A elaboração e instituição do currículo mínimo de matemática no Rio de Janeiro

O currículo traz subjacente a si, as ideias de seu tempo, o olhar de sua sociedade para questões humanas e outras tacitamente políticas. Traz em seu escopo toda uma trama de heranças históricas e a marca pessoal daqueles que se dedicaram a sua construção. E desta forma, analisar as tramas de um currículo de matemática é muito mais que olhar uma sequência de conteúdos linearmente organizados. É, sobretudo, entender, que aquela construção foi tecida de forma a sustentar um corpo de ideias que diz sobre seu tempo. Esta pesquisa evidenciou o processo de elaboração e instituição do currículo mínimo pela Seeduc/RJ e trouxe questionamentos e inquietações de naturezas cognitivas e sociais. Uma primeira inquietação concerne ao descarte de conteúdos do currículo anterior, que configura agora, este novo currículo. Esse processo de elaboração e instituição refletiu a inexistência de diálogo entre os diversos segmentos sociais e profissionais do campo educacional. Interesses governamentais interferiram diretamente nos educacionais, subtraindo a democracia das ações de políticas públicas implementadas. Ficou evidente que não houve clareza conceitual quando dessa e em contraste até mesmo com propostas nacionais e a legislação vigente. Através do Currículo Mínimo buscou-se unificar toda a rede de ensino da Seeduc/RJ, dentro de uma perspectiva academicista limitada, desconsiderando as especificidades locais e de cada grupo. Desta forma, foi desconsiderada a dialética educacional e a retórica da matemática enquanto disciplina acadêmica, que é uma forma particular da relação social. O processo instituído evidencia uma visão de professores passivos e alunos considerados mínimos.

Ensino primário e matemática dos imigrantes e descendentes germânicos em Santa Leopoldina (1857-1907)

O objetivo da pesquisa é descrever o cenário da imigração germânica no século XIX, tratando também, de trilhar o caminho da educação por meio de educadores e das comunidades na Colônia de Santa Leopoldina, criada em 1857, na Província do Espírito Santo, considerando 50 anos a partir do início da imigração (1857-1907). A pesquisa histórica ancorou-se em consultas a documentos oficiais do Império, documentos e relatórios oficiais dos Presidentes da Província do Espírito Santo, jornais de circulação da época, fotografias, mapas geográficos, mapas estatísticos, livros didáticos antigos e livros de autores que abordaram o processo imigratório do Espírito Santo. O diálogo com Marc Bloch ajudou a entender essa multiplicidade de documentos, na complexa relação entre o passado e o presente da educação do Espírito Santo. O trabalho apresenta uma trajetória do imigrante germânico vindo da Europa até a ex-colônia e como a administração da província tratou a imigração e a educação. O ensino primário iniciou-se a partir de iniciativas públicas e particulares. Foram identificados as primeiras escolas e os nomes de muitos professores que atuaram no período estudado. Os livros utilizados nas escolas das comunidades teuto-brasileiras eram oriundos da Alemanha e posteriormente foram produzidos no sul do Brasil. Entre os livros escritos em alemão encontrados destacam-se o livro texto de alfabetização „Lese – Schule I für Deutsche Kinder in Brasilien‟, editado na Alemanha no final do século XIX, de autoria do diretor de uma escola particular em Santa Leopoldina, Albert Richard Dietze, e o primeiro volume do livro de matemática „Rechenbuch für Deutsch-Brasilianische Volksschulen‟, de Ferdinand Hackbart, Konrad Glaus e Hermann Lange. Foi feita uma análise sob os aspectos físicos e formais, o processo de ensino e os conteúdos do livro de matemática. A análise evidenciou que a proposta de ensino apoia-se no “cálculo mental” e o escrito, com a repetição dos conteúdos, envolvendo o treino intensivo. Os conceitos de matemática são apresentados partindo de problemas com situações concretas do aluno para a aquisição de competências necessárias para inserir o aluno em sua comunidade. Levando-se em conta que o livro foi editado em 1906, conclui-se que se trata de uma obra relevante com uma proposta de ensino que se manteve presente nos livros didáticos de matemática até os dias atuais.

Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

Factors influencing amblyopia rehabilitation in occlusive therapy

Amblyopia develops in an early period and is a decrease of visual acuity (unilateral or bilateral) caused by a deprivation of vision or abnormal binocular interaction. Prognosis of Amblyopia is better when occlusive treatment is implemented in an early stage. Visual acuity of amblyopic eye does not improve without effective occlusive therapy. The aim of this study is to identify potential risk factors of noncompliance with treatment when it is implemented by parents in amblyopic children.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Scheduling of head-dependent cascaded reservoirs considering discharge ramping constraints and start/stop of units

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning head-dependent reservoirs under competitive environment. We propose a novel method, based on mixed-integer nonlinear programming (MINLP), for optimising power generation efficiency. This method considers hydroelectric power generation as a nonlinear function of water discharge and of the head. The main contribution of this paper is that discharge ramping constraints and start/stop of units are also considered, in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve two case studies based on Portuguese cascaded hydro systems, providing a higher profit at an acceptable computation time in comparison with classical optimisation methods based on mixed-integer linear programming (MILP).

