Educação Matemática Pesquisa

Alternative praxeological model for the identification of primary numbers

2023-06-05T20:16:56-03:00

This article aims to present an Alternative Praxeological Model for the Identification of Prime Numbers in any given range of numbers. The study carried out is based on the Anthropological Didactics Theory. The alternative model refers to the creation of two formulas that when combined generate prime numbers in any range of numbers, built from Basic Algebra reference models and from the concepts of Number Theory. It is expected that the model built will be applied in schools of basic education and in undergraduate courses that deal with Mathematics at various levels.

Knowledge of mathematics and chemistry embedded into integration curriculum materials

2023-08-31T17:14:48-03:00

The article is structured around the objective of understanding Mathematics and Chemistry embedded into integration curriculum materials in the Natural Sciences area, assessed and approved within the scope of the PNLD 2021. For this documentary research, we selected the teacher’s handbook from a material defined as an integration project. After reading the introductory part of the presentation texts and guidance for developing two projects using such material, the analysis was guided by discussions of curriculum integration, work with projects, the analysis was guided by discussions of curriculum integration, work with projects and the knowledge of curriculum embedded Mathematics and Chemistry (KCEMC). The results indicate that the introductory part and the development of both projects lack transparency in conceptualizing curriculum integration, working with projects, and organizing content, which can restrict professional teaching knowledge and imply teaching practices that can diverge from the purposes of the curriculum material.

From mathematical contents to process of meaning production: a possibility to mathematics teacher education

2023-11-17T20:28:47-03:00

In this essay, we present a discussion about the mathematical education of mathematics teachers. In the first part, we highlight notes from some researches that deal with the thematics, delimiting a ground for our discussions. In the second, we present some works that address this issue, which take as main theoretical-methodological reference the Model of Semantic Fields. In the third and last part, we problematize and point out some designs for the construction of others initial mathematics teachers education. One would be an organization of processes of teacher training by activities based on everyday life categories. From situations presented to teachers and prospective teachers, discussions and problematizations can be produced through sharing and expansion of ways of producing meanings, in an attempt to detail differences and not to substitute and hierarchize knowledge, which does not exclude approaches to content considered as mathematical and prescribed in curricula.

The academic-professional trajectory of a mathematics teacher trainer

2023-09-07T17:56:18-03:00

This research involves a trainer of future Mathematics teachers and the teaching of Linear Algebra, and it is part of an ongoing study. The study has the following objectives: (i) to reflect on and analyze the narratives of a teacher trainer regarding the characteristics of the Linear Algebra discipline in a Mathematics Education course, and (ii) to understand how the academic/professional profile of a teacher trainer shapes and/or influences the planning of the Linear Algebra discipline for the teaching of Linear Systems. The data were generated through documentary research and the observation of an episodic interview conducted individually with a Mathematics teacher trainer. Interpretative qualitative research was the methodological approach used for constructing the field texts, which involved documentary research and the selection of excerpts from a remote episodic interview. These excerpts were analyzed narratively for insights and reflections from the data. The results indicated that the personal experience of the Mathematics teacher trainer influenced the development of their teaching identity in higher education. Regarding the organization of the discipline through the teaching plan, it was observed that the teacher trainer aimed to emphasize formalization and argumentation, with the goal of covering the contents outlined in the course syllabus. There is a need for further studies on the roles and identities of Mathematics teacher trainers, the weaknesses of the Pedagogical Political Project related to teaching practice, and the involvement of teacher trainers in formative contexts.

Analysis of narratives/scenes on screen

2023-11-13T15:56:37-03:00

This article investigates how the scene analysis process and the construction of mathematics lesson plans on gender and sexuality (by mathematics teachers participating in a postgraduate course, which dealt with themes of exclusion/inclusion with cinematographic products) can contribute to the understanding/constitution of the social responsibility of these participants in the face of these aspects. Through Queer Theory, intersectionality and decoloniality of gender, we analyzed the discussion process of the scenes and the mathematics lesson plans developed by the teachers. Thus, we understand that the propositions of mathematics classes on themes related to gender and sexualities, based on the analysis of cinematographic works, establish the understanding/constitution of the social responsibility of the analyzed teachers, sometimes, in an initial and still fearful way in relation to trans issues, sometimes from a queer perspective of estrangement and provocation of fruitful reflections on the mathematics class.

