Aprender a ser crítico com a matemática num curso de educação e formação

Em Portugal, de acordo com os princípios gerais da Lei de Bases do Sistema Educativo, um dos objetivos da educação é responder às necessidades resultantes da realidade social, fomentando a evolução plena e harmoniosa de cada indivíduo, no sentido de este se tornar um cidadão livre, responsável, solidário e autónomo, capaz de julgar com espírito crítico e criativo o meio social em que está inserido e de se empenhar na sua progressiva mudança. Para educar matematicamente os alunos é necessário contribuir para o desenvolvimento das suas competências e saberes, ajudando-os a se tornarem cidadãos críticos e conscientes, para que participem criticamente na comunidade e percebam como a matemática é utilizada. O presente estudo visou compreender como é que a Educação Matemática Crítica contribui para o desenvolvimento de competências matemáticas e na formação de cidadãos críticos e conscientes. Para a realização desta investigação foi selecionada uma turma de um Curso de Educação e Formação (CEF), na qual quase todos os alunos, que tinham idades compreendidas entre os 15 e os 17 anos, revelavam um percurso de insucesso em Matemática. O estudo foi do tipo qualitativo e tomou como método a observação participante. Recorreu-se a um conjunto de informações sobre vários temas, retirada da internet, para que os alunos as analisassem criticamente. Este estudo defende a ideia de que a Educação Matemática Crítica contribui para a realização de aprendizagens mais significativas e na formação de cidadãos mais críticos e conscientes, permitindo-lhes participar criticamente na sociedade onde estão inseridos.

Aprendizagem cooperativa e colaborativa em matemática no espaço facebook

O programa de matemática do ensino básico revela que a escola exige uma formação sólida em Matemática para que os alunos, ao longo do seu percurso escolar, possam compreendê-la e utilizá-la, mas o façam igualmente depois da escolaridade, na sua vida pessoal, profissional e social. A investigação feita visa compreender como é que a Educação Matemática Crítica e a rede social Facebook potenciam a aprendizagem crítica da Matemática. A utilização mais frequente desta rede social, possibilita chegar a um maior fluxo de informação/publicidade. Sob a égide da Educação Matemática Crítica, com o objetivo de observar que alterações ocorriam na forma como os alunos aprendiam determinados conceitos matemáticos em situações rotineiras da nossa sociedade. Esta aprendizagem pode ocorrer cooperativamente e/ou colaborativamente conforme as atividades e os alunos que realizam o estudo. O estudo realizado foi de natureza qualitativa de caráter interpretativo. Os alunos realizaram três atividades. A primeira denominada “Atmosfera Terrestre” para introduzir o capítulo de intervalos de números reais e para os discentes se familiarizarem com as ferramentas do Facebook. As outras duas foram uma publicidade de uma empresa e uma notícia sobre as tabelas de IRS para o ano de 2013. Depois de concluído esse estudo, verificou-se que os alunos não tiveram qualquer problema ao nível do manuseamento das ferramentas proporcionadas pelo Facebook. Na atividade introdutória para o capítulo de intervalo de números reais, os alunos conseguiram transpor o que tinha sido discutido em espaço Facebook para a sala de aula, apresentando exemplos da referida atividade. Conseguiram retirar, através da matemática, conclusões e resultados muito pertinentes para uma melhor perceção do que estava implicitamente presente em cada uma das atividades. As conclusões evidenciadas pelos alunos aludem que após várias discussões, argumentos e mesmo algum cálculo matemático conseguiram observar e justificar criticamente que algumas informações estavam camufladas nas distintas atividades. Os alunos constaram que após estas atividades estão mais alertas para situações similares, o que constitui uma conquista do papel da Matemática na sua vida.

Atividades de natureza investigada no estudo de funções: uma experiência com estudantes de matemática aplicada às ciências sociais

ades de natureza investigativa contribuem para a aprendizagem matemática de alunos do ensino secundário. O estudo incidiu sobre uma turma do décimo primeiro ano de escolaridade do curso de línguas e humanidades. Foram trabalhadas três atividades no âmbito do capítulo Modelos Populacionais. Estas foram desenvolvidas com o auxílio de tecnologia, nomeadamente, calculadora gráfica e computador através da exploração do software Graph 4.4.2, no sentido de motivar os alunos e facilitar a compreensão dos conteúdos abordados. Tendo em conta que um dos objetivos deste estudo é analisar as atitudes reveladas pelos alunos aquando da realização das propostas, os dados obtidos são constituídos essencialmente por pormenores descritivos de tal forma que foi aplicada uma metodologia de natureza qualitativa através da observação participante. A utilização da tecnologia motivou os alunos, que se mostraram desde logo entusiasmados com a realização das atividades. Foi também visível, ao longo da realização das propostas, o desenvolv

