotic behavior is evaluated under three distinct conditions: variations in the Reynolds number, the use of geometries with different lengths, and the comparison of results with those obtained by the Marker-And-Cell (MAC) approach. The main objective of this work is to validate the prediction of the asymptotic behavior near the geometric singularity and to demonstrate the independence of this phenomenon concerning variations in operational parameters and the extension of the contraction geometry. The investigation also addresses the comparative effectiveness of the streamfunction-vorticity and MAC methodologies, highlighting the good agreement between the formulations. The results indicate that, although both approaches can capture the fundamental behavior of the flow, differences still exist at points closest to the singularity, suggesting the need for improvements in computational models for simulating flows with complex geometric characteristics.
subject: Applied Mathematics
  topic: section
subject: Newtonian flow
  topic: keywords
subject: 4:1 contraction
  topic: keywords
subject: streamfunction-vorticity formulation
  topic: keywords
subject: singularity
  topic: keywords
creator: Irineu Lopes Palhares Junior
creator: Larissa Vitória Ribeiro de Andrade
rights: Copyright (c) 2024 Irineu Lopes Palhares Junior, Larissa Vitória Ribeiro de Andrade https://creativecommons.org/licenses/by-nc/4.0
date: 2024-12-05
publication date: 2024-12-05
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v5-2024-73402

https://seer.ufu.br/index.php/BEJOM/article/view/74670
type: item
title: "A posture I would adopt"; "... made me think what kind of teacher I want to be..."; "... I want to make a difference in the lives of my students...": the impact of a course on the formation of the teaching identity of the future Mathematics teacher.
description: This article seeks to understand how the textualization of a semi-structured interview with a mathematics teacher and the writing of a memorial, carried out in the context of a discipline in the first period of a Mathematics degree course, influence the process of constructing teachers' teaching identity in initial training. The theoretical foundation of this study is based on (Deschamps; Moliner, 2009) and (Takahashi; Lorencini Júnior, 2019) who deal with the constitution of professional identity from the perspective of social psychology. The research methodology consisted of qualitative documentary analysis of two works carried out in the discipline (the textualization of the interview and the elaboration of a memorial) by three Mathematics graduates. The results indicate that both the writing of the memorial and the textualization of the interview developed in the discipline generate representations of teaching and promote the recognition of belonging to the social group of teachers. In addition to providing undergraduate students with direct contact with reflections related to teaching, which enabled integration into the group of teachers and distinction in relation to the group of students.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Identity
  topic: keywords
subject: teacher education
  topic: keywords
subject: mathematics teacher
  topic: keywords
creator: Carlos Eduardo Petronilho Boiago
creator: Viviane de Andrade Vieira Almeida
rights: Copyright (c) 2025 Carlos Eduardo Petronilho Boiago, Viviane de Andrade Vieira Almeida https://creativecommons.org/licenses/by/4.0
date: 2025-07-08
publication date: 2025-07-08
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v6-2025-74670

Binary numbers, finite fields and polynomial division, making a QR Code
type: item
description: Through a bibliographical review, we present all the processes of how a QR Code model 1, version 1, is made and the mathematical theories involved, making it possible to create a functional QR Code. We comment on how to write the data in the form of binary numbers, the correspondence between writing a number in base ten and in base two (binary). We emphasize the subject of finite fields, with a polynomial view, this subject being necessary to write the error correcting code data into a QR Code.
subject: Applied Mathematics
  topic: section
subject: Finite field
  topic: keywords
subject: polynomial
  topic: keywords
subject: euclidean division
  topic: keywords
creator: José Laudelino de Menezes Neto
rights: Copyright (c) 2025 José Laudelino de Menezes Neto https://creativecommons.org/licenses/by/4.0
date: 2025-05-28
publication date: 2025-05-28
starting page: 1
ending page: 21
doi: 10.14393/BEJOM-v6-2025-74898