Articulations between history of mathematics and mathematical modelling

2023-10-19T06:05:37-03:00

In this text we seek understandings, in terms of the teaching and learning process of Mathematics, about the possible articulations between the History of Mathematics (HM) and Mathematical Modeling (MM) revealed in research in the area. To this end, a systematic literature review was carried out, through which we searched for research in databases and national scientific events that addressed topics related to this objective, which led us to the identification of eight works. Through the procedures of Discursive Textual Analysis, initially, we fragmented and unified the data and, later, classified them into categories. From this analytical process, two categories emerged: I – Articulating HM and MM enables teaching and learning processes that generates understanding of the mathematical topics studied and desirable attitudes for the formation of the student and II – Articulating HM and MM makes it possible to highlight the human aspects, social, scientific, and cultural aspects linked to the development of mathematical models and the relationship between mathematics and other areas of knowledge. Based on the emerging categories, potentialities arising from articulations between HM and MM for the teaching and learning process of Mathematics were evidenced, which justify the reasons why it is relevant to do so.

The professional development of elementary and middle-basic school teachers

2023-08-09T08:11:59-03:00

This article aims to analyze elements related to the teacher professional development presented in a remote training process on statistical concepts during the pandemic. This exploratory qualitative research comprises 29 teachers who teach mathematics in elementary and middle school in seven municipalities, partners of a research network. With the following research question: What elements related to teacher professional development are presented by participants of a remote training process on statistical concepts, carried out by a research network in the pandemic period? To implement it, during the COVID-19 pandemic, a remote training process was developed, supported by digital tools, and organized into four modules, with the methodology of the flipped classroom and the RePARe spiral. Statistical concepts were selected using the PPDAC methodology, from the perspective of equity. In data collection, teachers answered an online questionnaire. Content analysis was adopted to read the data, and professional development emerged as a category of analysis. The thematic axis supporting the reflection was the “Training Process”, presenting elements that professional development is continuous, showing that teachers still have conceptual and pedagogical practice formative demands. Among the most mentioned factors was time, with discussions related to school, profession, the person, and the family. Finally, the internalization of research and the experience of teacher education in mathematics was promoted, especially in Brazilian Northeastern institutions. Thus, the work carried out provided equity for mathematics education.

Movement for the constitution of the professional identity of prospective Mathematics teachers within the scope of Pibid and Supervised Curricular Internship

2023-12-30T13:38:31-03:00

This article aims to discuss actions in the context of the Institutional Scholarship Program for Initiation to Teaching and the Supervised Curricular Internship which promoted the movement to constitute the Professional Identity (IP) of mathematics teachers. Interpretative qualitative research was carried out, based on interviews, discussions and written productions of students of the Mathematics degree course at the State University of Londrina. The results reveal that the contexts of initial education analyzed provided prospective teachers with: experiencing their first experiences as a teacher; experiencing situations of vulnerability and being able to operate their sense of agency; getting to know Basic Education students and identifying cognitive and relational demands; reflect on teaching behaviors in the teaching process; experience teaching methodologies different from directive teaching; and reflect on their teaching practice based on the elaboration of reports of the activities developed. Such actions promoted the movement of constitution of the IP of prospective mathematics teachers and pointed out the need to promote processes of initial education that provide opportunities for spaces that provoke reflections on topics such as professional self-knowledge, emotions in teaching work, the social role of the teacher of mathematics and its responsibilities. Such processes are promising for the constitution of a critical, solidary and aware teacher of the implications of his professional performance.

