Movimentos que permeiam o devir professor de matemática de alguns licenciandos

Pós-graduação em Educação Matemática - IGCE

Correspondências científicas como uma relação didática entre história e ensino de matemática: o exemplo das cartas de Euler a uma princesa da Alemanha

Lettres àune Princesse d'Allemagne sur divers sujets de physique et de philosophie (Letters to a Princess of Germany on various topics of physics and philosophy) is the work taken as an object of study of this thesis. It is a literary success written in the eighteenth century by the Swiss mathematician and physicist Leonhard Paul Euler (1707-1783) in order to meet a request from the Prussian king, Frederick II, the Great (1712-1786) to accept to guide the intellectual education of his niece, the young princess Anhalt-Dessau (1745-1808). The method of teaching and learning through letters elected to the education of the German monarch resulted in a collection of 234 matches in which Euler theory is about music, Philosophy, Mechanics, Optics, Astronomy, Theology and Ethics among others. The research seeks to point out mathematical content contained in this reference work based on the exploitation and adaptation of original historical works as an articulator of development activities for teaching mathematics in basic education and in accordance with the National Curriculum Parameters of Mathematics (NCP) work. The general objective point out the limits and didactic potential of Lettres à une Princesse d'Allemagne sur divers sujets de physique et de philosophie as a source of support for teachers of basic education in developing activities for teaching mathematics. The discussions raised point to concrete possibilities of entanglement between the extracted mathematical content of the bulge of the work with current teaching methodologies from resizing the use of letters according to Freire's pedagogical perspective of the correspondence, and especially the use of new communication channels in the century XXI, both aimed at dialogue and approximation between those who write and those who read.

Formação docente para a inserção da história e filosofia da ciência no ensino: textos histórico-pedagógicos em discussão

The present dissertation focuses on specific problems in the educational context: challenges in the construction of historical narratives for pedagogical use as well as the difficult task of using them in the classroom. In this context, we seek to work in teacher training for insertion of History and Philosophy of Science (HPS) in classroom, and historical narratives become mediation elements to advance the dialogue with this specific audience. This initiative is in line with a recurring concern: one of the main challenges related to the didactic transposition of HFC would be the lack of teacher preparation. Historical contents and Nature of Science are still absent in classrooms. Insecurity and lack of knowledge by teachers are often mentioned as factors that contribute to this situation. It is important, therefore, that teachers (active and in training) take part in discussions concerning the inclusion of HPS in classroom. It is relevant that they know examples of historic-philosophical didactic proposals to address science and contents on science, develop skills to adapt them to their specific contexts and to develop their own proposals. It is believed that these issues are significant to undertake conscious initiatives to insert HPS in classrooms. It is considered that adapting educational proposals to particular educational contexts depends on understanding what these proposals indeed mean and how flexible they can be. In order to address these objectives, we elaborated an educational product, a didactic material focused on teacher training, which was used in an extension course at UFRN. The didactic material discusses the role of HPS in Education, Nature of Science and historiographical issues. It presents a series of dialogical activities on aspects of didactic transposition of HPS, especially those regarding historical narratives. A set of historicpedagogical texts on the History of Vacuum and Atmospheric Pressure is used as a mediation element in discussions. We address potential, possibilities and limitations historical narratives. To carry out the course, it was taken into account methodological concerns of so-called action research. There have been expected changes, modifications and effective actions in the own teacher training material in face of the experience of the researcher-lecturer in interactions with the participants of the course as well as in face of impressions reported by the participants. Developments in this direction have been incorporated into the teacher training material.

A Física e a Matemática no século XVIII – contribuições para o estudo do newtonianismo na primeira obra de Verney

A maior parte dos estudiosos da obra de Verney destacam no domínio da filosofia natural a sua defesa do experimentalismo e a adopção, dentro do eclectismo filosófico, de uma postura de adesão ao newtonianismo. Nas linhas que se seguem propomo-nos aprofundar a matriz newtoniana do pensamento de Verney ao nível das fontes (autores e livros) mencionados no Verdadeiro Método de Estudar, em particular na sua Carta X. Analisa-se as suas referências aos Principia de Newton bem como ao Cálculo Integral e Diferencial com a citação de Leibniz, os irmãos Bernoulli e o Marquês de l’ Hôpital e outros matemáticos contemporâneos. Assinala-se a ausência de qualquer alusão à segunda grande obra de Newton, a Óptica. Por último, discute-se a inclusão sistemática de autores e obras italianas, menos conhecidos da Europa culta da época, que parece terem sido importantes na formação «moderna» do jovem Verney radicado em Roma.

