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All Journal Al-Jabar : Jurnal Pendidikan Matematika Indonesian Journal of Science and Mathematics Education Journal of Instructional Mathematics Journal of Advanced Sciences and Mathematics Education JRAMathEdu (Journal of Research and Advances in Mathematics Education)
Alves, Francisco Regis Vieira
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Chemistry Education Mathematics Physics Social Sciences

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Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra de Sousa, Renata Teófilo; Alves, Francisco Régis Vieira; Aires, Ana Paula
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 9 Issue 4 October 2024
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v9i4.5516

Abstract

In this text, we present a discussion about the Rubik's Cube and its relationship with Group Theory, particularly permutation groups, as well as possibilities for exploring it using the GeoGebra software interface. We bring a brief discussion about the concept of group, aspects of the Rubik's cube, the Rubik's group as a group of permutations and possibilities for its exploration in GeoGebra. Based on this study, we recognize the potential to delve into permutation groups in Abstract Algebra through a visual interface that associates their properties with a tangible and manipulable object. Additionally, there is the potential for simulating their movements using Dynamic Geometry software, such as GeoGebra. These findings highlight the relevance of GeoGebra as a useful tool for visualizing and understanding permutation groups, promoting a more intuitive and accessible approach to Group Theory in the educational context.
Didactic engineering supporting the use of gamification applied to the teaching of arithmetic operations Santiago, Paulo Vitor da Silva; Alves, Francisco Régis Vieira
Al-Jabar: Jurnal Pendidikan Matematika Vol 14 No 2 (2023): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v14i2.18125

Abstract

Background:This study proposes an instructional method aimed at resolving arithmetic problems in mathematics. It is specifically tailored to assist educators in their initial mathematical training and to enhance classroom mathematics teaching through the implementation of Gamification.Aim:The objective of this research is to explore the contributions of didactic engineering and digital technologies, particularly those incorporating gamification, in full-time secondary school education, with an emphasis on basic arithmetic operations.Method:The methodology employed in this study is based on and structured around Didactic Engineering research techniques. It is an exploratory, qualitative research designed to simplify the understanding of mathematical problems through the use of Digital Technologies.Results:The findings of this research are categorized into stages: preliminary analysis, a priori analysis, experimentation, and a posteriori analysis and validation. It was observed that the application of problems in the classroom validated the strategies employed.Conclusion:The results indicate that the implemented gamified activities positively influenced teachers’ perspectives on how these activities, particularly the two games designed in Google Presentations, support the teaching and learning processes in mathematics for students.
Didactic Engineering and Learning Objects: A Proposal for Teaching Parabolas in Analytical Geometry de Sousa, Renata Teófilo; Alves, Francisco Régis Vieira
Indonesian Journal of Science and Mathematics Education Vol. 5 No. 1 (2022): Indonesian Journal of Science and Mathematics Education
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ijsme.v5i1.11108

Abstract

This work aims to investigate the feasibility of using a Learning Object built in GeoGebra software and its potential for teaching parabolas in Analytical Geometry, having as support for its replication in a teaching session the Theory of Didactic Situations. The methodology adopted was Didactic Engineering, in its first two phases – preliminary analysis and a priori analysis. In the preliminary analysis, some epistemological and didactic aspects that permeate the teaching of parabolas, the concept of Learning Objects and the Theory of Didactic Situations were raised. In the a priori analysis, we present the Learning Object called Suspension Bridge and its manipulation in GeoGebra for the exploration of the parabola, as well as a student's attitudinal prediction. Thus, we seek to collaborate with the development of new approaches to teaching this topic, contributing to the advancement of the use of educational technologies integrated into the teaching of mathematics.
Record of Semiotic Representation Using Geogebra: An Olympiad Training on Brazilian Students Santiago, Paulo Vitor da Silva; Alves, Francisco Régis Vieira
Indonesian Journal of Science and Mathematics Education Vol. 5 No. 2 (2022): Indonesian Journal of Science and Mathematics Education
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ijsme.v5i2.12510

Abstract

This study aims to compile and develop an international didactic situtation presented with an approach to the center of an arbitrary triangle in visual exploration in 2D and 3D format using GeoGebra software as a technology for modification and construction of Olympiad questions. The methodology used in this study is an exploratory qualitative which is described from a didactic sequence of Mathematics Olympiad which were held in four online meetings using Google Meet. The results show that this exercise can be used as a resource that will provide a level of learning for students through command and visualization of images that serve a broad view of the international Olympiad situation. International didactic situations can be applied by mathematics teachers both in training for national and international Olympiad and for classroom teaching. In summary, it is noteworthy that the dynamic records of semiotic representations stimulated by the use of GeoGebra software has great potential to encourage the progress of students’ representative geometric thinking, through the development of visualization, perception, and mathematical intuition. It is hoped that this work can serve as a pedagogical and methodological tool by teachers for various competencies.
Symmetries of the equilateral triangle mediated by geogebra: a proposal for training rural mathematics teachers Santiago, Paulo Vitor da Silva; Alves, Francisco Régis Vieira; Santos, Maria José Costa dos
Journal of Advanced Sciences and Mathematics Education Vol 5, No 1 (2025): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v5i1.562

