Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

A Compreensão da idéia do número racional e suas operações na EJA: uma forma de inclusão em sala de aula

The awareness of the difficulty which pupils, in general have in understanding the concept and operations with Rational numbers, it made to develop this study which searches to collaborate for such understanding. Our intuition was to do with that the pupils of the Education of Young and Adults, with difficulty in understanding the Rational numbers, feel included in the learning-teaching process of mathematics. It deals with a classroom research in a qualitative approach with analysis of the activities resolved for a group of pupils in classroom of a municipal school of Natal. For us elaborate such activities we accomplished the survey difficulties and obstacles that the pupils experience, when inserted in the learning-teaching process of the Rational numbers. The results indicate that the sequence of activities applied in classroom collaborated so that the pupils to overcome some impediments in the learning of this numbers

Contribuições da investigação em sala de aula para uma aprendizagem das secções cônicas com significado

In this work, the didactical possibilities of investigation use in classroom, through an experience with high school students from Federal Center of Technological Education of Paraíba, as well as the study of conic sections were analysed. In order to fulfill our goals the theoretical conceptions concerning the meaninful learning in conection with the investigation of mathematics history were taken into account. The classroom research occurred by means of activities which encouraged the learner to investigate his own concepts on the conic sections. The results of the proposed activities showed the effectiveness and the efficiency of such a methodology as regards the making up of the required knowledge. They also reveal that the investigation in the classroom guides the ones involved, in this process, to have a wider look at the origins, the methods used and the several representations presented by mathematics that certainly lead, specially the students, to a meaninful learning

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

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Atribuição de significado ao conceito de proporcionalidade: contribuições da história da matemática

This study is the result of a work which approaches the Mathematics History how source of the meaning s attribution in the proportionality concept. We adopt the methodology of the source qualitative and we work with a group of teachers from instruction s public system of the fundamental and medium level from Pocinhos City Paraíba. For the data collection, we use the field notes, the questionnaire, a sequence of activities and the interview semistructured like instruments. The study had how objective to know the significates attributeds to proportionality concept through of the activity mediate from Mathematics History, besides to investigate if a approach of the nature enables modification according to this sense. The results obtaineds though the data analysis indicate that the activities bring contributions which refer to achieve objectives. On the other hand they also showed that we have a long trajectory to be trailed in the meaning of to turn the Mathematics History a subsidy effective in the teachers practice, in view of the formation absence in the knowledge area, besides the necessity of the approach adequated of the Mathematics History in the didatics books of Mathematic

Trajetória do ifrn em inclusão escolar

Discussions over the topic of inclusion of handicapped people at school are considered recent, but they have become more and more frequent within the national and international scenario. Such discussion has also being inserted in the speeches and actions of the school institution and with the formation of educators. This investigation is made necessary as a way to collect elements to reconsider the actions for the inclusion of the special education need youth. In special the visually handicapped ones, at Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN). The creation of a support unit functions as main vehicle for the actions of the institution. It is intended to know what young people with limitations have to say regarding their experiences as a way to signal paths to be and not to be followed by the support unit. Therefore, the experience which these young boys and girls have is of crucial importance. In order to accomplish the task, it was decided to use methodological elements based upon elements supported by the life reports of two deficient students here called Borges and Stéfano. Their reports are from childhood to their arrival at IFRN. From their reports, categories appeared: childhood and the role of family; school life and, finally, related to the actions of the support unit of IFRN, being divided in inclusive actions and obstacles. The first one takes a second look at the actions of the family within the learning-teaching process of these students. The second category presents the moment in which students started to receive formal education per se. The last category constitutes the cornerstone of the investigation, for it analyses the process of inclusion in the institution, according to the perception of the students with visual limitations. The results signaled the need for shared intervention between students with Special Education Needs and school professionals in the elaboration of the Educational Planning, which guarantees the defense of the rights to an efficient teaching practice and effective in the process of inclusion of these students

Análise das provas objetivas de química dos vestibulares da UFRN de 1997 a 2010: uma caracterização a partir das mudanças

