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

Questões objetivas sobre funções das provas de matemática do vestibular da UFRN dos anos de (2001 a 2008): um diagnóstico sobre os erros que os candidatos cometem

La dificultad que los alumnos encuentran en el aprendizaje de matemática viene siendo objeto de investigación por estudiosos en educación matemática, tanto en Brasil como en el exterior. El objetivo de este estudio consiste em investigar las dificuldades en el aprendizado sobre funciones matemáticas y la influencia de las concepciones alternativas a partir de los errores que los candidatos acerca de las cuestiones sobre funciones en la prueba objetiva de matemática del acceso a la universidad de los años de 2001 a 2008. Teniendo como cuestiones de estudio para alcanzar el objetivo propuesto: identificar la relevancia del tema funciones que son contemplados en las pruebas de acceso a la Universidad; asi como cuáles han sido los tipos de funciones más privilegiados y menos privilegiados; analizar si la contextualización de la pregunta y la presencia de elementos no textuales han influenciado en el aumento de tal dificultad; analizar si la representación semiótica agrega mayor exigencia a la pregunta; analizar respecto a la exigencia matemática de la pregunta; analizar lo que se refiere al desempeño de los candidatos para verificar cuál pregunta tuvo mejor desempeño y cuál el peor e identificar los errores más frecuentemente cometidos por los candidatos en esas pruebas. Las reflexiones de los estudiosos como: Radatz (1980), Cury (1994), Socas (1997), Borasi (1997), Franchi e Rincón (2004), Pochulu (2004) presentan las dificultades en el aprendizaje matemático, que aparecen a partir de los errores cometidos por los alumnos, quando estos errores reciben la influencia de las concepciones alternativas. El estudio que se presenta en esta disertación configura un análisis de los errores que los candidatos han cometido en las preguntas objetivas sobre el tema funciones de las pruebas de acceso a la Universidad de los años de 2001 a 2008, a partir de los relatorios de la Comissão Permanente do Vestibular COMPERVE/UFRN. Con la intención de alcanzar los objetivos propuestos para este estudio, fueran sido construidas categorías de análisis. Los resultados encontrados han sido: El tema funciones es el más frecuente entre los demás con (28,1%); el tipo de función priorizada durante esos años ha sido la función logarítmica con (24%); la contextualización de las preguntas exige una mayor comprensión por parte del candidato de lo que las situaciones directas; la caracterización semiótica posee elementos que estructuran esas preguntas que el educando debe saber asociar al texto; la exigencia matemática posibilitó analizar que el procedimiento medio ha sido el más requisitado; el desempeño de los candidatos ha sido en la mayoría bajo (50%); y los principales errores que ellos han cometido han sido de realizar traducciones incorrectas de las expresiones que aparecen en las situaciones-problema; utilizar todos los datos que aparezcan en el problema sin tomar en cuenta si el cálculo realizado responde a la pregunta solicitada; no interpretar coherentemente las informaciones del gráfico; decodificar incorrectamente los valores representados por literales en una recta numérica. Los resultados señalizan la necesidad de una revisión didáctico-metodológicas de la enseñanza de funciones a raíz de las cuales las dificultades en el aprendizaje se han presentado

Uma sequência didática a partir da temática terremotos com ênfase em CTS

Throughout its history the population of the region of Mato Grande, which includes the city of João Câmara, in Rio Grande do Norte, was subject to earthquakes. These events are caused by a geological fault, known as fault Samambaia. In the 1980s there was an intensification of this phenomenon culminating in an earthquake 5.1 on the Richter scale in the early hours of November 30, 1986, causing researchers from Brazil and other countries to shift to the region to conduct research in Seismology. During this period there was a strong interaction between scientists and local people. With the aim of studying how people experienced that moment that marked the history of the city of João Câmara, from interviews with some individuals who witnessed the incident, is that this research was developed. Taking as a theoretical approach to Science, Technology and Society (STS), aimed to thus carry the theme in a systematic way to the classroom, promoting ways to help teachers with the scientific training and guidance to students in case of occurrence of earthquakes

