Olhares sobre a formação do professor de matemática. Imagem da profissão e escrita de si

The main focus of this thesis is the formation of a mathematical teacher at a college institution. The general aim is to describe and to analyze the formation process of a mathematical teacher which is an undergraduate student in Mathematics at the Instituto de Educação Superior Presidente Kennedy IFESP, in Natal-RN. It is based on a qualitative ethnographic approach, and has its theoretical anchorage in the (auto)biographical narratives, the social representative theories, and the mathematical education. The number of participants in this investigation was 12 undergraduate students, which corresponds to 25% of the total number of students. The corpus utilized in our analysis included 48 (auto)biographical essays, 12 (auto)biographies (formation's memories), and 12 contextualization files, besides the research's diary. The sources were obtained from the whole program of studies, i.e. from November 2003 to December 2006. The analysis revealed that the reminiscences of the 12 students' academic trajectory influenced their professional formation, since their images of a mathematical teacher were intrinsically related to the one they had before. These representations were being either demolished or constructed in a network along the assertive image of their profession, changing afterwards the mathematical representation and the teaching way of this discipline. Our study also shows that the beginning of their teacher career was marked by mechanical practices influenced by their old teachers. The (trans)formation of themselves and their teaching practices happened in a smooth way as soon as they increased their knowledgements in Mathematics, and it reflected upon the way they learned mathematics. The writing of their (auto)biographies helped the set up of new knowledgements, leaving to a self-consciousness as well as a self-formation, and contributed for the construction of a new way to see and to live the profession. Therefore, a mathematical teacher, for the undergraduate students of the IFESP involved in this work, is made at the interface of the familiar, academic, and professional context, besides the reflexive writings about the formation path, the way of life and the relationships among them

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Política de formação de professores: uma leitura a partir da análise do programa especial de formação de professores para a educação básica PROEB/UFMA

Study of Teacher Education Policy: a reading from the analysis of Programa Especial de Formação de Professores para a Educação Básica Proeb - aims to analyze the initial teacher training developed by the Universidade Federal do Maranhão - UFMA. Proeb is a policy of in-service training of teachers, formulated and implemented in the context of current educational policies for basic education. This work assumes that the guidelines developed in the last decades of the twentieth century are linked to international organizations that spread in Latin America continent a homogeneous model of training which has as main features to be held in service through the mode the distance and the school as a leading locus. In Brazil, these guidelines are supported on the Law of Directives and Bases of National Education No. 9.394/96 and Report 09/2001, which deals with the Syllabus Guidelines for the formation of Basic Education Teachers. To carry out the study was taken as reference, the syllabus developed for the deployment of Proeb from 1998 to 2002, specifically the proposal operationalized in the Degree Course of Mathematics in the city of Vitória do Mearim in Maranhão. To conduct the study, it was used literature as a way to deepen understanding, clarify and aim the conceptual aspect of the object researched. The documental research was consisted in the analysis of legal documents concerning the reform of education policies, teacher training and pedagogical project Proeb/UFMA and, finally, the semi-structured interviews were used to allow a better understanding of the subjects involved with research. The data analysis has shown that the curriculum designed to operationalize the course of undergraduate mathematics Proeb/UFMA, despite having guidelines that point to the separation of theory/practice dichotomy and establish as a principle work as an educational principle, has an disciplinary curriculum organization that reinforces the instrumental view of the syllabus, not enabling in practice, the execution of their initial proposal. Concerning to the view of graduates on the course, they highlight the weaknesses of the course, but also evidence that it has allowed an improvement of initial training, through the disciplines of the common core syllabus of courses and special training. It is possible seeing in graduates words, that the course have had repercussions in their teaching and improving their integration into the labor market and in the community of Vitória do Mearim. Overall, these developments have indicated evidence of teacher professionalization, although they are incipient. The work has shown that for the professionalization of teachers is introduced, the syllabus of undergraduate teacher education must overcome the traditional view of syllabus and implement contextualized curricula in a multidisciplinary approach involving, in equal proportions, the general education and training specific course. Accordingly, it is believed in need to review the role of the University in the formative process, as well as recovering as part of educational policies, the omnilateral size of teacher education

