Educação Matemática Sem Fronteiras: Pesquisas em Educação Matemática
A Revista Educação Matemática Sem Fronteiras está vinculada aos Programas de Pós-Graduação em Educação - PPGE Campus de Chapecó e PPGPE Campus de Erechim e PROFMAT Campus de Chapecó da UFFS, bem como, a Licenciatura em Matemática e Grupos de Pesquisa com temáticas relacionadas à Educação Matemática. A prioridade deste periódico se dá no sentido de incentivar publicações nessa tendência atual de pesquisa e docência. Assim, considerando a sua ideia original, a revista se constitui em um espaço para divulgação da discussão e reflexão a respeito de temas afetos à Educação Matemática, na forma de trabalhos de pesquisa, análise de experiências e resenhas. ISSN 2596-318X | indexada em: Miguilim, Diadorim, Sumários
Copyright (c) 2025 Nilce Fatima Scheffer http://creativecommons.org/licenses/by/4.0
Copyright (c) 2025 Nilce Fatima Scheffer, Dionísio Burak http://creativecommons.org/licenses/by/4.0
PHILOSOPHY OF MATHEMATICS IN SECONDARY SCHOOL: PATHS TO CONCRETE LEARNING
Mathematics and its results govern the way we interpret the world from a scientific perspective, representing an important language for describing phenomena and everyday life itself. Mastering its results, principles, and basic operations is an indispensable means for collective life, since all relationships established within society directly or indirectly involve specific mathematical knowledge. In this sense, considering that learning mathematics is essential for the education of elementary school graduates, this article, configured in a bibliographic study of a narrative-qualitative nature, intends to analyze the importance of mathematical philosophy as a link for consolidating teaching practices, capable of bringing students closer to the content, giving it meaning in the context of secondaryschool. For this purpose, works published between 2014 and 2024, available on the open access portal CAPES Journals, were researched and gathered through search descriptors, inclusion andexclusion criteria, and analysis categories. At the end of this research, it was observed that the philosophy of mathematics, wheninternalized in teachingpractice in a strategic way, tends to reinforce the logical thinking of students, ensuring real meaning for the content, stimulating historical debate, leading the student to understand the origins, evolution and importance of mathematics.
Copyright (c) 2025 Educação Matemática Sem Fronteiras: Pesquisas em Educação Matemática http://creativecommons.org/licenses/by/4.0
TRIGONOMETRY IN INITIAL TEACHER EDUCATION: A LITERATURE REVIEW
Trigonometry is a topic that deserves studies in the initial training of mathematics teachers. The objective of this study was to identify and analyze theoretical and methodological approaches in research on trigonometric concepts in the initial educationof mathematics teachers. This is a bibliographical researchthat was used by the PRISMA methodology, based on the selection of 12 articles that address the importance of exploring trigonometric concepts during the initial training of future mathematics teachers. The theoretical approaches Professor Thinking and Technological Media stand out, and the methodological approaches Theoretical Modeling and Cooperative Research stand out considering the selected articles. The results indicate the need for initial teacher training to be guided by aspects of mathematical modeling, educational technologies and two didactic-pedagogical resources
Copyright (c) 2025 Josevaldo de Almeida Lago, Vinícius Pazuch http://creativecommons.org/licenses/by/4.0
INQUIRY-BASED LEARNING FOR CRITICAL STATISTICAL LITERACY
This work analyzes how Inquiry-Based Learning activities in the context of Statistics can contribute to the development of Critical Statistical Literacy in future Mathematics teachers. The aim is to promote reflection on the social nature of data, overcomethe ideology of certainty and build critical pedagogical practices. To this end, an activity was conducted with Mathematics degree students, involving the collection, organization and presentation of statistical data in a dynamic carried out in the Mathematics Education Laboratory. The research focuseson measures of central tendency, percentages and graphical representations. The dynamic investigated how pre-service teachers analyze and present statistical results, both orally and through visual representations. At the end, a questionnaire was administered to evaluate the effectiveness of the proposal and possible applications in Basic Education. The results, discussed in the light of Critical Mathematics Education, show that undergraduate students have potential for criticalreflection and for connecting Mathematics with social themes, when inserted in an investigative scenario that encourages such discussions. We conclude that InquiryTeaching is a powerful way to promote Critical Statistical Literacy in Mathematics Education.