Matemática Védica no ensino das quatro operações

This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school

Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

História da ciência como estratégia didática no ensino médio: um breve olhar de conteúdos da óptica

From a critique of aspects of the current teaching of physics, we propose in this paper an investigation into the conceptions of Nature of Science (NOS) submitted by students from the high school level, as well as the inclusion of discussions about some elements of NOS, through the History and Philosophy of Science, understanding them as facilitating strategy for more effective learning of Physics and, more specifically, the contents of optics. Based on the historical period corresponding to Greek antiquity to the mid-nineteenth century, built and applied a teaching unit to a high school class at the Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN) Ipanguaçu campus. Our teaching unit involved the reading and interpretation of texts with historical content, observation and assembling five experimental activities, among other activities. Data analysis occurred through questionnaires investigative applied before and after the completion of the teaching unit, as well as questionnaires for content present in the texts. Although not significant, the results indicated that the application of the teaching unit allowed the (re) construction of some conceptions about NOS targets students present in our work, and contribute to a better learning content and greater optical science approach and its nature

Ensinando sobre a natureza da ciência: uma abordagem explícita e contextualizada a partir da história do vácuo

In last decades, the importance of including the contents of the Nature of Science (NOS) in Science Education has been emphasized. Several studies have focused on investigating the conceptions of NOS, supported by students and teachers, as well as design, implement and evaluate proposals that aim to provide a reflection on this theme in the educational context. Considering the complexity of such content, studies indicate the need for explicit and contextualized approaches and the History of Science (HS) is one of the possible paths to this inclusion. We started from the premise that, through a historical study, that aims to discuss the meaning and the basis of our "beliefs", we can know the process of building on what we "believe" and better understand its meaning. This thesis is part of this perspective, proposing to explore the History of the Vacuum, a themed high didactic potential still little used, in order to collaborate with the teaching content of NOS. We present actions on different fronts that originated three products in the context of this research. On the first front, we insert the research and production of instructional materials (three historical texts) to subsidize people interested in the implementation of HPS for educational context through this material. The relevance of this front is justified by the existence of gaps with regard to the production of such material for the context of teacher training. However, we consider that the preparation of instructional material of good quality and accessible does not guarantee that these resources will be used, if they will not be accompanied by discussions in teacher training, on how to use them, contexts and obstacles to be faced. The second part presented refers to the organization and implementation of a workshop for undergraduate students in physics and physics teachers, considering the instrumentalization of these individuals to the preparation and use of teaching strategies to approach aspects of NOS through episodes of History of the Vacuum, as well as the preparation of the text orientation for people interested in implementing the instructional material for secondary education. This guidance text contemplates the difficulties anticipated by the literature of the area and the main challenges faced by the participants about the didactic transposition of HPS for the educational context they were noted during the workshop. The relevance of this second front, in particular, is justified by the existence of gaps with regard to the inclusion of the theme of NOS and the HPS teacher training

Fontes primárias da história do vácuo e da pressão atmosférica na sala de aula: cartas e jornais históricos em articulação com o livro-texto do ensino médio