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

Estudo histórico e pedagógico sobre ternos pitagóricos à luz de eugène bahier

At the present investigation had the purpose to achieve a descritive analysis pedagogy in the work of Recherche méthodique et propriétés des triangles rectangles en nombres entiers. According to the analysis achieved, we made and applyed the teaching module called Pitagories: one of tools to comprehension Pitagory Theorema, there were studying by public students in mathematic course in the UFRN , the new mathematic teachers in future. The analysis the was made with writen test the was showed that all students got the view comprehension in the teaching approach module, to apointed the difference in the learning qualytative with other reseach that was made with quastionaire and enterview. With this module that was made with the new future teacheres there was more attention the better comprehension with the Pitagory Theorema, that was good focus in the pitagory about the potential historical pedagogyc in the work studied.

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

O erro produzido pelo aluno no contexto pedagógico: uma luz ou uma pedra no meio do caminho?

Student’s mistakes as viewed in a didactic and pedagogical perspective are a phenomenon inevitably observed in any context in which formal teaching-andlearning processes are taking place. Researchers have shown that such mistakes are viewed most of the times as undesirable and often as a consequence of lack of attention or poor commitment on the part of the student and rarely considered didactically useful. The object of our reflections in this work is exactly those mistakes, which are born in the entrails of the teaching-and-learning processes. It is our understanding that a mistake constitutes a tool which mediates knowledge and may therefore become a strong ally of the instructor’s actions in her/his teaching tasks and thus should be taken into the teacher’s best consideration. Understanding a mistake as so, we postulate that the teacher must face it as a possibility to be exploited rather than as a negative occurrence. Such an attitude on the part of the teacher would undoubtedly render profitable didactic situations. To deepen the understanding of our aim, we took a case study on the perception of senior college students in the program of Mathematics at UFRN in the year 2009, 2nd term. The reason of this choice is the fact that Mathematics is the field presenting traditionally the poorest records in terms of school grades. In this work we put forth data associated to ENEM1 , to the UFRN Vestibular2 and the undergraduate courses on Mathematics. The theoretical matrixes supporting our reflections in this thesis follow the ideas proposed by Castorina (1988); Davis e Espósito (1990); Aquino (1997); Luckesi (2006); Cury (1994; 2008); Pinto (2000); Torre (2007). To carry out the study, we applied a semi-structured questionnaire containing 14 questions, out of which 10 were open questions. The questions were methodologically based on the Thematic Analysis – One of the techniques for Content Analysis schemed by Bardin (1977) – and it was also used the computer program Modalisa 6.0 (A software designed by faculties the University of Paris VIII). The results indicate that most of the teachers training instructors in their pedagogical practice view the mistakes made by their students only as a guide for grading and, in this procedure, the student is frequently labeled as guilty. Conclusive analyses, therefore, signal to the necessity of orienting the teachers training instructors in the sense of building a new theoretical contemplation of the students’ mistakes and their pedagogical potentialities and so making those professionals perceive the importance of such mistakes, since they reveal gaps in the process of learning and provide valuable avenues for the teaching procedures.

A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Opiniões sobre estágio curricular e prática de ensino na licenciatura em química: o caso do CEFET-PB