Copyright (c) 2025 Leonardo Corrêa Sabbado, Rita Ramos http://creativecommons.org/licenses/by/4.0
PROBLEM EXPLORATION IN MATHEMATICS TEACHING AND LEARNING: SYSTEMATIC LITERATURE REVIEW
This article aims to present a systematic literature review about productions on exploration-solving-posing of problems for mathematics teaching-learning, not only an organization of data, but also a notion of what has been being Produced by academic research seeking to show on the subject, possible gaps and convergence points, as well as guiding the ERP field. The research was guided by the following question: What are the potentialities and limitations that the exploration-resolution-has been proving to problems bringing to the teaching-learning process of mathematics? The systematic literature review was based on the Prisma Protocol. Potentialities were found in the use of ERP that affect the teaching-learning of mathematics, such as the development of characteristics such as autonomy, trust, creativity, consciousness in decision making, strategy development, high-esteem, curiosity and interest in the subject and for social, political, economic and cultural themes. Regarding the limitations, it was evidenced that the use of time, the multicontexuality of the classroom were variables that challenged the researchers, but these same aspects, with the development of research, were favorable for a teaching and constructive learning, critical it is efficient.
Copyright (c) 2025 Saul Barbosa de Oliveira http://creativecommons.org/licenses/by/4.0
ORIENTAÇÕES DIDÁTICAS PARA O ESTUDO DO CONCEITO DE PROPORCIONALIDADE BASEADAS NAS DUAS RÉGUAS PARA CÁLCULO
The concept of proportionality is present in the student's life from Elementary School to High School, so it is necessary for the teacher to consider different types of resources that will help the student in understanding this concept. In view of this, the Two Rulers for Calculation, an instrument designed by William Oughtred (1574-1660) in the 17th century, is characterized as one of these resources, coming from the History of Mathematics, which can contribute to the construction of mathematical knowledge of proportionality. Thus, through qualitative descriptive and documentary research, we intend to present a proposal for an activity involving the concept of proportionality for the Final Years of Elementary School, through the handling of a historical mathematical instrument. Therefore, when presenting the concept of direct proportion and the handling of rulers, the student can mobilize other mathematical concepts that are linked to proportionality, such as the orders of units and tens of the decimal numbering system, as well as the notion of ratio and the equality between two ratios, forming a proportion, leading the student to relate what is seen on the instrument to what is worked on by the teacher in the classroom, thus contributing to the construction of knowledge of proportionality.
TEACHING THE VOLUME OF GEOMETRIC SOLIDS: A SYSTEMATIC LITERATURE REVIEW
This article consists of a Systematic Literature Review aiming to discuss national and international research, published between 1998 and 2024, which presents and discusses strategies for teaching volume of geometric solids in Basic Education. To achieve the objective, a bibliographical survey was carried out based on dissertations, theses and articles, of which 12 met the research protocol criteria. The results highlighted the following strategies: use of Geogebra software; teaching through Problem Solving; teaching through activities and use of manipulative materials.
Geometric solids, Teaching spatial geometry, Volume.
COGNITIVE PROCESSES OF SEGMENTATION AND RECONTEXTUALISATION IN LEARNING THE VERTICAL THROW/FREE FALL MOVEMENT
Duval, in his most important book published in 1995, on his semiocognitive theory of intellectual learning, provides a very comprehensive study of text comprehension, an important subject for any discipline; in mathematics, for example, understanding the wording of problems, theorems and definitions are integral parts of learning; this author sought to identify and relate the significant units in the natural language register to each other using two cognitive procedures called segmentation and recontextualisation. The significant units are important in the formation and operations related to the semiotic representation registers; these procedures, which seek to highlight the significant units, point to didactic perspectives, such as the one intended in this study: to consider the algebraic and Cartesian registers as the basis for the cognitive operations of segmentation and recontextualisation. In text comprehension, in addition to the variable associated with organisation, there is another pertinent to cognitive content, which is what the text seeks to convey: in this work, a case governed by the equations of uniformly varied rectilinear motion - vertical throw/free fall - was chosen for this purpose. In this way, a study was carried out in which algebraic and Cartesian representations are coordinated to help understand this movement based on the cognitive processes of segmentation and recontextualisation.
