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.

História, filosofia e sociologia da educação matemática na formação do professor: um programa de pesquisa

We present and discuss in this article some features of a research program whose central object of investigation is the way in which the recent fields of history, philosophy, and sociology of mathematical education could take part in a critical and qualified manner in the initial and continuing training of teachers in this area. For that, we endorse the viewpoint that the courses for mathematics teacher education should be based on a conception of specificity through which a new pedagogical project could be established. In such project those new fields of investigation would participate, in an organic and clarifying way, in the constitution of multidimensional problematizations of school practices, in which mathematics would be involved, and that would be guided by academic investigations about the issues that currently challenge teachers in the critical work of incorporation, resignification, production, and transmission of mathematical culture in the context of the school institution.

Influence of dental metallic artifact from multislice CT in the assessment of simulated mandibular lesions

OBJECTIVE: This study evaluated the influence of metallic dental artifacts on the accuracy of simulated mandibular lesion detection by using multislice technology. MATERIAL AND METHODS: Fifteen macerated mandibles were used. Perforations were done simulating bone lesions and the mandibles were subjected to axial 16 rows multislice CT images using 0.5 mm of slice thickness with 0.3 mm interval of reconstruction. Metallic dental restorations were done and the mandibles were subjected again to CT in the same protocol. The images were analyzed to detect simulated lesions in the mandibles, verifying the loci number and if there was any cortical perforation exposing medullar bone. The analysis was performed by two independent examiners using e-film software. RESULTS: The samples without artifacts presented better results compared to the gold standard (dried mandible with perforations). In the samples without artifacts, all cortical perforation were identified and 46 loci were detected (of 51) in loci number analysis. Among the samples with artifacts, 12 lesions out of 14 were recognized regarding medullar invasion, and 40 out of 51 concerning loci number. The sensitivity in samples without artifacts was 90% and 100% regarding loci number and medullar invasion, respectively. In samples with artifacts, these values dropped to 78% and 86%, respectively. The presence of metallic restorations affected the sensitivity values of the method, but the difference was not significant (p>0.05). CONCLUSIONS: Although there were differences in the results of samples with and without artifacts, the presence of metallic restoration did not lead to misinterpretation of the final diagnosis. However, the validity of multislice CT imaging in this study was established for detection of simulated mandibular bone lesions.

Evaluation of simulated bone lesion in the head of the mandible by using multislice computed tomography

Conventional radiography has shown limitation in acquiring image of the ATM region, thus, computed tomography (CT) scanning has been the best option to the present date for diagnosis, surgical planning and treatment of bone lesions, owing to its specific properties. OBJECTIVE: The aim of the study was to evaluate images of simulated bone lesions at the head of the mandible by multislice CT. MATERIAL AND METHODS: Spherical lesions were made with dental spherical drills (sizes 1, 3, and 6) and were evaluated by using multislice CT (64 rows), by two observers in two different occasions, deploying two protocols: axial, coronal, and sagittal images, and parasagittal images for pole visualization (anterior, lateral, posterior, medial and superior). Acquired images were then compared with those lesions in the dry mandible (gold standard) to evaluate the specificity and sensibility of both protocols. Statistical methods included: Kappa statistics, validity test and chi-square test. Results demonstrated the advantage of associating axial, coronal, and sagittal slices with parasagittal slices for lesion detection at the head of the mandible. RESULTS: There was no statistically significant difference between the types of protocols regarding a particular localization of lesions at the poles. CONCLUSIONS: Protocols for the assessment of the head of the mandible were established to improve the visualization of alterations of each of the poles of the mandible's head. The anterior and posterior poles were better visualized in lateral-medial planes while lateral, medial and superior poles were better visualized in the anterior-posterior plane.

Comparison between cone-beam and multislice computed tomography for identification of simulated bone lesions

There are many studies that compare the accuracy of multislice (MSCT) and cone beam (CBCT) computed tomography for evaluations in the maxillofacial region. However, further studies comparing both acquisition techniques for the evaluation of simulated mandibular bone lesions are needed. The aim of this study was to compare the accuracy of MSCT and CBCT in the diagnosis of simulated mandibular bone lesions by means of cross sectional images and axial/MPR slices. Lesions with different dimensions, shape and locularity were produced in 15 dry mandibles. The images were obtained following the cross sectional and axial/MPR (Multiplanar Reconstruction) imaging protocols and were interpreted independently. CBCT and MSCT showed similar results in depicting the percentage of cortical bone involvement, with great sensitivity and specificity (p < 0.005). There were no significant intra- or inter-examiner differences between axial/MPR images and cross sectional images with regard to sensitivity and specificity. CBCT showed results similar to those of MSCT for the identification of the number of simulated bone lesions. Cross sectional slices and axial/MPR images presented high accuracy, proving useful for bone lesion diagnosis.