The lesson study and the Inicial training of mathematics teachers in Brazil

2024-01-10T18:24:52-03:00

Lesson Study is a teacher training process that seeks to improve the quality of teaching and learning through collective and reflective work, which involves defining the objective of the class, studies related to the topic to be taught, detailed lesson planning, conducting of the class by one of the participants and analysis after its completion, which culminates in the improvement of the planning. This process originated in Japan at the end of the 19th century and has been developed in several countries with teachers in service and/or preservice teachers training, undergoing adaptations. In this text we present an overview of the scientific productions related to the Lesson Study developed within the scope of the preservice training of Mathematics teachers, which took place in Brazil until the year 2021. Our intention is to highlight possibilities and challenges for the development of this formative process, as well as their contributions. The surveys analyzed show that the Lesson Study can bring several contributions to the training of future Mathematics teachers, mainly in relation to the articulation between theory and practice and, also, to favor an approximation between university and basic school.

Teaching algebra to visually impaired students

2023-07-12T14:03:53-03:00

Considering the need to combine theory and practice in planning teaching situations for visually impaired students, this research adopted the assumptions of the Historical-Cultural Theory and the Activity Theory, and was based on the Teaching Guiding Activity. Learning triggering situations for algebraic knowledge were developed, and interventions carried out with a 7th-grade student and another from 8th grade, both visually impaired and attending the multifunctional resource room of a public school in the state network, were analyzed. The aim of this article is to recognize the appropriation of algebraic knowledge by visually impaired students from learning triggering situations. To this end, the data were organized into two categories: manifestations of conceptual nexuses and manifestations of thought and language. These two categories allow understanding the phenomenon of "appropriation of algebraic knowledge" from the situations presented to the students. At the end of the study, it is highlighted that the elaborated situations allowed symbolic and instrumental mediation, enabling the appropriation of the conceptual nexuses of algebra (variation, variation field, and fluency) and of some selected school contents (recognition of unknowns, dependency of variables, and operations with monomials and polynomials). It should be noted that the proposed triggering situations achieved these results through a teaching organization process that considered the conditions for accessibility of the students served.

The The validating process in modelling activities

2024-01-30T05:46:19-03:00

The article addresses the investigation of validation in mathematical modelling activities. For research interests in outlining a framework for validation in these activities, data triangulation is used as an alternative to provide coherence and cohesion to what is intended to be done. For the organization of the framework, a theoretical framework regarding the theme is captured. In addition, an empirical research is carried out with students of a Mathematics Degree course. The gathering of empirical data and the theoretical structure allows characterizing understandings, the importance and ways of carrying out validation in mathematical modelling. Although it can be recognized as the final step in the modelling cycles, validation cannot be thought of as a cumulative process that only begins at the end of the activity and from which only acceptance or refutation results. Instead, it can act as an iterative agent and guide students' decision-making processes, and validation mechanisms can be activated at different stages of the activity. What can be concluded, therefore, is that, even if specific actions are recognized, it is in the validation of the totality of the modelling that the efficiency of validation resides as a means of generating reliability in what can be said about a situation of reality by using mathematics.

The curricular component “inclusive education” in initial teacher education

2024-02-21T07:43:56-03:00

The work discusses the contributions of the “Inclusive Education” curriculum component in the initial education of mathematics teachers. It is characterized as a case study with a qualitative approach, whose data were collected from undergraduates and graduates from a mathematics degree course at the Federal Institute of Ceará (IFCE) attending the component from 2016 to 2019. Relevant perspectives were highlighted from participants' views on the curriculum component, highlighting a better understanding of the concept of disability, types, and education from an inclusive perspective, in addition to a greater understanding of the need for initial/continuing teacher education to promote inclusion, favoring didactic-pedagogical adjustments necessary for the effective learning of people with disabilities. The emphasis on the importance of the “Inclusive Education” curriculum component allows us to infer that it aroused interest and instigated the search for subsidies that favor a professional practice that promotes learning in diversity.