One an alternative method for solving fourth degree polynomial equations
type: item
description: This article presents an alternative method for solving fourth degree polynomial equations. Although such a result had already been aimed for some time ago, back in the 16th century, by the Italian mathematician Lodovico Ferrari, this work gains originality for being relatively outside of other methods previously discussed. In this work, we will present two original theorems and two corollaries. We will start by introducing a special model of a fourth degree polynomial, which allows us to clearly visualize all its roots. Next, we will demonstrate the main result of this study: the ability to convert any generic fourth-degree polynomial into a special format, thus facilitating the identification of its roots. This method offers a different perspective on solving complex polynomial equations, providing a clear and systematic framework for dealing with problems that have defied conventional methods. Finally, practical examples will be presented that illustrate the application of this method. It is hoped that this result can serve as inspiration and basis for future work that addresses this topic in contemporary mathematics.
subject: Pure Mathematics
  topic: section
subject: Polynomial equations
  topic: keywords
subject: roots of equations
  topic: keywords
subject: fourth degree polynomial
  topic: keywords
creator: Edvalter da Silva Sena Filho
creator: Ailton Campos do Nascimento
rights: Copyright (c) 2024 Edvalter da Silva Sena Filho, Ailton Campos do Nascimento https://creativecommons.org/licenses/by-nc/4.0
date: 2024-12-02
publication date: 2024-12-02
starting page: 1
ending page: 13
doi: 10.14393/BEJOM-v5-2024-74272

Pythagoras’ Theorem
type: item
description: The present article is an excerpt from a master's thesis aimed at investigating the potentials and limitations of a structured teaching intervention using tactile materials on the Pythagorean theorem for visually impaired students. The qualitative study, conducted in the form of a case study, was grounded in Vygotsky's sociocultural theory and involved two blind students attending the 2nd year of high school in two public schools located in the municipalities of Barueri and Itapevi, in the state of São Paulo. The results indicated that the interaction of the students with the adapted material and the mediation of the teacher allowed the participants to articulate the zone of proximal development, the level of actual development, and the level of potential development, making the transformation of potential and actual development evident.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Pythagoras’ theorem
  topic: keywords
subject: visual impairment
  topic: keywords
subject: geometry teaching
  topic: keywords
subject: sociocultural theory
  topic: keywords
creator: Nasael Martins Luiz
creator: Rogério Fernando Pires
rights: Copyright (c) 2025 Nasael Martins Luiz, Rogério Fernando Pires https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v6-2025-72733

The Hermite normal form
type: item
description: The Hermite normal form is similar of reduced echelon form for matrices with integer entries. In this article some results on this topic are presented, among which we highlight the existence and uniqueness Theorem, which states that every matrix is row equivalent to one, and only one, matrix in the Hermite normal form. An algorithm for computing the Hermite normal form of a matrix by the elementary unimodular operations is also given. Finally, some concepts and preliminary results on lattices are presented, including three problems that are answered using the Hermite normal form, namely, the problem of finding a basis of a lattice and the problems of equality and union of lattices.
subject: Pure Mathematics
  topic: section
subject: Hermite normal form
  topic: keywords
subject: unimodular matrices
  topic: keywords
subject: lattices
  topic: keywords
creator: Paola Assis Rola
creator: Eleonesio Strey
rights: Copyright (c) 2025 Paola Assis Rola, Eleonesio Strey https://creativecommons.org/licenses/by/4.0
date: 2025-08-20
publication date: 2025-08-20
starting page: 1
ending page: 21
doi: 10.14393/BEJOM-v6-2025-73442

Presentation
type: item
description: It is with great satisfaction that the Editorial Board of the BEJOM journal presents the dossier "Trajetórias e Aprendizagens de Professores que Ensinam Matemática." The articles that make up this volume are part of the work presented at the Symposium on "Trajetórias e Aprendizagens de Professores que Ensinam Matemática" (SiTAPEM). This is a national event, created in 2023 with the aim of promoting interaction among students, teachers, and researchers in the field of mathematics education, integrating elementary and secondary schools, higher education institutions, and the community (which often interacts indirectly). This collection of articles represents a significant contribution to the understanding of the complex professional trajectories and learning processes experienced by mathematics educators.
subject: Editorial
  topic: section
creator: Editores do BEJOM e organizadores do SiTAPEM
rights: Copyright (c) 2024 Editores do BEJOM e organizadores do SiTAPEM https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-12
publication date: 2024-07-12
starting page: ii
ending page: vii