The use of the History and the Philosophy of Science (HPS) for the teaching of science and scientific subjects has been advocated in recent decades. It has been pointed out that the History of Science could make for a deeper learning of scientific concepts, since it would promote a contact with the problems which that knowledge has set out to solve. Furthermore, historical episodes would serve to put the discussions about the nature of scientific knowledge into context. With a view to explore those potentialities, the literature in the field has sought to identify the challenges and obstacles for the didactic transposition of subjects from the History of Science. Amongst many aspects, the deficiencies in the training of teachers, so that they can work with the insertion of HPS in the classroom have been highlighted. Another aspect that has been mentioned to be a challenge has to do with the didactic transposition of the Primary Sources, that is, of the original texts on the History of Science. The Primary Sources have significant potentialities: making a connection possible between scientists and concepts, showing the difficulties faced during scientific endeavors, perceiving the role of mistakes as obstacles to be surpassed, not as defeat, etc. On the other hand, there has been little exploration of these concepts in an educational context, due to their own peculiarities. The original texts are often hard to understand and their interpretation demands knowledge of the historical and scientific context in which they were written, as well as skills pertaining to the conduction of research in the field of the History of Science. With this scenario in mind, the research towards this Professional MSc degree starts from the challenge of elaborating and discussing proposals which could enable the didactical transposition of the Primary Sources. We have worked specifically with Primary Sources on the History of the Vacuum and of the Atmospheric Pressure, because of the insertion of these subjects in the Brazilian High School curriculum, in connection with the didactical textbooks. "Historic Journals" were made up from clippings of the original historical texts, as was a Didactical Unit, which takes the usual textbooks as a basis and contemplates using the Journals and the entire Primary Sources in High School. At last, we have elaborated and implemented a course designed for the preparation of teachers and for being an opportunity for the discussion of the feasibility of putting these kinds of proposal into practice

"Espaços (mal) ditos": representações dos bordéis Mossoroenses nas décadas de 1950 e 1960

The city that presents itself to our eyes is not just made of stone. The urban layout hides the tactics of the subjects who subjectivate spaces, giving it meaning through the representations that it produces, whether written or oral. The city's art, is represented, is home to the place where the good and bad places. The aim of this study is to analyze the representations about the spaces occupied by mossoroenses brothels in the 1950 and 1960. With this goal we organize the work into three chapters. At first, we present the formation of red-light district in the city, highlighting the composition of the bohemian spaces in good and bad places. In the second chapter we discuss how the representations developed by the newspaper O Mossoroense created a space damn for identifying the area as a place of crime and misdemeanor. In the last chapter we seek to identify and reconstruct the residents of Mossoró, in contemporary times, their memories about the peak time of the brothels in the city. In oral narratives seek to understand how people describe the places of the brothel, comparing the spatiality of the past with this experienced in the city. Therefore, we discuss how these spaces have been turned into places of pleasure and a curse, as places become common in places marked morally.

No tempo dos brotos: juventude e diversão em Petrópolis e no Tirol (1945-1960)

The urban growth of Rio Grande do Norte capital gave his boldest step in the three earlier decades of the twentieth century seeking to catch up with foreign metropolis and also most developed Brazilian cities, for example, Rio de Janeiro. Novelties were such bulky that we can notice the rise of a new city which in many aspects superseded that one considered provincial by local intelligentsia. These urban interferences scratched city ground leaving indelible marks until the present day. The exacerbated growth of the city related to the 1940s, when Natal begins hosting the largest allied military base outside United States in the advent of World War II is important at a time when the city´s population doubled. The emergence of new leisure institutions, amidst already existing ones, continued marking the places as sociabilities and leisure permeated with meanings and representations are revealed. This work sought to know the sociability of Tirol and Petrópolis neighborhoods in Natal, in the period from 1945 to 1960, when the city witnesses the consolidation of a market increasingly focused on leisure and young people start to have a special participation in this process.

O Bairro da Ribeira como um palimpsesto: dinâmicas urbanas na Cidade de Natal (1920-1960)

As cidades são textos. Textos escritos pelas sociedades que compõe os espaços. A partir dessa perspectiva, propõe-se aqui uma leitura do bairro da Ribeira Natal/RN. Esse espaço se consolidou no início do século XX como centro comercial e cultural da capital potiguar, lugar de ação e de interação da Zona Central desta sociedade, espaço de inscrição dos signos da modernidade e do progresso então em voga. Contudo, com o decurso do tempo e as transformações por ele exigidas, o panorama da Cidade de Natal sofreu intensas modificações e o bairro da Ribeira foi relegado à margem desse processo, o que culminou na desvalorização, segregação e, posteriormente, na degradação do seu espaço, que se tornou um palimpsesto. Ao abordar a dinâmica urbana que se processou no bairro da Ribeira, esta pesquisa dividiu o fenômeno em três fases distintas: valorização, transição e decadência