The insertion of the language dimension in the analysis of the teaching problem

2024-03-16T21:53:26-03:00

The purpose of this article is to insert the language dimension into the analysis of the didactic problem with the same degree of relevance attributed to the epistemological, ecological and economic dimensions when studying a mathematical object. We planned a meeting with twelve Engineering and Mathematics students from two public universities in the interior of Bahia and proposed a task with the theme Double Integral of a Quadric Surface, the hyperbolic paraboloid. As theoretical assumptions we take as a contribution the Anthropological Theory of Didactics (TAD) and Peircean Semiotics and the construct elaborated by the authors of the four languages: counterfactual, dictated, in course, in (dis) course. Five of the students solved the task, three from Engineering, who created a question in the context of their degree, the other two, from the Mathematics Degree, focused on developing calculations. The results obstained revealed that future engineers strongly applied counterfactual and (dis)course language, while those in the bacherlor’s degree used dictated and in course language; the twelvw students experienced difficulties in co-authoring the elaboration, solution, and analysis of the activities, as they did not find similar models in textbooks and the media. We infer that the language dimension was relevant for the development of abductive reasoning and for the student’s co-authorship in the creation and solution of Double Integral question statements.

Dialogues about the ongoing challenge of combating racism in “people’s” sport

2024-02-21T07:23:39-03:00

The challenges faced by teachers in Mathematics teaching are perceptible, with regard to students’ interest in the subject and students’ understanding of mathematical concepts. The justification for this work is given by the need to think about new possibilities for teaching mathematics, so that there is the development of critical and democratic thinking by the students. The question posed is: will the contextualization of mathematical concepts through soccer using technological resources contribute to a better understanding of the content being taught? The general aim of this article is to develop the construction of knowledge of statistics and percentage content through the lens of Critical Mathematics Education, contextualizing the ongoing challenge of combating racism in soccer. Discussing topics such as the history of Brazilian soccer in parallel with the fight against racism in mathematics classes is of paramount importance so that we can form critical and reflective citizens, thus being able to transform the society in which we live. It is hoped that the activities proposed here will make math teaching more meaningful for students.

The nature of global estrutures of argumentation in a teaching context based on collective argumentation

2024-01-10T18:00:54-03:00

The aim of this study was to investigate the nature of global argumentation structures in a teaching context based on collective argumentation during a mathematical investigation. To this end, a case study was carried out with students entering a teacher training course in mathematics at a federal educational institution. Data were collected through written records surrounding the group activity as well as through video recording of the collective argumentation. Based on the theoretical methodological framework regarding the subject, the data were analyzed in order to identify the argumentation structure generated and the role of the teacher in its design. As a result, 6 distinct structural compositions were identified, with the “divergent source” structure being an unprecedented contribution to the research literature. The study also revealed that the type of support provided by the teacher during collective argumentation interferes with the anatomy/design of these structures.

Probability for high school in PNLD 2021 mathematics textbooks

2024-02-21T07:08:46-03:00

Probability is an area of mathematics focused on predicting chances, making decisions and analyzing risks, making it one of the main areas of knowledge developed at school. Knowing that the textbook is an essential tool in the teacher's work, this article aims to analyse the perspective of teaching probability in the Probability and Statistics textbooks approved by the PNLD 2021 for High School. Based on documental research, we analyzed the activities considering the meanings of probability, sample spaces and the structuring of events. We found an asymmetry in relation to the meanings, with a great predominance of the classical meaning, the expressive use of discrete sample spaces and limitations in the conceptual approach to important theorems, such as conditional probability for the composition of events. As a result, teachers' skills are fundamental for complementing and correcting the teaching and learning process of probability.

Ethnomathematics

2024-03-14T14:21:35-03:00

This study, of a bibliographic nature, is characterized as a systematic review, whose objective consisted of mapping the panorama of Brazilian academic research in Ethnomathematics, from 2005 to 2023. The search base used was the catalog of theses and dissertations of the Coordination of Improvement of Higher Education Personnel (Capes). 501 works were found, 418 dissertations and 83 theses. The preparation of the study was based on a guide formulated for systematic reviews in the area of Teaching and Mathematics Education, which is constituted, respectively, by the following five stages: objective and question; search for jobs; selection of studies; analysis of productions and presentation of the systematic review. The study has a theoretical foundation centered on theoretical contributions from the Ethnomathematics Program. According to the data collected, the research mapped in this study is focused on issues involving the teaching and learning process, the curriculum, models aimed at Mathematics Education, as well as describing or presenting parts or Ethnomathematics. The studies cover a diversity of cultural contexts, however, there is a focus on investigations focused on peasant and indigenous culture.