A motivação dos alunos face à utilização de materiais manipuláveis na aula de matemática: um estudo realizado no 8º ano

O presente trabalho foi elaborado no âmbito do Mestrado em Ensino da Matemática no 3º Ciclo do Ensino Básico e Secundário, da Universidade da Madeira, no ano letivo de 2012/2013. Tem como objetivo analisar e refletir sobre o trabalho implementado nas duas turmas do 8º ano que me foram atribuídas, incidindo sobre a motivação dos alunos face à presença de outros materiais além do típico caderno de exercícios e do manual na aula de matemática. Deste modo, relatarei algumas aulas onde foram propostas atividades com recurso a materiais manipuláveis, jogos e computadores. Esta pesquisa foi realizada com base numa avaliação qualitativa que incidiu sobre a observação direta do trabalho desenvolvido pelos alunos, através dos registos escritos e de gravações de vídeo e áudio de algumas aulas, de forma a poder transmitir com maior exatidão a postura e o empenho dos alunos no decurso destas atividades.

Estudo das características físico-químicas e biológicas pela adesão de osteoblastos em superfícies de titânio modificadas pela nitretação em plasma

SILVA, J. S. P. Estudo das características físico-químicas e biológicas pela adesão de osteoblastos em superfícies de titânio modificadas pela nitretação em plasma. 2008. 119 f. Tese (Doutorado) - Faculdade de Medicina, Universidade de São Paulo. São Paulo, 2008.

Avaliação do estresse oxidativo induzido por superfícies de titânio

Commercially pure Titanium (cp Ti) is a material largely used in orthopedic and dental implants due to its biocompatibility properties. Changes in the surface of cp Ti can determine the functional response of the cells such as facilitating implant fixation and stabilization, and increased roughness of the surface has been shown to improve adhesion and cellular proliferation. Various surface modification methods have been developed to increase roughness, such as mechanical, chemical, electrochemical and plasma treatment. An argon plasma treatment generates a surface that has good mechanical proprieties without chemical composition modification. Besides the topography, biological responses to the implant contribute significantly to its success. Oxidative stress induced by the biomaterials is considered one of the major causes of implant failure. For this reason the oxidative potential of titanium surfaces subjected to plasma treatment was evaluated on this work. CHO-k1 cells were cultivated on smooth or roughed Ti disks, and after three days, the redox balance was investigated measuring reactive oxygen species (ROS) generation, total antioxidant capacity and biomarkers of ROS attack. The results showed cells grown on titanium surfaces are subjected to intracellular oxidative stress due to hydrogen peroxide generation. Titanium discs subjected to the plasma treatment induced less oxidative stress than the untreated ones, which resulted in improved cellular ability. Our data suggest that plasma treated titanium may be a more biocompatible biomaterial.

Desenvolvimento de um protótipo para análise dinâmica da dureza de superfícies metálicas

In this paper we developed a prototype for dynamic and quantitative analysis of the hardness of metal surfaces by penetration tests. It consists of a micro-indenter which is driven by a gear system driven by three-rectified. The sample to be tested is placed on a table that contains a load cell that measures the deformation in the sample during the penetration of micro-indenter. With this prototype it is possible to measure the elastic deformation of the material obtained by calculating the depth of penetration in the sample from the difference of turns between the start of load application to the application of the load test and return the indenter until the complete termination of load application. To determine the hardness was used to measure the depth of plastic deformation. We used 7 types of steel trade to test the apparatus. There was a dispersion of less than 10% for five measurements made on each sample and a good agreement with the values of firmness provided by the manufacturers.