Governamentalidade democrática e ensino de Filosofia no Brasil contemporâneo

This article takes the concepts of biopower and governmentality as the starting point for an analysis of certain recent Brazilian government documents about the introduction of Philosophy as a subject in secondary school. In the 1980s, this argument centered on Philosophy's so-called criticism and its potential for preparing citizens for a democratic society, was used by the movements aimed to restore democracy in Brazil. This argument appears to have been assimilated by the Brazilian government, because it is stated in the Guidelines and Bases of Education Law, secondary school students should demonstrate knowledge of philosophy necessary for the exercise of citizenship. The argument also appears in documents such as the PCN and PCN+ (National Curricular Parameters) and OCEM (Curriculum Guidelines for Secondary School) in their chapters on Philosophy. These documents are examined here in the light of governmentality, making explicit how Philosophy is equipped to train young people according to what is understood as a modern democratic society.

Modelagem matemática e simulação numérica do resfriamento rápido de morango com ar forçado

This work approaches the forced air cooling of strawberry by numerical simulation. The mathematical model that was used describes the process of heat transfer, based on the Fourier's law, in spherical coordinates and simplified to describe the one-dimensional process. For the resolution of the equation expressed for the mathematical model, an algorithm was developed based on the explicit scheme of the numerical method of the finite differences and implemented in the scientific computation program MATLAB 6.1. The validation of the mathematical model was made by the comparison between theoretical and experimental data, where strawberries had been cooled with forced air. The results showed to be possible the determination of the convective heat transfer coefficient by fitting the numerical and experimental data. The methodology of the numerical simulations was showed like a promising tool in the support of the decision to use or to develop equipment in the area of cooling process with forced air of spherical fruits.

Projeto de um cortador de base para colhedora de cana-de-açúcar utilizando otimização matemática

A base-cutter represented for a mechanism of four bars, was developed using the Autocad program. The normal force of reaction of the profile in the contact point was determined through the dynamic analysis. The equations of dynamic balance were based on the laws of Newton-Euler. The linkage was subject to an optimization technique that considered the peak value of soil reaction force as the objective function to be minimized while the link lengths and the spring constant varied through a specified range. The Algorithm of Sequential Quadratic Programming-SQP was implemented of the program computational Matlab. Results were very encouraging; the maximum value of the normal reaction force was reduced from 4,250.33 to 237.13 N, making the floating process much less disturbing to the soil and the sugarcane rate. Later, others variables had been incorporated the mechanism optimized and new otimization process was implemented .

Sociedade, cultura, matemática e seu ensino

One of the effects of the globalized world is a strong tendency to eliminate differences, promoting a planetary culture. Education systems are particularly affected, undergoing strong pressure from international studies and evaluations, inevitably comparative, and sadly competitive. As a result, one observes the gradual elimination of cultural components in the definition of education systems. The constitution of new social imaginaries becomes clear; imaginaries empty of historical, geographical and temporal referents, characterized by a strong presence of the culture of the image. The criteria of classification establish an inappropriate reference that has as its consequence the definition of practices and even of education systems. On the other hand, resistance mechanisms, often unconscious, are activated seeking to safeguard and recover the identifying features of a culture, such as its traditions, cuisine, languages, artistic manifestations in general, and, in doing so, to contribute to cultural diversity, an essential factor to encourage creativity. In this article, the sociocultural basis of mathematics and of its teaching are examined, and also the consequences of globalization and its effects on multicultural education. The concept of culture is discussed, as well as issues related to culture dynamics, resulting in the proposition of a theory of transdisciplinar and transcultural knowledge. Upon such basis the Ethnomathematics Program is presented. A critique is also made of the curriculum presently used, which is in its conception and detailing, obsolete, uninteresting and of little use. A different concept of curriculum is proposed, based on the communicative (literacy), analytical (matheracy), and material (technoracy) instruments.