unidades significantes; segmentação cognitiva; recontextualização cognitiva; movimento de arremesso vertical/queda livre; aprendizagem científica
This interview was conducted with Professor Dr. Regina Célia Grando by email, on 12/11/2023. In this dialogue, she recounts her life and work in Education and Mathematics Education, from when she entered the school, until she became a teacher, in the Mathematics Degree. Her life is focused on Education and Mathematics Education, dedication to research, extension and postgraduate studies. In this interview, Regina presents a snippet of her story and life trajectory from choosing a career in teaching to be a Mathematics teacher, to the training of Mathematics teachers, a path that she has been following, for many years, in Mathematics Education, alongside researchers and teachers, by working in Undergraduate and Postgraduate courses and at SBEM.
Copyright (c) 2024 Educação Matemática Sem Fronteiras: Pesquisas em Educação Matemática http://creativecommons.org/licenses/by/4.0
FINANCIAL MATHEMATICS FROM A PROBLEM-SOLVING PERSPECTIVE IN YOUTH AND ADULT EDUCATION
This study investigates how students in Youth and Adult Education mobilize knowledge of Financial Mathematics from the perspective of Problem Solving. This investigation occurred during the first stage of the High School Supervised Internship in a High School Youth and Adult Education class, located in a school in the southwest of Paraná. The presente study constitutes a qualitative research, whose data collection took place through participante observation and application of questionnaires. The data shows that, in general, the students solved the proposed situations, which enabled them to think productively, develop logical reasoning, and get involved with mathematical applications. It should be noted that Financial Mathematics offered an opportunity to engage students, providing them with a practical and meaningful understanding of mathematical concepts. Finally, it was observed that the activities contributed to improving mathematics teaching, enabling students to develop essential mathematical skills and promoting a deeper and more critical understanding of the concepts of Financial Mathematics.
INFLUENCE OF THE MATHEMATICS TEACHING LABORATORY ON THE DEGREE COURSE IN MATHEMATICS AT UNIFAP
Mastery of mathematical content is not a sufficient condition for the teacher to promote the teaching and learning process. The Mathematics Teaching Laboratory plays a fundamental role in the initial training of mathematics teachers, functioning as a space that transcends the traditional classroom. In it, future educators have the opportunity to experience innovative pedagogical practices, explore different teaching methodologies and interact directly with concrete and technological resources that enhance the learning process. The present work aims to carry out a historical review of the Mathematics Teaching Laboratory (LEM) linked to the Mathematics Teaching Degree course at the Federal University of Amapá (UNIFAP), identifying the main contributions of the use of LEM for the initial training of mathematics teachers. The study uses a qualitative approach, developed in two stages: bibliographic research, considering the influential authors on the subject, and oral history research, through interviews, collecting testimonies from professors of the mathematics degree course at UNIFAP. It was possible to perceive that LEM has been used as an environment for experimentation, where academics test, create and recreate ways of teaching mathematics with different resources available in the LEM collection, contributing significantly to the initial training of mathematics teachers.
FINANCIAL EDUCATION IN THE FINAL YEARS OF ELEMENTARY EDUCATION
The aim of this study was to analyze publications about research related to the teaching and learning of Financial Education for the Final Years of Elementary School. Of a qualitative nature, the research used the assumptions of Content Analysis to analyze a corpus composed of 15 articles obtained through a search in the Capes Periodicals database. Among the results, 6 emerging categories were generated: C1 -school year of application of the research, C2 -financial education and technology, C3 -production of teaching material, C4 -network of application of the research, C5 -specific purposes of the work, and C6 -work carried out during the COVID-19 pandemic. Among them, we highlight the possibility of using different methodologies to teach the studied content, considering that the 7th grade was the period in which research was least applied and that only three works involved technology in the education of the investigated topic, which demonstrates the lack of such tools for the development of students in relation to finances. Furthermore, we identified the researchers' concern regarding learners' understanding of Financial Education, which was evident due to the number of articles with this objective.