The The philosophy of difference through mathematics education

2024-04-04T21:37:34-03:00

This article sought to map the compositions woven, over the last 10 years, between mathematics and the philosophy of difference, in the works published in the annals of the Mathematics Education working group (GT-19) carried out by the National Association of Postgraduate Studies and Research in Education (ANPEd). During this period, five meetings took place, totaling 87 works presented, nine of which were designed and woven based on the philosophy of difference, more precisely on the thoughts of Giles Deleuze and Felix Guattari. It is noticeable the predominance of works by the Group of the University of Juiz de Fora, called “Travessia”. Of the nine works presented, five problematize teaching and learning in the classroom, three were created after the training meetings and one was an invitation to discuss possibilities for building bridges and resisting the necrophilic policies that have devastated Brazilian education in a of a conversation between the participants of the 40th ANPEd GT-19 Meeting. It is concluded that there is a minor mathematics concerned with the movement of forces that resist and re(exist) from the perspective of a less prescriptive and more inventive mathematics.

Epistemological study of standard deviation

2024-04-11T21:20:42-03:00

Since ancient times, mathematics has displayed a high level of creativity and impressive dynamism. However, in teaching/learning programs, they appear as relics to be displayed within the walls of the school. To break with this archaism, Statistics has emerged as the part of mathematics that can shed light on its dynamism and societal roots. Here, too, computational, and theoretical aspects have left little room for a clear understanding of the concepts studied. The aim of this article is to show, through the epistemological study of the notion of standard deviation, how the study of the evolution of concepts can help us understand their meaning and serve as a resource for their teaching.

State of Knowledge

2024-02-21T07:00:12-03:00

It is currently known that problems for teaching mathematics are present in the teacher's school teaching processes, in official documents as well as in textbooks. However, is it possible to say that the problems have always been present in educational practices and in official documents linked to teaching? Based on these initial considerations, this production is affiliated with the research field of the History of mathematics education and aims to present some permanences and transformations, at different historical moments, of the meanings and purposes of “problems” for mathematics teaching from of a literature review, based on the State of Knowledge methodology. From the survey of works such as theses, dissertations and scientific articles, in different digital repositories, it is clear that there have been changes in the conception of problems over time. Between the transition from traditional teaching periods to the Intuitive Method, there is no mention of the term problems. Subsequently, the term problems is presented as a synonym for exercises, for teaching arithmetic. In New School times, on the other hand, problems became dissociated from exercises. They gained both a teaching support character and are also structured as a teaching method to be followed. Finally, problem solving is gaining ground in research in Mathematics Education.

Reflections on the concept of mathematical literacy

2024-03-18T05:47:08-03:00

This article, of a theoretical nature, presents the movement of concepts produced within the scope of Mathematics Education to refer to the term mathematical literacy. Literacy appears in Brazil when the term literate was no longer sufficient to characterize society's new reading and writing demands. From this perspective, based on Brazilian studies, we searched for different terms that directed us to others in the literature in the area, in which we highlight: alfabetização matemática, numeramento, numeramentalização, literacia matemática, matemacia e materacia. From these, we aim to identify the different concepts presented and the (in)existing relationships between them, paying attention to the diversity of perspectives that make up this plot. Thus, despite the lack of uniqueness in relation to the term mathematical literacy, we understand that there is a historical perspective of the construction and evolution of ideas about being mathematically literate. Furthermore, we point out the existence of a relational dynamic between the terms, as well as the categorization in the perspectives of individual acquisition, social practice and criticism, not in an isolated way, but with greater or lesser nuances in each of them.

Experiences of teachers teaching mathematics leading to the challenge of the exercise paradigm

2024-02-21T06:58:05-03:00

This study aims to understand how teachers who teach Mathematics in Basic Education relate their experiences to learning aimed at challenging the exercise paradigm. To do so, we start from an understanding of teacher learning as a change in their participation in school pedagogical practice. The data for this qualitative study were produced through semi-structured interviews with six teachers who teach Mathematics in Basic Education. The analysis indicates that these teachers relate the way they challenge the exercise paradigm in the school context to a dynamic process of learning, in which various shared practices are involved. Thus, we highlight the relevance of the articulation between teachers' life experiences and initial and continuing education courses and programs, so that different modes of professional action are offered to them.