Além das xícaras: a construção do Café São Luiz como lugar de memória em Natal (1950-1980)

This research stands in discussions involving the relationship between memory, history and space. We will work with the Café São Luiz in the neighborhood of Cidade Alta in Natal, an place which remains open and founded in 1953. The place was opened in the district of greater movement of the 1950s, a zone of concentration of commerce and leisure. In consequence an impulse of memory, the Café São Luiz was represented by different statements, which they built a space that serves to support memory and identity of a group. The speeches elaborate the Café São Luiz as a monument, a place of memory according to Pierre Nora. Among these discourses of construction of the Café São Luiz stands out the 1982 book titled Na Calçada do Café São Luiz by José Luiz Silva. This research aims to discuss the construction of the Café São Luiz as a place of memory, questioning their representations, traversing the authorship of speeches over the place

A participação feminina no movimento estudantil secundarista como espaço de luta política (anos de 1980)

The history of women has been an important thematic in the field of Historiography in recent years. Many History scholars have discussed thematics related to genre, pointing out their relationship and conflicts. These new thematics are also the result of a series of changing in history that bring out new problems, subjects and approaches. Our aim in this work is to analise the experience of women militants inserted into the student secondarist movement (ME) in Rio Grande do Norte in the years of 1980 s. Discussing the concepts of History and Spaces, we try to analise the political spaces of ME through public and private spaces that make part of the student militant life, pointing out the conflicts faced during their standing into the movement. To a better understanding of the ME political overview, we set a summary to point out the reconstruction of the student entities reorganized after the military governments, as well as we picture a general picture of this women s insertion in history. We use the oral source as the main methodological resource to the development of our work

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Sobre pedras, entre rios: modernização do espaço urbano de Caicó/RN (1950/1960)

thèse de maîtrise, qui a été idealizée et exécutée à partir de la réunion et les relations dialogiques établies entre la géographie et l'histoire, et l'espace et le temps, a considéré l'environnement urbain comme le thème général et, comme la référence empirique, l'espace urbain de Caicó, incrusté dans les terres semi-arides du Sertão do Seridó Potiguar, plus précisément à la mi-sud de l'État du Rio Grande do Norte. Dans cet espace, à travers de recherche des fragments de mémoires acquis de diverses sources historiques, on a tenté de faire des investigations sur les transformations urbaines qui ont eu lieu dans la ville au cours des années 50 et 60 du XXe siècle. Ces transformations, dans l espace urbain de Caicó à un moment du pic de l'activité de développement de coton, reflétaient et conditionnaient les propres projets de modernization urbaine qui représentants des élites locales eurent conçu avec l'objectif de la construction d une ville idéal dans les regions isolées du Seridó: moderne, civilisé, progressive et capitale régionale du Seridó. Pour cette construction, les nouveaux équipements et services urbains ont passé du plan imaginaire à l espace réel, installés dans plusieurs quartiers de la ville en transformant le paysage urbain. Face à cette situation, cinémas, magasins, station de radio, énergie électrique, institutions de l'éducation, téléphonie, maison de soins infirmiers, usine de bénéficiement de coton, banques, politiques urbaines, hygiéniques et sanitaires, modes de comportement, sociabilités urbaines distincttes, parmi d'autres éléments géographiques se sont institués à travers la réalisation de certains idéaux de progrès social et dans un esprit de modernité urbaine, dans de nouveaux espaces et pratiques inventés, tramés et éprouvés sur les rochers et entre le cours d eau au milieu d'un quotidien urbain marqué par ruptures et permanence de certaines coutumes et habitudes antiques et de certains paysages et environnement ridé