The becoming of the teacher who teaches mathematics in multi-grade schools in the countryside: affects and subjectivities at play
type: item
description: The trajectory followed within Rural Education is neither new nor recent, but it inaugurates a new paradigm of consciousness in the fight for public policies that guarantee rural workers some rights, such as the right to education and a living school where knowledge peasants are respected and valued. In this sense, with the present work, we seek to understand the constitution of the self and its subjectivities regarding the teaching subject that enters the territory of Rural Education. This game was very important because we observed the passes and plays that served as a kick-off for future games of new, more in-depth studies in the area of ​​mathematics in Rural Education, as some teachers demonstrate, through narrative maps, an attachment to practiced mathematics and aimed at urban schools. This is a text that converges with the studies of Deleuze and Guattari, which point to the Philosophy of Difference as surrounded by multiplicity, singularity, becoming, alterity and subjectivity. Therefore, we consider these aspects when studying the teacher. We use the concepts of becoming, rhizome, subjectivation, device, outside, vibrating body, cartography, lines of force and territories, as they are compatible with the expression of emotions based on bodily vibrations.
subject: Mathematics Education
  topic: section
subject: Rural education
  topic: keywords
subject: cartography
  topic: keywords
subject: philosophy of difference
  topic: keywords
subject: maths teacher
  topic: keywords
subject: subjectivity
  topic: keywords
creator: Lucilio Halter Sobral Mendes
creator: Simone Moura Queiroz
rights: Copyright (c) 2024 Lucilio Halter Sobral Mendes, Simone Moura Queiroz https://creativecommons.org/licenses/by-nc/4.0
date: 2024-12-24
publication date: 2024-12-24
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v5-2024-74242

Complex Structures on Real Vector Spaces
type: item
description: In this article, complex structures in real vector spaces are studied from an algebraic perspective. One of the main results guarantees the existence and uniqueness of complex structures, up to equivalence, in spaces of even dimension or infinite dimension. Additionally, a description of the set of complex structures as a homogeneous space of the general linear group is presented, and finally, it is shown how to construct complex structures in some different settings from known complex structures. There is a lack of a comprehensive and detailed text in the literature with complete proofs of these results, and one of the objectives of this article is precisely to help fill this gap.
subject: Pure Mathematics
  topic: section
subject: Complex structure
  topic: keywords
subject: complex vector spaces
  topic: keywords
subject: linear algebra
  topic: keywords
creator: Daniel Rotmeister Teixeira de Barros
creator: Laércio José dos Santos
rights: Copyright (c) 2024 Daniel Rotmeister, Laércio dos Santos https://creativecommons.org/licenses/by-nc/4.0
date: 2024-10-01
publication date: 2024-10-01
starting page: 1
ending page: 21
doi: 10.14393/BEJOM-v5-2024-73258

The use of the Vicmeter as an instrument for the study of trigonometric concepts in the rectangle triangle
type: item
description: Faced with the difficulties of students, with regard to the assimilation of mathematical content, and of a portion of teachers, with regard to the lack of didactic resources, research has been carried out in recent years with the aim of producing concrete and manipulable materials to help in teaching mathematics, and one of them is the Vicmetro designed to mobilize mathematical knowledge, in particular, trigonometry. Thus, this study aims to present a didactic sequence using the Vicmetro to teach trigonometric concepts, with a view to mobilizing different elements of the right triangle and their trigonometric ratios. For this, it was based on qualitative research, whose procedures were based on bibliographical research and finally, a didactic sequence involving this instrument was produced. It was composed of two activities, both involving the Vicmetro, but with different focuses, the first aimed to identify the different elements of a right triangle, such as angles and legs, and the second, to mobilize the different trigonometric ratios. This study is configured as an initial proposal for the use of the instrument, aiming that through it the students can not only verify a result, but put into motion different mathematical concepts around the construction of a triangle. Thus, this work seeks to promote, through a didactic sequence, a more dynamic and interactive teaching.
subject: Mathematics Education
  topic: section
subject: Vicmetro
  topic: keywords
subject: rectangle triangle
  topic: keywords
subject: trigonometric ratios
  topic: keywords
subject: following teaching
  topic: keywords
creator: Francisco Wallisson Moreira de Souza
creator: Ana Carolina Costa Pereira
creator: Antonia Naiara de Sousa Batista
rights: Copyright (c) 2024 Francisco Wallisson Moreira de Souza, Ana Carolina Costa Pereira, Antonia Naiara de Sousa Batista https://creativecommons.org/licenses/by-nc/4.0
date: 2024-12-19
publication date: 2024-12-19
starting page: 1
ending page: 22
doi: 10.14393/BEJOM-v5-2024-70708

A note on the Tetrarrin sequence
type: item
description: This study explores an extension of the Perrin sequence, defining the Tetrarrin sequence. Thus, we investigated Tetrarrin numbers and their mathematical relationships, allowing a deeper understanding of Perrin numbers. In this context, we analyze Binet?s formula, the matrix form, among other theorems, making it possible to obtain the terms of this new sequence using different methods. It is important to highlight that the Tetrarrin sequence is of higher order and derived from the Perrin sequence. For future work, we intend to integrate this content with other areas of study, in addition to using tools and software that enable the visualization of the mathematical properties of this sequence in a more intuitive and accessible way.
subject: Pure Mathematics
  topic: section
subject: Extension
  topic: keywords
subject: Perrin sequence
  topic: keywords
subject: Tetrarrin sequence
  topic: keywords
creator: Renata Passos Machado Vieira
creator: Francisco Regis Vieira Alves
creator: Paula Maria Machado Cruz Catarino
rights: Copyright (c) 2024 Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino https://creativecommons.org/licenses/by-nc/4.0
date: 2024-08-20
publication date: 2024-08-20
starting page: 1
ending page: 11
doi: 10.14393/BEJOM-v5-2024-69801