This Interview was carried out with professor Dr. Ademir Damazio by email, on 02/28/2024. In this dialogue, historical information about his life and work in Education and Mathematics Education in the state of Santa Catarina was recovered, since when he entered the old Normal Gymnasium, followed by the Normal Course to become a teacher; and, later, in the Degree in Mathematics when he decided to actually become a Mathematics teacher. After that, he had a life dedicated to Mathematics Education and, in recent times, he has turned to studies and research, whose central objects are thinking theoretically. This, translated into the school curriculum context, means being based on the essential relationship of each mathematical concept, which necessarily relates to other constituents of a broader system. Finally, in this interview, Professor Ademir presents part of his story and life trajectory, from choosing a teaching career to become a Mathematics teacher, to his complete dedication to teaching, research and training Mathematics teachers. A path followed, for many years, by Mathematics Education, alongside researchers and teachers, to work in Undergraduate and Postgraduate courses.
INTERACTIONS AND UNDERSTANDING ABOUT VECTOR IN TWO VIRTUAL ENVIRONMENTS
This article comes from a research project focused on learning in virtual environments. Interactions of mathematics under graduates (Study1) and 7th grade students (Study2) in a task on translation are briefly illustrated and analyzed. In Study1 (S1) the subjects interacted in a synchronous device integrated with GeoGebra and in Study2 (S2) in the VLE-Cap. In S1, the analysis was based on written records, screen constructions, tables and graphs – shown in Figures – generated on the Virtual Math Team with GeoGebra (VMTcG) and in S2 was based on written interactions. The way in which subjects constructed what was proposed based on doubts and emerging as is highlighted. The importance of designing tasks that improve the understanding of transformation and functional relationship is emphasized (S1), and the need for more analysis on the forms of vector understanding and on the possibility of visualizations of representations of 2D - 3D translations (S2).
Copyright (c) 2024 Educação Matemática Sem Fronteiras: Pesquisas em Educação Matemática
THE NOTION OF SYSTEMATIC AND NON-SYSTEMATIC SETS OF SEMIOTIC REPRESENTATIONS: DIDACTIC PERSPECTIVES
The register is a particular set of semiotic representations, an idea developed by Duval, which comprises three poles: the representation itself, which in order to reach us has a form perceptible by the senses; the represented object; and the content of this representation, which can be different from the represented object. The notion of register is fundamental, since it forms part of Duval's fundamental hypothesis in his semiocognitive theory of intellectual learning. This text addressed the characterization of various semiotic sets with the aim of identifying those that can be classified simply as an unsystematic semiotic set, a systematic semiotic set and a register. The didactic possibilities of this classification were realized.
unsystematic set of semiotic representations
systematic set of semiotic representations
COMPLEMENTARY EVENTS IN PROBABILITY: EXPLORATION BY PROSPECTIVE PRIMARY SCHOOL TEACHERS
The article presents a study with students, prospective primary school teachers, about complementary events, based on the objectives: 1) to verify if two given events are complementary or not; 2) to state the definition of complementary events; and 3) to formulate examples of complementary events. Participated in the study 37 students of the 2nd year of the Degree in Basic Education, who attended a university in the north of Portugal. The data were obtained through the application of a questionnaire with several tasks about different types of events, and in the study the data resulting from the answers given by the students to only one task with four items, involving the classification, definition and formulation of complementary events were used. In terms of results, it is noteworthy that more than half of the students were able to classify events as complementary or non-complementary and formulate examples of complementary events, but very few adequately justified their answers. Students, on the other hand, had more difficulty in defining complementary events, with about one in three enunciating the definition correctly. However, even students who presented correct and complete definitions had difficulty in applying these definitions to justify the classification of events in complementary or non-complementary and the exemplification of complementary events, which highlights the need for students to practice such justifications.
CONSTRUCTION OF MEANINGS WITH SEMIOTCI MODES IN MATHEMATICAL CARTOONS
This article will presente a section of the results of a master’s degree research that proposed understanding the meaning that the diferente semiotic modes used in the production of mathematical Cartoons generatr in collectives of human and non-human actors participating in the VI Festival of Digital Videos and Mathematics Education. A qualitative methodology was used, and the data production procedures and instruments were the selection of Cartoons-type vídeos that were finalists at the VI Festival of Digital Videos and Mathematics Education in the Higher Education (ES) category and interviews with the vídeo producers which took place online, via Google Meet and Whatsapp. The analysis took place based on the requirements of the Beings-Humans-With-Media System (S-H-C-M) according to the principle of the Theory of Activity and Multivocality ando n the lens of Social Semiotics (SS), considering the multimodal approach. The results indicated that, in the contexto of mathematical Cartoons, semiotic modes are used to share mathematical concepts in na uncomplicated way. For students, meanings can be related to accessible language, engagement, understanding complex concepts, contextualization and personalization. For teachers, the semiotic modes used in these vídeos can help presente modes used in these vídeos can help presente concepts in a more engaging and attractive way.