Periodic dynamic systems for infected hosts and mosquitoes

A mathematical model for the purpose of analysing the dynamic of the populations of infected hosts anf infected mosquitoes when the populations of mosquitoes are periodic in time is here presented. By the computation of a parameter lambda (the spectral radius of a certain monodromy matrix) one can state that either the infection peters out naturally) (lambda <= 1) or if lambda > 1 the infection becomes endemic. The model generalizes previous models for malaria by considering the case of periodic coefficients; it is also a variation of that for gonorrhea. The main motivation for the consideration of this present model was the recent studies on mosquitoes at an experimental rice irrigation system, in the South-Eastern region of Brazil.

Nonlinear optimization method for short-term hydro scheduling considering head-dependency

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head-dependency is considered on short-term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head-dependency.

Evaluating Tsunami Impact on the Gulf of Cadiz Coast (Northeast Atlantic).

The Gulf of Cadiz coasts are exposed to tsunamis. Emergency planning tools are now taking into account this fact, especially because a series of historical occurrences were strikingly significant, having left strong evidence behind, in the mareographic records, the geological evidence or simply the memory of the populations. The study area is a strip along the Algarve coast, south Portugal, an area known to have been heavily impacted by the 1 November 1755 event. In this study we use two different tsunami scenarios generated by the rupture of two thrust faults identified in the area, corresponding to 8.1-8.3 magnitude earthquakes. Tsunami propagation and inundation computation is performed using a non-linear shallow water code with bottom friction. Numerical modeling results are presented in terms of flow depth and current velocity with maximum values of 7 m and 8 m/s for inundation depth and flow speed, respectively. These results constitute a valuable tool for local authorities, emergency and decision planners to define the priority zones where tsunami mitigation measures must be implemented and to develop tsunami-resilient communities.

Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

How to teach mathematics with MOODLE

The aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

New challenges in mathematics for the european higher education

In this paper we will talk about a math project submitted to the Lifelong Learning Programme. European higher education needs a reform in order to play its full role in the Europe of Knowledge. Modernisation of higher education is necessary in the areas of curricula (Bologna process), funding and governance so that higher education institutions can face the challenges posed by globalisation and contribute more effectively to the training and retraining of the European workforce. On the other hand Mathematics is an essential component of all educational systems. Mathematical literacy is being scrutinized in assessment efforts such as the OCDE Programme for International Student Assessment (PISA). This showed a low level in Europe. Due to the Bologna Process, which brought several didactical implications for Higher Education (HE) institutions, there is the need of lifelong learning. This evolution is in conflict with the earlier mentioned lack of competencies on basic sciences, such as Mathematics. Forced by this duality, efforts are combined to share expertise in the Math field and the integration of pedagogical methodologies becomes a necessity. Thus, several European countries have proposed an International Project to the Lifelong Learning Programme, Action ERASMUS Modernisation of Higher Education, to make institutions more attractive and more responsive to the needs of the labour market, citizens and society at large. One of the main goals of the project is to attract students to math through high-quality instructional units in an understandable, exciting and attractive way.

A checkpointing-enabled and resource-aware Java Virtual Machine for efficient and robust e-Science applications in grid environments

Object-oriented programming languages presently are the dominant paradigm of application development (e. g., Java,. NET). Lately, increasingly more Java applications have long (or very long) execution times and manipulate large amounts of data/information, gaining relevance in fields related with e-Science (with Grid and Cloud computing). Significant examples include Chemistry, Computational Biology and Bio-informatics, with many available Java-based APIs (e. g., Neobio). Often, when the execution of such an application is terminated abruptly because of a failure (regardless of the cause being a hardware of software fault, lack of available resources, etc.), all of its work already performed is simply lost, and when the application is later re-initiated, it has to restart all its work from scratch, wasting resources and time, while also being prone to another failure and may delay its completion with no deadline guarantees. Our proposed solution to address these issues is through incorporating mechanisms for checkpointing and migration in a JVM. These make applications more robust and flexible by being able to move to other nodes, without any intervention from the programmer. This article provides a solution to Java applications with long execution times, by extending a JVM (Jikes research virtual machine) with such mechanisms. Copyright (C) 2011 John Wiley & Sons, Ltd.