Las pruebas de vestibular, en los últimos años en el Brasil, han sido objeto de diversas investigaciones, considerando que ese proceso selectivo es una de las vias para ingresar en las universidades públicas y termina por influenciar la enseñanza en las escuelas. De esa forma, algunos vestibulares han pasado por cambios, de un simple proceso selectivo clasificatorio a un proceso fundamentado en reflexiones sociológica, pedagógica y crítica, lo que ha promovido cuestionamientos respecto del aprendizaje y de su papel en la escuela. Delante de esa realidad, la Universidad Federal de Rio Grande del Norte (UFRN) ha implementado cambios en sus vestibulares procurando una aproximación a las Orientaciones Curriculares Nacionales, como los PCNEM, los PCN+ y las OCEM. Siendo así, el objetivo de este estudio fue caracterizar el avance cualitativo en las pruebas de preguntas objetivas a partir de los cambios ocurridos en el vestibular de la UFRN en el periodo de 1997 a 2010, definiéndose las siguientes cuestiones de estudio: ¿Cuáles son los tipos de preguntas que caracterizan las pruebas objetivas de Química del vestibular? ¿Cuáles cuestiones presentan las mayores dificultades para los candidatos? ¿Cuáles son los contenidos conceptuales privilegiados? ¿En qué tipo de preguntas los candidatos presentan mayores índices de éxitos? ¿Qué diferencias pueden ser establecidas entre las preguntas antes y después del periodo que establece los cambios en el vestibular de la UFRN? Las discusiones teóricas del estudio están fundamentadas en las siguientes referencias: PCNEM (BRASIL, 1999), PCN+ (BRASIL, 2001), OCEM (BRASIL, 2006), Zabala (1999), Jiménez Aleixandre et al. (2003), Pozo (1999), Álvarez de Zayas (1992), Núñez (2009), Relatorios Comperve/UFRN (1997 a 2010), e en relación a las evaluaciones: Pasquali et al. (2003), Silva y Núñez (2008), Marín y Benarrouch (2009). Para el estudio fueran construidas las siguientes categorías que permitieran el análisis de las cuestiones: contextualización de la cuestión, temas conceptuales, problema, representación semiótica, cálculo matemático, pertinencia de la cuestión e índice de acierto. Los resultados muestran un avance cualitativo de las preguntas de Química, en los cuales se observa un modelo de prueba que prioriza el uso de verdaderos problemas, de situaciones contextualizadas, de pocos cálculos, dándose prioridad al razonamiento que implica la comprensión, la aplicación y la interpretación de los conocimientos conceptuales, todo lo que puede estimular una enseñanza más adecuada en relación a las exigencias actuales de la Educación en Química

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Formação continuada de professores que ensinam matemática: o papel do ábaco na ressignificação da prática pedagógica

The present dissertation performs a study about abacus part on the continuous education of Elementary School s Mathematic teachers on what concerns the basic operations of addition and subtraction with (re)unification by using the manipulative and/or informatical abacus. Therefore, the research intends to answer the following question: How does a teacher reframe the pedagogical practice while teaching the Decimal Numeral System and the conventional operations of addition and subtraction with (re)unification through manipulative and informatical abacus? In order to do so, we rely ourselves on the Guy Brousseau s Theory of Didactic Situations (TDS) from 1996 that affirms the necessity to trace a way in accordance with the teaching situations that lead the student s learning; and on the work of Pierre Lévy (1993), in which the poles of communication oral, written and virtual create three ways of communication through which the learning process happens. The methodology of this paper was based on the Strategic Research-Action of Franco (2005). The didactic sequence was elaborated in accordance with TDS and used the manipulative and informatical abacus as didactic resource. With the application of the didactic sequence, it was verified that the continued formation of Elementary School s teachers concerning the operations of addition and subtraction on the initial years/levels is pertinent once it has been observed some difficulties of the teachers concerning this mathematical subject. Besides, the analysis of the didactic sequence has allowed one to realize that teachers had some difficulties concerning the numeric representation with order zero, the resolution of operations of addition and subtraction using the manipulative and informatical abacus and the realization of (re)unification on the subtraction with meaning. These observations has been discussed with the teachers and, after that, it has been done some didactic-methodological routings of the operations of addition and subtraction with re(unification) that contributes with the teaching and learning process.

A leitura como instrumento facilitador da compreensão matemática

This research builds on a qualitative approach and proposes action research to develop, implement and evaluate a strategy grounded in the teaching of geometry reading from different text types, in order to enhance the understanding of mathematical concepts by students in the 6th grade of elementary school. The teaching of mathematics, strengthened by a reading practice that fosters a greater understanding of science, because it would contribute to the expansion of vocabulary, acquire a higher level of reasoning, interpretation and understanding, providing opportunities thus a greater contextualization of the student, making out the role of mere spectator to the builder of mathematical knowledge. As a methodological course comply with the following steps: selecting a field of intervention school, the class-subject (6 years of elementary school) and teacher-collaborator. Then there was a diagnostic activity involving the content of geometry - geometric solids, flat regions and contours - with the class chosen, and it was found, in addition to the unknown geometry, a great difficulty to contextualize it. From the analysis of the answers given by students, was drawn up and applied three interventional activities developed from various text (legends, poems, articles, artwork) for the purpose of leading the student to realize, through reading these texts, the discussions generated from these questions and activities proposed by the present mathematics in context, thus getting a better understanding and interaction with this discipline as hostility by most students. It was found from the intervention, the student had a greater ability to understand concepts, internalize information and use of geometry is more consistent and conscientious, and above all, learning math more enjoyable

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

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

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