Fractals in nature and Mathematical Modelling
type: item
description: This article deals with fractals in nature, presenting an experience report that aimed to build fractal models, inspired by nature, verifying the possibilities of use in teaching and learning Mathematics in Basic Education. Fractals are discussed, focusing on botany, the main characteristics, such as self-similarity, used as a basis to characterize a natural fractal. The concept of Mathematical Modelling is also presented, the perceptions of some authors, and the relationship between this trend and fractals, which served as a reference for the organization and development of data analysis. The methodology is based on the characteristics of qualitative research in education and the Mathematical Modelling phases, in addition to exploratory research and documentary analysis as a basis for data production. The analysis of the data obtained during the research focused on the modelling process and the construction of the model in the GeoGebra software, through categories listed a priori, in line with the theory that underpins the research. The results showed that the constructed model can be classified as a physical analogy, and that, although it has not preserved the self-similarity characteristic of fractals, it is possible to be developed in Basic Education, and can collaborate with the teaching and learning of Mathematics.
subject: Mathematics Education
  topic: section
subject: Teaching mathematics
  topic: keywords
subject: fractals
  topic: keywords
subject: mathematical modelling
  topic: keywords
creator: Alan dos Santos Sousa
creator: Zulma Elizabete de Freitas Madruga
rights: Copyright (c) 2025 Alan dos Santos Sousa, Zulma Elizabete de Freitas Madruga https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 19
doi: 10.14393/BEJOM-v6-2025-73678

Mapping of published productions on the presence of Digital Technologies and Mathematics Education in teacher training (2012-2021)
type: item
description: The study aims to map scientific publications from 2012 to 2021 in journals rated as Qualis A1 and A2 in the field of Education, focusing on the presence of Digital Technologies (DT) and Mathematics Education in pedagogue training. The research has an exploratory and descriptive nature, with a qualitative approach and adopts a bibliographic mapping methodology. The study found a limited number of publications on the specific topic, highlighting that only one article is dedicated to integrating DT in the mathematical training of pedagogues. Other reviewed studies address digital technologies in teacher training in general, serving as useful references for researchers and professionals interested in this subject. The results show a significant gap in the literature, suggesting the need for further research to promote the effective inclusion of DT in pedagogue training curricula, aimed at preparing future educators for the demands of today’s digital society.
subject: Mathematics Education
  topic: section
subject: Digital technologies
  topic: keywords
subject: mathematics education
  topic: keywords
subject: pedagogue training
  topic: keywords
creator: Carloney Alves de Oliveira
creator: Wilker Araújo de Melo
creator: Mariana Tenório da Silva
rights: Copyright (c) 2024 Carloney Alves de Oliveira, Wilker Araújo de Melo, Mariana Tenório da Silva https://creativecommons.org/licenses/by-nc/4.0
date: 2024-11-26
publication date: 2024-11-26
starting page: 1
ending page: 19
doi: 10.14393/BEJOM-v5-2024-72944

Didactic guide for teaching practice for teaching mathematics
type: item
description: This article is about the educational product, entitled “Teaching Guide: a reinterpretation of teaching practice”, developed in the professional master's course, at the Federal University of Uberlândia – UFU, in the postgraduate program in Science and Mathematics Teaching, whose dissertation entitled ``Pedagogical Residency: contributions to the training of future mathematics teachers”. The objective of this educational product is to present and carry out a re-reading, among the seven activities developed by residents of the Pedagogical Residency Program – PRP in the city of Ituiutaba, state of Minas Gerais, linked to UFU. Randomly, the activity entitled Ladrilho was chosen, for reinterpretation being developed in three parts, the first, a historical approach to teacher training, the second a presentation of the activities developed by PRP residents in the city of Pontal, linked to Ituiutaba – MG, during a school Saturday, open to the school community. The third part is to develop a didactic script, by rereading the activity called tile. To appreciate the educational product, a qualitative research was carried out with the participation of twenty-four teachers from Basic Education, mathematics area, from the cities of Uberlândia, Patos de Minas and Ituiutaba. To validate this educational product, we created and applied a questionnaire using the Google Forms platform, divided into four parts: (a) teacher profile; (b) teaching activities; (c) extra-class activity and (d) appreciation of the didactic script. This questionnaire aims to analyze the contribution of the educational product to teacher training. With the result we observed the diversity of training of those surveyed, they attributed the importance of knowing the evolution of teacher training, opportunities for improvement and training more involved with theory and practice. That training must be constant and that teaching practices must be inclusive, it is necessary to participate in training programs, helpi…
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Teacher training
  topic: keywords
subject: PRP
  topic: keywords
subject: educational product
  topic: keywords
creator: Vlademir Marim
creator: Renata Cristina da Fonseca
rights: Copyright (c) 2025 Vlademir Marim, Renata Cristina da Fonseca https://creativecommons.org/licenses/by/4.0
date: 2025-06-23
publication date: 2025-06-23
starting page: 1
ending page: 16
doi: 10.14393/BEJOM-v6-2025-73591