MATHEMATICS TEACHING LABORATORIES AS A FEEDBACK ELEMENT OF THE TEACHING-RESEARCH-EXTENSION TRIAD
The Mathematics Teaching Laboratory is a physical environment that favors the development of materials and activities for teaching and learning mathematics. Although it has already been consolidated Undergraduate Program in Mathematics Education and, its performance and relationship to activities out of higher education institutions are still emerging. In the Undergraduate Program in Mathematics Education Laboratory on Campos do Jordão campus of the Federal Institute of São Paulo, the covid-19 pandemic imposed negative consequences on the activities being developed in a physical space. Therefore, incentives have emerged to elaborate virtual environments with aims and motions similar to those available in live environments. From this context, this article seeks to show that, in addition to physical and virtual laboratories having a potential for complementarity, when associated with extension actions, there is potential to strengthen their approach to Basic Education. The research is methodologically characterized by the principles of Inquiry-Action, as it was constituted from the analysis of experiences lived and investigated by the authors. Lastly, analysis indicate that extension projects involving school community and related environments can lead to a feedback process between teaching, research and extension axes that strengthen the principles of actions developed in Undergraduate Program in Mathematics Education.
Undergraduate Program in Mathematics Education
Educação Matemática; Laboratório de Ensino de Matemática
CYCLIC QUADRILATERALS AND GEOGEBRA: AN EXPERIENCE WITH STUDENTES FROM INTEGRATED HIGH SCHOOL TO PROFESSIONAL EDUCATION
This work relates an experience with students in the 3rd year of High School Integrated to Professional Education at a Federal Institute, which had as its theme the learning of cyclic quadrilaterals using the GeoGebra software, being carried out remotely from the use of digital information and communication technology tools. The experience took place in the form of four workshops, which sequentially addressed the contents of inscribed angle and corresponding central angle; the necessary and sufficient condition for a quadrilateral to be inscribed to a condition; Ptolemy's theorem; and, the Brahmagupta formula. At the end of the application in all workshops, it was concluded that the use of GeoGebra contributed to the students' learning of Geometry content. However, during the discussions regarding Ptolemy's theorem and Brahmagupta's formula, GeoGebra presented some inconsistencies that refer to the accuracy of values, probably demonstrating a problem inherent to its computational and numerical architecture, but these inconsistencies were bypassed by research professors using a tool in the software itself that allows changing the number of decimal places in their values, thus without causing harm to the learning objectives.
AGAINST EPSILON-DELTA ORTHODOXY: A MANIFESTO IN DEFENSE OF THE TEACHING OF DIFFERENTIAL AND INTEGRAL CALCULUS WITH INFINITESIMALS
The work presented here can be read as a manifesto in defense of a teaching methodology for Differential and Integral Calculus that is based on the deliberate and ostentatious use of infinitesimal elements, privileging the students' most intuitive and spontaneous conceptions. In this sense, a manifesto in favour of the adoption of the most diverse approaches based, directly or indirectly, on the non-standard analysis developed by Abraham Robinson in the early 1960s, which rehabilitated the infinitesimal elements for analysis. Furthermore, the present work outlines a set of relevant research themes to guide future research work, whose ultimate purpose consists of the detailed definition of alternative teaching strategies, as well as the elaboration of corresponding teaching material, capable of making successful the teaching learning process of Differential and Integral Calculus’s subject in higher education courses
Teaching Differential and Integral Calculus
DIGITAL TECHNOLOGIES: VIDEO PRODUCTION IN TRAINING OFFERED TO TEACHERS WHO TEACH MATHEMATICS
This article is a clipping of a master’s research whose main objective is to understand how video production contributes to the continuing education of teachers of the early years, in the teaching of mathematics, by developing skills for video production with Activepresenter software. Was held a course in the online mode via Platform Google classroom, Google Meet in 2020 for teachers of the early years of Basic Education. The work has a qualitative nature, for analysis we used the data triangulation method. It was concluded that the continuous training aimed at the production of video enables the development of skills to deal with the Digital Technologies that are increasingly present in school life as well as training to assist teachers in use of DT in the classroom.