Propriedades tribomecânicas de superfícies de titânio carbonitretadas por plasma

Interstitial compounds of titanium have been mainly studied due to the large range of properties acquired when C, N, O and H atoms are added. In this work, surfaces of TiCxNy were produced by thermochemical treatments assisted by plasma with different proportions of Ar + N2 + CH4 gas mixture. The Ar gas flow was fixed in 4 sccm, varying only N2 and CH4 gas flows. During the thermochemical treatment, the plasma was monitored by Optical Emission Spectroscopy (OES) for the investigation of the influence of active species. After treatments, C and N concentration profile, crystalline and amorphous phases were analyzed by Nuclear Reaction (NRA). Besides tribomechanical properties of the Ti surface were studied through the nanohardness measurements and friction coefficient determination. The worn areas were evaluated by profilometry and Scanning Electronic Microscope (SEM) in order to verify the wear mechanism present in each material. It has been seen which the properties like nanohardness and friction coefficient have strong relation with luminous intensity of species of the plasma, suggesting a using of this characteristic as a parameter of process

Influência das espécies do plasma de N2 + O2 nas propriedades físicoquímicas das superfícies do pet

This work reports the influence of the poly (ethylene terephthalate) textile and films surface modification by plasmas of O2 and mixtures (N2 + O2), on their physical and chemical properties. The plasma surface polymeric modification has been used for many researchs, because it does not affect the environment with toxic agents, the alterations remains only at nanometric layers and this technique shows expressive results. Then, due to its good acceptance, the treatment was carried out in a vacuum chamber. Some parameters remained constant during all treatment, such as: Voltage 470 V; Pressure 1,250 Mbar; Current: 0, 10 A and gas flow: 10 cm3/min, using oxygen plasma alternating the treatment time 10 to 60 min with an increase of 10 min to each subsequent treatment. Also, the samples were treated with a gas mixture (nitrogen + oxygen) which was varied only the gas composition from 0 to 100% leaving the treatment time remaining constant to all treatment (10 min). The plasma treatment was characterized in-situ with Optics Emission Spectroscopy (OES), and the samples was characterized by contact angle, surface tension, Through Capillary tests, Raman spectroscopy, Infrared attenuated total reflection (IR-ATR) and atomic force microscopy, scanning electronic Microscopy (SEM) and X-ray Photoelectron Spectroscopy (XPS). The results showed that oxygen treated fabrics presented high wettability, due to the hydrophilic groups incorporation onto the surface formed through spputering of carbon atoms. For the nitrogen atmosphere, there is the a film deposition of amine groups. Treatment with small oxygen concentration in the mixture with nitrogen has a higher spputered species of the samples

Síntese de pigmento cerâmico ferrita de cobalto utilizando planejamento experimental

Synthetic inorganic pigments are the most widely used in ceramic applications because they have excellent chemical and thermal stability and also, in general, a lower toxicity to man and to the environment. In the present work, the ceramic black pigment CoFe2O4 was synthesized by the polymerization Complex method (MPC) in order to form a material with good chemical homogeneity. Aiming to optimize the process of getting the pigment through the MPC was used a fractional factorial design 2(5-2), with resolution III. The factors studied in mathematical models were: citric acid concentration, the pyrolysis time, temperature, time and rate of calcination. The response surfaces using the software statistica 7.0. The powders were characterized by thermal analysis (TG/DSC), x-ray diffraction (XRD), scanning electron microscopy (SEM) and spectroscopy in the UV-visible. Based on the results, there was the formation of phase cobalt ferrite (CoFe2O4) with spinel structure. The color of the pigments obtained showed dark shades, from black to gray. The model chosen was appropriate since proved to be adjusted and predictive. Planning also showed that all factors were significant, with a confidence level of 95%

Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media

Caracterização de superfícies de titânio modificado por oxidação à plasma

Recent years have seen a significant growth in surface modifications in titanium implants, resulting in shorter healing times in regions with low bone density. Among the different techniques, subtraction by chemical agents to increase oxidation has been applied for surface treatment of dental implants. However, this technique is generally unable to remove undesirable oxides, formed spontaneously during machining of titanium parts, raising costs due to additional decontamination stages. In order to solve this problem, the present study used plasma as an energy source to both remove these oxides and oxidize the titanium surface. In this respect, Ti disks were treated by hollow cathode discharge, using a variable DC power supply and vacuum system. Samples were previously submitted to a cleaning process using an atmosphere of Ar, H2 and a mixture of both, for 20 and 60 min. The most efficient cleaning condition was used for oxidation in a mixture of argon (60%) and oxygen (40%) until reaching a pressure of 2.2 mbar for 60 min at 500°C. Surfaces were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), atomic force microscopy (AFM), adhesion and cell proliferation. SEM showed less cell spreading and a larger number of projections orfilopodia in the treated samples compared to the control sample. AFM revealed surface defects in the treated samples, with varied geometry between peaks and valleys. Biological assays showed no significant difference in cell adhesion between treated surfaces and the control. With respect to cell proliferation, the treated surface exhibited improved performance when compared to the control sample. We concluded that the process was efficient in removing primary oxides as well as in oxidizing titanium surfaces

