Área e volume da esfera

In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

NORDSIECK FORMS OF STIFFLY-STABLE ADAMS-TYPE CYCLIC METHODS THAT ARE INSENSITIVE TO STEP-SIZE CHANGES

In this paper we determine a matrix S and a vector l for stiffly-stable Adams-type cyclic methods that are insensitive to step size changes by using the definition of equivalent methods, (see, e.g. [l]), in the Nordsieck notation. The elements S and l, written in a parametric form, permit us to represent in Nordsieck form the methods that were constructed in [7] and the new methods that satisfy the above properties.

Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

As diferentes “personalidades” do número racional trabalhadas através da resolução de problemas

We address the different "personalities" of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number - rational point, quotient, fraction, ratio, and operator - are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different "personalities" of the rational number. In general, these "personalities" are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these "personalities", the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics.

Características dos Problemas que os Alunos Constroem a partir do Enunciado de uma Questão Aberta de Matemática

The present paper shows characteristics of problems that students in the 4(th), 8(th), and 12(th) grades built in response to the enunciation of an open-ended question, taken from their written work in the common question of AVA-2002 (Parana State Large-Scale Assessment-2002). These problems are characterized, in part, by a linear resolution structure constituted based on students' interpretation of individual bits of information contained in the enunciation, one by one, without establishing relations between them; and partly by a non-linear resolution structure constituted based on relations established among the bits of information in the enunciation. Analysis of students' written work is one alternative for teachers to know students' mathematical activity, as well as their particular ways of interpretating enunciations.

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.