Copyright (c) 2023 Educação Matemática Sem Fronteiras: Pesquisas em Educação Matemática
PERFORMANCE OF ANGOLAN HIGHER EDUCATION STUDENTS IN DESCRIPTIVE STATISTICS: SELECTION VERSUS APPLICATION
This article studies the performance of Angolan higher education students when selecting and applying Descriptive Statistics tools, graphical and numerical tools, as well as comparing the performance when selecting and applying these tools. Eighty-seven higher education students participated in the study, who were attending the 2nd year of the Degree in Accounting and Management and in Animal Science, at a Higher Polytechnic Institute of Angola. The students answered a questionnaire about the selection and application of Descriptive Statistics tools, namely, table and graphic representations, location and dispersion statistics, symmetry and dispersion of a distribution and linear correlation and regression statistics. In terms of results, in general, the poor performance of students in both the selection and application of statistical tools and a better performance in selection than in the application of these tools stand out. These results highlight the need to improve student performance, as Descriptive Statistics tools are of the utmost relevance for employment, everyday life, and social participation.
This Interview was carried out with professor Dr. Sergio Lorenzato by email, on 12/14/2023. In this dialogue, historical information about his life and work in Education and Mathematics Education was recovered, since when he joined UNICAMP to be a teacher; It was a life dedicated to Mathematics Education and the training of teachers who teach mathematics. In this interview, Professor Sergio presents a little about his history and life path, from choosing a teaching career to become a Mathematics teacher, to his complete dedication to teaching, research and training Mathematics teachers. A path that has been followed, for many years, by Mathematics Education in this country, alongside many researchers and teachers who dedicate themselves to this cause, through Undergraduate and Postgraduate courses. Keywords: Mathematics Education; Teacher training; Teaching and Learning Mathematics.
TECHNOLOGIES IN TEACHING METHODOLOGIES FOR STUDENTS WITH DEVELOPMENTAL DYSCALCULIA
This article aims to research, about the use of technologies in the teaching practices of teachers who teach mathematics to students with developmental dyscalculia (DD). From qualitative bibliographical research carried out in the Catalog of Theses and Dissertations of the Coordination for the Improvement of Higher Education Personnel (CAPES) it is noticed the lack of research on this subject which generated the following problem: What are the implications of the use of technological resources by teachers to help students with DD teach math? The results show that the use of technological resources such as games, specific websites, applications and recreational activities bring significant results for teaching mathematics to students with the aforementioned specific learning disorder. But for technologies to be part of the educational scope, there are many factors that must be taken into account, such as obstacles that hinder the use of technological resources in educational institutions.
BNCC CONTRADICTIONS ABOUT THE DEVELOPMENT AND USE OF DICT AND COMPUTATIONAL THINKING
The present work discusses via theoretical analysis the form of elaboration and implementation of the National Common Curricular Base (BNCC) in Basic Education, with a view to the development and use of digital information and communication technologies (DICT) and Computational Thinking in the area of Mathematics. In this context, researches related to the reform of Secondary Education, conferences for the construction of the curricular proposal, as well as the use of DICT in the area of Mathematics are discussed. There are many criticisms and contradictions throughout the process of creating this regulation, notably due to its neoliberal characteristics and the lack of dialogue and contributions on the part of teachers, researchers and specialists in the field of Education.
NON-LINEAR SYSTEMS: DIDACTIC SEQUENCE FOR NEWTON'S METHOD TEACHING IN HIGH SCHOOL
This paper presents a Didactic Sequence to the transposition of the Undergraduate Education content known as the Newton's Method. This transposition aims at the teaching of the topic to High School students, seeking to adapt it to the students’ level using, for example, software for a better understanding of topics such as limits and derivatives. The data contained in this article show that this teaching is possible and opens ample opportunities for reaching more complex topics. We show here the steps developed, going through the review of linear systems and the students’ contents acquisition as limits, derivatives and the resolution of non-linear systems with the Newton Method, in addition to the performance of students during and after the application of the sequence. The study took place during the Covid-19 Pandemic that occurred in Brazil. Measures were taken during the application for the safety of all involved.