The Brazilian legal documents are directing the reformulation of the courses that prepare students to be teachers. Through out the country many institutions look for to fit themselves in such documents. On the other hand, other IES (Superior Education Institutions), when they are setting up such courses they looked for to be adequate to the new public politics. Based on the National Curricular Norms to form teachers for Basic Education, in tertiary level, in 2004 it was created at the CEFET-PB,the Chemistry Course (Licenciatura) to prepare people to be teachers, whose organization. This work presents the results of a research of phenomenological nature that aimed to comprehend the teachers opinions, in the range of discussions about the current politics of formation, particularly related to the CNE/CP 1 and CNE/CP 2/2002 resolutions. This work based on the curricular proposal for the Chemistry Course (Licenciatura), presents the relationship between the probationary period and the teaching practice at the CEFET-PB, in order to contribute for a reflection about these categories to clarify the teachers of the course. It started from the consideration of all changes operated in contemporary society implies changes on teacher's pedagogical practices. It was used tow instruments for the data collection: a questionnaire with open and closed questions and recordable interviews. Nine teachers form the CEFET-PB took apart and four licensed teachers. It was based in a theoretic frame as a support for discussions about the different models of teachers formation. We concluded that the representations of teachers about probationary period the practice on the activity for the teachers formation was strongly anchored in characteristic elements of the formative tendency of a institution that historically acted on a technician formation, and the results pointed to strong signs of attitudes based on a model of the technical rationality

A desistência de alunos na licenciatura em física no Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN): causas e sugestões para o combate

This dissertation proposes studying the issue of withdrawal undergraduate in physics at the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN) and collaborate with suggestions for dealing with this problem. The first chapter begins with an overview of two significant problems in the Brazilian educational system: the high dropout rates in degrees in physics and the lack of teachers with specific training in this science. Then, we discuss the relevance of this research to the area of physics teaching, as well as justify its completion as part of a professional master's degree. After, we present a proper definition for the term withdrawal, which is based on the existing problem in the IFRN. And, in the same chapter, we explicitly the focus, the objectives and the methodological aspects of this work. The results obtained in our investigation are presented in next four chapters. In the second chapter of this dissertation, we present: a brief history of the creation of IFRN degree in physics, the functioning of this course and the foundation of classrooms 2004.2 and 2006.1. We also show a kind of map of the withdrawal of the groups investigated (the dropout rate was 84.4% in both groups) and an analysis of the relationship between the curricula of each of them and the number of dropouts. In the third chapter, we display a descriptive statistics of the students which dropout and found that the largest dropout occurred with students who are women, married, parents of one kid; workers, joined with a minimum age of 23 years and completed high school at least 6 years. Then in the fourth chapter, we reveal and discuss the students' reports on the causes of their dropout. From the data presented, we can say that the answer to the question "What was the main reason for your dropout?" Is mainly in personal injury claims: another option for upper-level course and lack of time to devote to the course. In the fifth chapter, we show the results related to teacher s opinions about the phenomenon in question. We detected three main causes for the abandonment, according to teachers: the lack of dedication, the lack of interest and lack of integration in the course. In the sixth and final chapter, we discuss the results and present our conclusion and the proposed report - the product of this dissertation, presented as Annex. This report contains mainly suggestions for curricular and institutional actions that can contribute to reducing the dropout degree in Physics in the IFRN. The main actions suggested are: implementation of the curriculum in disciplines, implementation of programs or actions to combat this poor content of basic training, implementation of specific programs or actions for the student worker, and dissemination of IFRN degree in physics in schools through seminars or workshops

História da matemática na formação de professores: sistemas de numeração antigos

This essay aims to present and describe a proposal of insertion of Mathematics History into teachers undergraduation. Such addition proposal is expected to take place as curricular component to be taught on initial undergraduation for mathematics teachers. The selection of contents for the proposal has been based on the national Curriculum Guidelines (DCN, 2001, acronym in portugueses) for bachelor’s degree in Mathematics; the National Curricular Guidelines for Elementary School (PCNEF, 1998, acronym in Portuguese); and the National Curricular Guidelines for High School (PCNEM, 1999, acronym in Portuguese). The curricular component now presented is supposed to take a 60 hour workload, and includes the following topics: History of Ancient Numbering Systems, History of Trigonometriy and History of fuctions. For the sake of exemplification, the topic History of Ancient Numbering Systems is discussed and analysed in detail as practice for the new curricular component.