Jogo Mega-Duque: uma proposta para o ensino de probabilidade

Pós-graduação em Matemática em Rede Nacional - IBILCE

A formação de professores de matemática no contexto da resolução de problemas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O ensino de geometria através da pavimentação do plano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma proposta de sequência didática para o ensino de Programação Linear no Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

O processo constitutivo da Resolução de Problemas como uma temática da pesquisa em Educação Matemática: um inventário a partir de documentos dos ICMEs

Pós-graduação em Educação Matemática - IGCE

A resolução de problemas no contexto do estágio curricular supervisionado: dificuldades e limites de licenciandos em matemática

The aim was to investigate the difficulties and limits of four future mathematics teachers to conduct classes in regencies approach of problem solving. Based on participation in a course this approach, undergraduates elaborated three didactic sequences, which were taught by the activity of conducting classroom discipline Supervised Curricular Training. After this work, participated in an individual interview to report what had developed in classroom. The results showed difficulties in the following aspects: in the elaboration of didactic sequences; in providing an environment for discussion of resolution strategies students. Furthermore, the data analysis showed limits related: the lack of space at the school teacher to allow implementation of lessons developed; lack of basic mathematical knowledge of the students.

Programação no ensino de matemática utilizando Processing 2: Um estudo das relações formalizadas por alunos do ensino fundamental com baixo rendimento em matemática

Pós-graduação em Educação para a Ciência - FC

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Cognitive Interventions with Children with Special Needs - Transfer effects and multidisciplinary perspectives

Our last study with regularly developed children demonstrated a positive effect of working memory training on cognitive abilities. Building upon these findings, the aim of this multidisciplinary study is to investigate the effects of training of core functions with children who are suffering from different learning disabilities, like AD/HD, developmental dyslexia or specific language impairment. In addition to working memory training (BrainTwister), we apply a perceptual training, which concentrates on auditory-visual matching (Audilex), as well as an implicit concept learning task. We expect differential improvements of mental capacities, specifically of executive functions (working memory, attention, auditory and visual processing), scholastic abilities (language and mathematical skills), as well as of problem solving. With that, we hope to find further directions regarding helpful and individually adapted interventions in educational settings. Interested parties are invited to discuss and comment the design, the research question, and the possibilities in recruiting the subjects.

Verbalization of Dependencies Between Concepts Built Through Fuzzy Cognitive Maps

The new computing paradigm known as cognitive computing attempts to imitate the human capabilities of learning, problem solving, and considering things in context. To do so, an application (a cognitive system) must learn from its environment (e.g., by interacting with various interfaces). These interfaces can run the gamut from sensors to humans to databases. Accessing data through such interfaces allows the system to conduct cognitive tasks that can support humans in decision-making or problem-solving processes. Cognitive systems can be integrated into various domains (e.g., medicine or insurance). For example, a cognitive system in cities can collect data, can learn from various data sources and can then attempt to connect these sources to provide real time optimizations of subsystems within the city (e.g., the transportation system). In this study, we provide a methodology for integrating a cognitive system that allows data to be verbalized, making the causalities and hypotheses generated from the cognitive system more understandable to humans. We abstract a city subsystem—passenger flow for a taxi company—by applying fuzzy cognitive maps (FCMs). FCMs can be used as a mathematical tool for modeling complex systems built by directed graphs with concepts (e.g., policies, events, and/or domains) as nodes and causalities as edges. As a verbalization technique we introduce the restriction-centered theory of reasoning (RCT). RCT addresses the imprecision inherent in language by introducing restrictions. Using this underlying combinatorial design, our approach can handle large data sets from complex systems and make the output understandable to humans.

An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

Measuring the influence of Cooperative Learning and Project Based Learning on problem solvin skill.

The aim of this study is to evaluate the effects obtained after applying two active learning methodologies (cooperative learning and project based learning) to the achievement of the competence problem solving. This study was carried out at the Technical University of Madrid, where these methodologies were applied to two Operating Systems courses. The first hypothesis tested was whether the implementation of active learning methodologies favours the achievement of ?problem solving?. The second hypothesis was focused on testing if students with higher rates in problem solving competence obtain better results in their academic performance. The results indicated that active learning methodologies do not produce any significant change in the generic competence ?problem solving? during the period analysed. Concerning this, we consider that students should work with these methodologies for a longer period, besides having a specific training. Nevertheless, a close correlation between problem solving self appraisal and academic performance has been detected.

On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach.

Abstract?We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)