Integrating financial education into the elementary school curriculum

2024-04-04T18:41:12-03:00

This article highlights the relevance of School Financial Education (SFE) as a component of the Elementary Education (EE) curriculum, emphasizing its importance in shaping individuals competent in managing their financial resources. Through the analysis of current public policies, particularly the National Common Curricular Base (BNCC), the text delves into the integration of personal finance concepts in the school curriculum and discusses pedagogical strategies for its implementation. The article is qualitative in nature and illustrates the applicability of SFE in practice, describing the design and execution of SFE pedagogical activities tailored for students in the early years (4th and 5th grades) of Elementary Education. These activities showcase the possibility of introducing SFE effectively and meaningfully from the earliest years of education. Based on the responses obtained, it is inferred that students still have difficulties in formulating numerical expressions and interpreting problems, indicating areas that may require reinforcement or different pedagogical approaches. The outcomes of these activities and their contribution to students' understanding of financial management are also discussed, underscoring the effectiveness of SFE as a teaching tool.

Mathematical aspects of the n-queens problem and the construction of knowledge by Computer Science students

2024-04-24T22:09:28-03:00

This article reports qualitative research, which had as subjects a group of students from a higher education course in Computer Science, with the proposal of solving an issue related to the n-queens problem, a generalization of the original problem, which consisted of having 8 queens on a chessboard, considering different positions, so that the pieces do not capture each other. The specific didactic sequence consisted of proposing a generalization whose application provides the number of diagonals to be considered for solving the problem on any n-by-n board, with n greater than 3. Based on the assumptions of Didactic Engineering, and having as main theoretical supports the Theory of Didactic Situations (TSD) and the work of Zazkis and Liljedahal on close and distant generalizations, the students developed an autonomous investigative trajectory, based on collaborations, to present acceptable solutions to the proposed problem. The results allow us to infer that the experience around solving mathematical problems is relevant as a learning resource in higher education Computer Science courses, considering a scenario of intensive use of digital technologies.

Problem solving and teaching equations of 2nd degree

2024-03-14T18:51:04-03:00

This paper aimed to analyze proposals of teaching 2nd degree Equations developed in research's postgraduate with a focus on problem solving and the conceptions of Algebra. We developed bibliographic research in which we obtained two dissertations that underwent a meta-analysis. The results show that both are interested in teaching approaches to 2nd degree Equations related to Problem Solving. However, misunderstandings between theory and practice are evident regard to limitations and potential of each approach to Problem Solving, in addition to the recurrence of exercises related to the systematization of techniques through repetition, reinforcing a fundamentalist-analytical view of Algebra. It is necessary to consider the importance of expanding studies that present sequential proposals for teaching 2nd degree Equations in the midst of Problem Solving, consistently employing the different approaches (about, for and via), and the conceptions of Algebra that are linked to this teaching.

Methodology focused on the order of chemical reaction, stemming from a problem of developing student and teacher skills and competences

2024-04-07T11:43:27-03:00

This study presents a proposal for an action-research approach to teaching practice following a qualitative document research methodology, applying the anthropological theory of the didactic and the theory of meaningful learning to Chemical Kinetics, a curriculum present in Brazilian high school education. Within this practice, developing a methodology to facilitate the calculation of reaction orders, enhancing the roles of teachers and students, raised questions to be answered: What impact does a methodology focused on the order of chemical reaction have, starting from a problem whose aim is to develop skills and competences that promote the formation of teachers and students, provoking a change in attitude towards socio-environmental issues? Many omissions in wise knowledge and few didactic creations related to experimentation and the process of mathematical modeling were identified in the literature researched. However, in this work, the teaching time in relation to the content and the learning time of the students was respected, and the strategy proved effective in the meaningful, transposition, and praxeological scopes.

Editorial for volume 26.1

2024-04-27T12:16:41-03:00