Assessment of simulated mandibular condyle bone lesions by cone beam computed tomography

There are many limitations to image acquisition, using conventional radiography, of the temporomandibular joint (TMJ) region. The Computed Tomography (CT) scan is a better option, due to its higher accuracy, for purposes of diagnosis, surgical planning and treatment of bone injuries. The aim of the present study was to analyze two protocols of cone beam computed tomography for the evaluation of simulated mandibular condyle bone lesions. Spherical lesions were simulated in 30 dry mandibular condyles, using dentist drills and drill bits sizes 1, 3 and 6. Each of the mandibular condyles was submitted to cone beam computed tomography (CBCT) using two protocols: 1) axial, coronal and sagittal multiplanar reconstruction (MPR); and 2) sagittal plus coronal slices throughout the longitudinal axis of the mandibular condyles. For these protocols, 2 observers analyzed the CBCT images independently, regarding the presence or not of injuries. Only one of the observers, however, performed on 2 different occasions. The results were compared to the gold standard, evaluating the percentage of agreement, degree of accuracy of CBCT protocols and observers' examination. The z test was used for the statistical analysis. The results showed there were no statistically significant differences between the 2 protocols. There was greater difficulty in the assessment of small-size simulated lesions (drill # 1). From the results of this study, it can be concluded that CBCT is an accurate tool for analyzing mandibular condyle bone lesions, with the MPR protocol showing slightly better results than the sagittal plus coronal slices throughout the longitudinal axis.

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.

Influence of Annealing Heat Treatment and Cr, Mg, and Ti Alloying on the Mechanical Properties of High-Silicon Cast Iron

The influence of annealing on the mechanical properties of high-silicon cast iron for three alloys with distinct chromium levels was investigated. Each alloy was melted either with or without the addition of Ti and Mg. These changes in the chemical composition and heat treatment aimed to improve the material's mechanical properties by inhibiting the formation of large columnar crystals, netlike laminae, precipitation of coarse packs of graphite, changing the length and morphology of graphite, and rounding the extremities of the flakes to minimize the stress concentration. For alloys with 0.07 wt.% Cr, the annealing reduced the impact resistance and tensile strength due to an enhanced precipitation of refined carbides and the formation of interdendritic complex nets. Annealing the alloys containing Ti and Mg led to a decrease in the mechanical strength and an increase in the toughness. Alloys containing approximately 2 wt.% Cr achieved better mechanical properties as compared to the original alloy. However, with the addition of Ti and Mg to alloys containing 2% Cr, the chromium carbide formation was inhibited, impairing the mechanical properties. In the third alloy, with 3.5 wt.% of Cr additions, the mechanical strength improved. The annealing promoted a decrease in both hardness and amount of iron and silicon complex carbides. However, it led to a chromium carbide formation, which influenced the mechanical characteristics of the matrix of the studied material.

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.

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.

Characterisation of the effect of a simulated hydrocarbon spill on diazotrophs in mangrove sediment mesocosm

An analysis of the effect of an oil spill on mangrove sediments was carried out by contamination of mesocosms derived from two different mangroves, one with a history of contamination and one pristine. The association between N(2) fixers and hydrocarbon degradation was assessed using quantitative PCR (qPCR) for the genes rrs and nifH, nifH clone library sequencing and total petroleum hydrocarbon (TPH) quantification using gas chromatography. TPH showed that the microbial communities of both mangroves were able to degrade the hydrocarbons added; however, whereas the majority of oil added to the mesocosm derived from the polluted mangrove was degraded in the 75 days of the experiment, there was only partially degradation in the mesocosm derived from the pristine mangrove. qPCR showed that the addition of oil led to an increase in rrs gene copy numbers in both mesocosms, having almost no effect on the nifH copy numbers in the pristine mangrove. Sequencing of nifH clones indicated that the changes promoted by the oil in the polluted mangrove were greater than those observed in the pristine mesocosm. The main effect observed in the polluted mesocosm was the selection of a single phylotype which is probably adapted to the presence of petroleum. These results, together with previous reports, give hints about the relationship between N(2) fixation and hydrocarbon degradation in natural ecosystems.

Annealing effects on microstructure and coercive field of ferritic-martensitic ODS Eurofer steel

Oxide dispersion strengthened reduced-activation ferritic-martensitic steels are promising candidates for applications in future fusion power plants. Samples of a reduced activation ferritic-martensitic 9 wt.%Cr-oxide dispersion strengthened Eurofer steel were cold rolled to 80% reduction in thickness and annealed in vacuum for 1 h from 200 to 1350 degrees C to evaluate its thermal stability. Vickers microhardness testing and electron backscatter diffraction (EBSD) were used to characterize the microstructure. The microstructural changes were also followed by magnetic measurements, in particular the corresponding variation of the coercive field (H(c)), as a function of the annealing treatment. Results show that magnetic measurements were sensitive to detect the changes, in particular the martensitic transformation, in samples annealed above 850 degrees C (austenitic regime). (C) 2010 Elsevier B.V. All rights reserved.