Abstract

Background: The equilateral triangle is a fundamental object in geometry, notable for its symmetrical properties, which are best understood through dynamic visualization. Traditional methods often fall short in making these concepts accessible, especially in rural educational contexts with limited resources.Aims: This study aimed to explore the effectiveness of GeoGebra software as a mediating tool to enhance rural mathematics teacher training, particularly in understanding the symmetries of equilateral triangles.Methods: Employing a qualitative and descriptive methodology, the research collected data through classroom observations, analysis of participants’ digital constructions using GeoGebra, and reflective interviews. These methods were chosen to capture how pre-service teachers engage with geometric concepts via dynamic tools.Results: The results demonstrated that GeoGebra significantly improves the visualization of geometric transformations such as rotations and reflections. Participants reported increased comprehension and engagement due to the interactive nature of the software. The teaching approach also encouraged deeper geometric reasoning and fostered the ability to connect abstract group theory with concrete visual representations.Conclusion: The use of GeoGebra in rural teacher training is not only feasible but transformative. As a free, accessible platform, it bridges gaps caused by resource limitations and aligns well with local educational realities. The software empowers future educators to adopt student-centered approaches that make geometry both meaningful and contextually relevant. This proposal supports the integration of digital tools in teacher education and provides a replicable model for similar contexts globally. Future research should investigate broader applications of GeoGebra across other geometric topics and assess its long-term impact on classroom practice in rural environments.
Math for olympiad: a didactic proposal for high school from the perspective of the international mathematical olympiad Santiago, Paulo Vitor da Silva; Alves, Francisco Régis Vieira
Journal of Advanced Sciences and Mathematics Education Vol 2, No 2 (2022): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v2i2.135

Abstract

The concept of the International Mathematics Olympiad (IMO) in learning mathematics in the classroom is something that can inspire students by structuring didactic proposals. This study aims to present a didactic proposal from the perspective of the International Mathematics Olympiad , using digital technology, particularly the GeoGebra software to be included in the mathematics Olympiad discipline. For theoretical studies, the analysis of the mathematical elements of the structured images in the GeoGebra software and the identification of their properties is included, through the structuring of the Olympic teaching situation, which allows the subject to seek solutions to the posed mathematical problems. olympics and validating the teaching of geometry. This study describes the arrangements made to build Olympic math objects that will be applied by math teachers. The research methodology is based on bibliographic reviews from authors such as Alves, Santiago, Almouloud and Brousseau. It is proven that the GeoGebra software helps in the elaboration of mathematical examples and problem solving situations.
Some Elementary Combinatory Properties and Fibonacci Numbers Alves, Francisco Régis Vieira; Sousa, Renata Teófilo de
Journal of Instructional Mathematics Vol. 4 No. 1 (2023): Mathematical Learning: Strategies, Factors, and Challenges
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v4i1.1756

Abstract

In general, in the midst of History of Mathematics textbooks, we are faced with a discussion due to curiosity about the emblematic Fibonacci Sequence, whose popularization occurred with the proposition of the reproduction model of immortal rabbits. On the other hand, in the comparison of the multiple approaches and discussions of certain subjects in Elementary Mathematics, in the present work, we highlight combinatorial interpretations that, with the support of a characteristic and fundamental reasoning for the mathematics teacher, can be generalized and formalize some eminently intuitive components. In particular, this work deals with properties derived from the notion of tiling and decomposition of an integer that, depending on the board, will correspond to the numbers of the Fibonacci Sequence. We bring a theoretical discussion supported by great names that research in this area.
A Note on Leonardo’s Combinatorial Approach Vieira, Renata Passos Machado; Alves, Francisco Regis Vieira; Catarino, Paula Maria Machado Cruz
Journal of Instructional Mathematics Vol. 4 No. 2 (2023): Enhancing Mathematics Learning through Innovative Pedagogies
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v4i2.1862

Abstract

The purpose of this research is to carry out a study of Leonardo's combinatorial approach so that it is possible to visualize these numbers through combinatorial interpretation. Thus, research is being developed regarding methods and approaches to linear and recurring sequences, based on the combinatorial study of the Fibonacci sequence. In fact, the Fibonacci sPquence is related to other sequences, one of which is the Leonardo sequence, which has similarities with the Fibonacci numbers according to some researchers in the field. Given this scenario, the present research addresses the combinatorial interpretation of Leonardo's sequence, allowing the definition of Leonardo's combinatorial model, considering the notion of board and bracelets in Lucas' sequence. As research results, the study deals with the integration of sequence content with the area of Combinatorial Analysis, allowing a mathematical advancement of Leonardo's sequence. Furthermore, you can visualize the sequence numbers in front of the tiles. The aspects studied in this research are linked to the teaching of sequences in the History of Mathematics, allowing the teaching of Mathematics.
Co-Authors Aires, Ana Paula Catarino, Paula Maria Machado Cruz de Sousa, Renata Teófilo Santiago, Paulo Vitor da Silva Santos, Maria José Costa dos Sousa, Renata Teófilo de Vieira, Renata Passos Machado