Avaliação em matemática: uma leitura de concepções e análise do vivido na sala de aula

Este artigo traz uma reflexão acerca da avaliação em Matemática, destacando os modos pelos quais essa avaliação pode vir a ser compreendida e discutida em um curso de formação de professores da área. Explicita-se como, a partir das situações de sala de aula, o olhar para as possibilidades da avaliação pode contribuir para a formação desse professor no que diz respeito ao compreendido pelos alunos. São analisadas três situações-problema, propostas aos alunos do curso de graduação em Matemática, cujo foco é o modo de avaliar. O olhar avaliativo e o fazer Matemática são entendidos como uma forma de o aluno voltar-se para o conteúdo matemático, abrindo-se ao que, no seu lidar cotidiano, se mostra. Diz-se da importância de se considerarem os "dados relevantes" e o "a ser conhecido" nas situações de avaliação que permitem, ao professor, ler a aprendizagem do aluno em seu modo de se expressar.

Modelagem matemática do controle de brucelose bovina por vacinação

As fêmeas bovinas, por sua importância na transmissão e na manutenção da brucelose, constituíram o alvo dos inquéritos do Programa Nacional de Controle e Erradicação da Brucelose e da Tuberculose Animal. Com base em informações obtidas em unidades federativas onde foram realizados inquéritos sorológicos e observadas prevalências de animais acima de 2%, elaborou-se um modelo para simular a dinâmica da brucelose em rebanhos bovinos formados exclusivamente por fêmeas, analisando o efeito de estratégias de vacinação. Para baixa cobertura vacinal, da ordem de 30%, o tempo para reduzir a prevalência a 2%, valor adotado como referência, pode ser longo, aproximando-se do dobro do tempo necessário para uma cobertura mais alta, de 90%. De acordo com o modelo, o tempo para reduzir a prevalência a 1% ou 2%, que permitam passar à fase de erradicação, pode chegar a uma década. Recomenda-se a intensificação do esforço para a vacinação de fêmeas, procurando atingir alta cobertura vacinal.

Avaliação do Processo de Ensino e Aprendizagem em Matemática: contribuições da teoria histórico-cultural

This article presents the results of a study that investigated the meaning of evaluation in mathematics from the historical cultural perspective, focusing on activity theory. In order to develop the investigation, a collaborative group was formed from the Oficina Pedagogica de Matematica de Ribeirao Preto - Sao Paulo (Math Pedagogic Workshop of Ribeirao Preto - OPM/RP), constituted of pre-school teachers and early elementary school teachers, who were participants in this research. The main role of the collaborative group was to offer guided development to the teachers about the teaching of mathematics from the historical-cultural perspective, aiming at collecting data on the process of appropriation of mathematical knowledge by the teachers. The syntheses about the teachers' learning process have contributed to systematize the guiding elements of evaluation in mathematics from the historical-cultural perspective.

Disciplinas de Fundamentos de Matemática: uma discussão à luz dos significados da palavra “fundamentos”

Based on a survey of summaries of courses on the Foundations of Mathematics, from Mathematics Teacher Education programs in the southern part of Brazil, and some remarks on the legislation related to the course syllabuses, we discuss the meaning of the word ""Foundations"" in order to reflect on the proposals of these issues in the courses, which will be undergoing reformulation. The opinions of students in one of these courses regarding the meaning of the term ""foundations"", as well as the data obtained from the survey and the remarks regarding legislation, may lead to considerations about the possibilities for a better qualification of the initial education of Mathematics teachers.

Epistemologia ou filosofia da Ciência da Informação?

It discusses the philosophical proposal by Luciano Floridi for Library and Information Science (BCI) and the response of information theorists to the proposal. The article points out the courage of the young Italian philosopher - from the computational field - who breaks the hegemony of epistemology as foundation for BCI. However, it takes distance from the philosophy of information in favor of a philosophy of Information Science, in which the creation of concepts, in Deleuze and Guattari's inspiration, is mandatory. In this sense, the article presents two philosophical concepts for the area of knowledge organization, such as: minor documentary language and descriptive classification by affects. These same concepts consider all elements of the philosophical concept: the problem the concept refers to; the components of the concept, the neighborhood and its boundaries and, most importantly, the becoming of the philosophical concept on scientific or artistic practices.

A Análise Matemática no Ensino Universitário Brasileiro: a contribuição de Omar Catunda

The goal of this paper is to show the diffusion, reception, and utilization of Omar Catunda's book Course of Mathematical Analysis for mathematics and engineering teaching in Brazilian universities, e. g., University of Sao Paulo and the University of Bahia from 1950 to 1976. We used interviews of some ex-alumni or users of his book. We also present some signs of the influence of his book and of Catunda himself at University of Rio Grande do Sul. We argue that Catunda and his book were important agents of process of modernizing the teaching of calculus and analysis, through his classes as well as his book.

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.