The perceptions of undergraduate students and teachers who teach Mathematics about Dyscalculia
type: item
description: Dyscalculia is a Mathematics Learning Disorder little known by education professionals and debated in the literature. In this sense, this research aimed to investigate the perceptions about Dyscalculia of graduate students of the Mathematics Degree course and trained teachers from a university in the interior of Bahia. Adopting a qualitative approach, we conducted semi-structured and individual interviews with four participants, two undergraduate students and two basic education teachers. After producing and transcribing the data, we proceeded with analysis and discussions, based on the literature review, aiming to understand their perceptions. In this process, three categories were constructed. In the category Knowledge and identification of Dyscalculia, undergraduates stated that they knew Dyscalculia, without an in-depth explanation, while teachers were able to express some knowledge about Dyscalculia. In general, all interviewees had difficulties in identifying students with Dyscalculia. In the Use of resources and methodologies category, the interviewees indicated different strategies, but we noticed that they resolved momentary learning difficulties. And, finally, in the Importance of Training category, the interviewees pointed out that they had limited contact with this topic, representing a gap in their training. From these results, we conclude that the interviewees have limited knowledge about Dyscalculia, particularly in relation to its difficulties, as well as identifying the urgency of these discussions in the context of teacher training.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Inclusive education
  topic: keywords
subject: learning disorder
  topic: keywords
subject: dyscalculia
  topic: keywords
creator: Lilian Aragão da Silva
creator: Gabriela da Silva Santos
rights: Copyright (c) 2025 Lilian Aragão da Silva, Gabriela da Silva Santos https://creativecommons.org/licenses/by/4.0
date: 2025-06-16
publication date: 2025-06-16
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v6-2025-72948

Narrative mobilizations and teacher training (Mathematics): potential of diaries and portfolios
type: item
description: This text deals, among other aspects, with some results and investigations created in research linked to a larger project entitled “Mobilizations of Narratives in and for the Initial Training of Teachers (who Teach Mathematics)”. Through Oral History, operated in the context of Mathematics Education, the studies created understandings about the mobilizations of narratives in the context involving subprojects of the Institutional Program for Teaching Initiation Scholarships (Pibid) of two public Higher Education institutions located in the State of São Paulo. In general terms, such studies have fruitful possibilities for teacher training processes (of Mathematics), by problematizing some of these potentialities in light of the mobilization of diaries and portfolios in such a scenario. Writing diaries can make pre-service teachers look inside themselves and make them understand who they are and how they think. When it comes to working with portfolios in the context of teacher training, it is possible to say that they evaluated by textualizing traces of experiences that, in other times, with new experiences and practices, can be taken up and given new meaning, that is, the portfolios can be seen as a means of reflection and organization of practices. In this sense, diaries and portfolios are potential for the process of initial teacher training as they open a path for inscribing the personal and professional path of future teachers in history, signaling contributions to the development of understanding and critical stance regarding the performance of future teachers.
subject: Teachers Who Teach Mathematics: For What, For Whom
  topic: section
subject: Mathematics education
  topic: keywords
subject: narratives
  topic: keywords
subject: teacher training
  topic: keywords
subject: daily
  topic: keywords
subject: portfolios
  topic: keywords
creator: Vinícius Sanches Tizzo
creator: Ana Cláudia Molina Zaqueu-Xavier
rights: Copyright (c) 2025 Vinícius Sanches Tizzo, Ana Cláudia Molina Zaqueu-Xavier https://creativecommons.org/licenses/by/4.0
date: 2025-05-15
publication date: 2025-05-15
starting page: 1
ending page: 17
doi: 10.14393/BEJOM-v6-2025-72844