Proportion in school mathematics textbooks: A comparative study

This paper analyses how proportion is introduced and developed in selected mathematics textbooks for middle school students of Portugal, Spain, Brazil, and USA. The analysis focuses on the nature of the approach and on the cognitive demand, structure, and context of the tasks. The results show that the textbooks tend to present tasks at an intermediate level of cognitive demand and with a closed structure. Nonmathematical contexts predominate in three of the four textbooks. However, there are marked differences in the way textbooks approach the conceptual and procedural aspects of proportion. The way the students are addressed also varies, ranging from a questioning/problem solving style, to an explaining/practicing style, each of these styles supporting a rather different kind of activity.Este artigo analisa como proporção é introduzida e desenvolvida nos livros didáticos matemática para alunos do ensino médio (Ensino Fundamental II) em Portugal, Espanha, Brasil e EUA. A análise incide sobre a natureza da abordagem e na demanda cognitiva, estrutura e contexto das tarefas. Os resultados mostram que os livros didáticos tendem a apresentar as tarefas em um nível intermediário de demanda cognitiva e com uma estrutura fechada. Contextos não-matemáticos predominam em três dos quatro livros didáticos analisados. No entanto, há diferenças marcantes no modo como os livros abordam os aspectos conceituais e procedimentais de proporção. A forma didática de tratar o assunto também varia, indo de um estilo de questionamento / resolução de problemas, a um modo explicativo/prático; cada um deles ampara-se em um tipo diferente de atividade

Case Study in Intellectual Capital and Territorial Development: Analysing Portuguese Local Governments WEB Pages

Multiple authors argue that the digital infrastructure of municipalities and regions, such as websites, have an important role to play in local and regional development since they enable the access and sharing of information, knowledge and the provision of certain services. Functioning as an entrance way to a territory, the websites provide important contributions in the knowledge and intellectual capital management activities. In this sense, an evaluation of websites is a core activity for the updating of content and delivery of services, contributing to their best management in the context of e-government. However, there are a limited number of studies on evaluation of websites from the perspective of intellectual capital, although the importance of this asset, either in business or public sector, and also to the development of territories is recognized. So, this study intend to show the importance of intellectual capital in the public sector, more specifically on local government, by assessing the intellectual capital of its web pages by implementing a model of intellectual capital for the public sector

Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an H\"{o}lder drift component

We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded H\"{o}lder term; in spite of this, due to the space-time white noise it is possible to prove pathwise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilbert spaces or concrete SPDEs

Money, Credit and Default

This paper develops a quantitative model of unsecured debt, default, and money demand for heterogenous agents economies. The paper generates a theory of money demand for the case in which money is a dominate asset that is not needed to carry-out transactions. In this environment holding money helps the agents to smooth their consumption during those periods in which they are excluded from credit markets following a default in their debts. In the model the welfare of the individuals is affected by the inflation rate: high inflation rates preclude individuals of using money as an asset that helps them smooth their consumption profile but low inflation rates tend to make softer the punishment for default making it diffcult to sustain high levels of debt at equilibrium. This two opposite effects imply that in equilibrium the inflation rate that maximizes individuals welfare is positive but not too high.Default, Inflation, Money, Endogenous Borrowing Constraint

Algebraic thinking of grade 8 students in solving word problems with a spreadsheet

This paper describes and discusses the activity of grade 8 students on two word problems, using a spreadsheet. We look at particular uses of the spreadsheet, namely at the students’ representations, as ways of eliciting forms of algebraic thinking involved in solving the problems. We aim to see how the spreadsheet allows the solution of formally impracticable problems at students’ level of algebra knowledge, by making them treatable through the computational logic that is intrinsic to the operating modes of the spreadsheet. The protocols of the problem solving sessions provided ways to describe and interpret the relationships that students established between the variables in the problems and their representations in the spreadsheet

A Ciência e a Produção do conhecimento no modo de Produção capitalista e seus reflexos na qualificação do trabalho

XX Encontro Nacional de Economia Política: desenvolvimento Latino-Americano, Integração e Inserção Internacional - UNILA, Foz do Iguaçu, 26 a 29 de maio de 2015A produção do conhecimento se realiza por meio do trabalho, na relação entre os seres humanos e destes com a natureza. Ao longo da história da humanidade, a ciência, assim como os meios de produção, foi capturada pelo capital, e se apresenta como força produtiva do capital, sendo por ele explorada. Este artigo se destina a demonstrar, à luz da teoria marxista, quais os fundamentos econômicos que estão na base dessa apropriação da ciência pelo capital, qual o sentido do desenvolvimento técnico para Marx e quais os refl exos que tal apropriação produz na qualifi cação do trabalho. Também, verifi car como o desenvolvimento atual das forças produtivas vem alterando as demandas de qualifi caçãoBanco Nacional de Desenvolvimento Econômico e Social (BNDES); Usina Hidrelétrica de Itaipu (ITAIPU); Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e Universidade Federal da Integração Latino-Americana (UNILA

Direito fundamental à filiação e a negatória de paternidade

Trata-se de jurisprudência comentada.Comenta acórdão decorrente de apelação interposta sobre ação negatória de paternidade com anulatória de registro