Superfícies de titânio modificadas termoquimicamente por plasma : avaliação da resposta biológica

This laboratory study involves the participation of a group with professionals from different areas that had contributed to the construction of a multidisciplinary knowledge, about biological response of titanium surfaces modified through thermochemical treatment by plasma. Thus, the crystalline phase was previously characterized in relation to the topography, roughness, molhability and nitrogen concentration in the samples surface. It s indispensable that materials implanted can influence in a good cellular response as well as promotes a bacteria action. Surfaces modified by plasma were exposed to different cultures such as: cellular (human osteoblastic) and bacteria (Staphylococcus epidermidis ATCC35984 and Pseudomonas aeruginosa ATCC 27853) in order to evaluate the biological response. It was evaluated the adhesion, proliferation, morphology and cellular preference of human ostheoblastic cells (HOST), as well as the formation of a biofilm and bacteria proliferation. It was still analyzed the bacteria selectivity ability in relation to the surfaces. The software Image Pro Plus was used to the counting of cells and bacteria adhered to the surface of disks. The results were submitted to the variance analysis (ANOVA), and then, by the Kruskal-Wallis test, using GraphPad Instat ® software, version 3.5 to Windows. The nitrided samples in spite of show a higher roughness and molhability showed a smaller bacteria growing and higher cellular proliferation, when compared to non treated samples, indicating that the treated material present a high efficiency to biomedical implants

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

Professores em contexto formativo: um estudo do processo de mudanças de concepções sobre o ensino da matemática

El objetivo en esta tesis consistió en estudiar el proceso de los cambios de los conceptos de profesores de la educación infantil y de los años iníciales de la educación básica referente a la enseñanza de la matemática. La investigación se desenvolvió en la escuela Presidente Kennedy, en la ciudad de Natal, en Rio Grande do Norte, teniendo como participante 05 (cinco) profesores del curso normal superior a través de la educación superior del instituto relacionado. El trabajo asocia el programa a él Programa de Pós-Graduação em Educação da Universidade Federal do Rio Grande do Norte, en la base de pesquisa Formação e Profissionalização Docente coordinada de los doctores Betânia Leite Ramalho e Isauro Beltran Núñez. El referencial teórico-metodológico en quien si apoya el trabajo se inserta en la señal conceptual usada por Giordan y de Vecchi (1996), de Carrillo y Contreras (1994), Ramalho; Núñez y Gauthier (2003), Ponte (1998), Guimarães (1988), Ernest (1989). En esta investigación, los conceptos de los profesores habían sido estudiados en el contexto educativo de la formación del nivel superior, usándola reflexiva crítico práctico como estrategia formativa. Estos conceptos se entienden como estructuras subyacentes al pensamiento del profesor. Dado la naturaleza del objeto del estudio, la información, para las intenciones de esta investigación, habían sido cosechados a través de los instrumentos siguientes: cuestionario, plan de la lección, entrevista diaria y del campo. El cuestionario fue constituido de preguntas abiertas y de las entrevistas de la mitad-structuralized. La organización de los datos permitió a La inferencia de los conceptos, usando la técnica de la triangulación de datos. La investigación divulgó que los conceptos de los profesores, a través del proceso formativo, se habían desarrollado de una plataforma para otra, yéndose puesto que los modelos didácticos tradicionales para otros modelos dirigidos a una tendencia didáctica de espontaneísta/investigativa. La reflexión crítica era considerada como elemento catalítico de los cambios de los conceptos de los profesores en la educación de las matemáticas, sin embargo déjenos verifican que estos cambios son difíciles de ocurrir para la naturaleza compleja de estos conceptos. Como facilitadores de los factores de estos cambios, encontramos y el investigativo el trabajo, la dinámica y la naturaleza de las actividades se convirtió en el colaborativo de proceso formativo, entre otros. Como obstáculos a los cambios, identificamos el contexto del trabajo de los profesores, de la cultura de los individualistas prácticos de sus profesores de los colegas, del concepto linear, estático y de los mecánicos de los procesos para enseñar, el conocimiento profesional construído durante la formación inicial, alineación con los modelos didácticos de sus viejos profesores, entre otros