Proof in classroom social practice

How does the construction of proof relate to the social practice developed in the mathematics classroom? This report addresses the role of diagrams in order to focus the complementarity of participation and reification in the process of constructing a proof and negotiating its meaning. The discussion is based on the analysis of the mathematical practice developed by a group of four 9th grade students and is inspired by the social theory of learning

Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

Producing an explanatory proof in a 9th grade classroom

Este artigo apresenta parte de um estudo fundamentado na problemática da demonstração na matemática escolar. Descreve o modo como quatro alunos do 9.º ano exploraram uma tarefa relacionada com a descoberta de eixos de simetria em várias figuras geométricas. A demonstração, que os mesmos construíram, teve essencialmente uma função explicativa. O papel da professora na negociação do significado de demonstração e da sua necessidade é igualmente analisado. Os alunos desenvolvem primeiro uma compreensão prática sem consciência das razões que fundamentam as afirmações matemáticas e só depois uma compreensão teórica que os conduz à construção de uma demonstração.

The telegraph as an omen of the future in James W. Carey's vision

In the history of modern communication, after the development of the printing press, the telegraph unleashed a revolution in communications. Today, Internet is in many ways its heir. Reflections on the telegraph may open up perspectives concerning tendencies, possibilities and pitfalls of the Internet. The telegraph has been well explored in important literature on communication and media which tends to emphasize the history of this technology, its social context and institutional meaning [e.g. Robert L. Thompson, 1947, Tom Standage, 2007 [1998]. James W. Carey, the North- American critical cultural studies' mentor, in his essay "Technology and Ideology. The Case of the Telegraph" (2009 [1983]), suggests a distinctive approach. In the telegraph, Carey sees the prototype of many subsequent commercial empires based on science and technology, a pioneer model for complex business management; an example of interest struggle for the patents control; an inductor of changes both in language and in structures of knowledge; and a promoter of a futurist and utopian thought of information technologies. Having in mind a revolution in communications promoted by the Internet, this paper revisits this seminal essay to explore its great attainment, as well as the problems of this kind of approach which conceives the innovation of the telegraph as a metaphor for all the innovations announcing the modern stage of history and determining still today the major lines of development in modern communication systems.

Ansiedade na performance: causas e possíveis curas

I - Este relatório pretende descrever o estágio especializado em ensino de música realizado no âmbito do mestrado em Ensino de Música na Escola Superior de Música de Lisboa. Este estágio decorreu no Instituto Gregoriano de Lisboa e no Conservatório de Música, de Dança e de Arte Dramática de Lisboa, duas escolas de ensino oficial especializado. Sendo a primeira pública e a segunda privada, estas escolas apresentam realidades muito diferentes do ponto de vista organizacional e de gestão, que resultam em situações heterogéneas e dependentes de vários factores que serão mencionados ao longo deste relatório. A análise SWOT efectuada para cada uma destas organizações descreve mais objectivamente os factores e variáveis que permitiram construir este relatório. Foram caracterizados três alunos, um de cada curso: preparatório, básico e secundário. A Maria M. é a aluna do 2º ano do curso preparatório, o Pedro R. é aluno de 3º grau do curso básico de instrumento e o Diego M. é aluno de 7º grau. Foram aprofundadas as práticas pedagógicas desenvolvidas com cada um dos alunos e os avanços e metas atingidas por cada um destes alunos. Este estágio resulta numa reflexão sobre a prática pedagógica aplicada e as suas motivações.

Probing wrong-sign Yukawa couplings at the LHC and a future linear collider

We consider the two-Higgs-doublet model as a framework in which to evaluate the viability of scenarios in which the sign of the coupling of the observed Higgs boson to down-type fermions (in particular, b-quark pairs) is opposite to that of the Standard Model (SM), while at the same time all other tree-level couplings are close to the SM values. We show that, whereas such a scenario is consistent with current LHC observations, both future running at the LHC and a future e(+)e(-) linear collider could determine the sign of the Higgs coupling to b-quark pairs. Discrimination is possible for two reasons. First, the interference between the b-quark and the t-quark loop contributions to the ggh coupling changes sign. Second, the charged-Higgs loop contribution to the gamma gamma h coupling is large and fairly constant up to the largest charged-Higgs mass allowed by tree-level unitarity bounds when the b-quark Yukawa coupling has the opposite sign from that of the SM (the change in sign of the interference terms between the b-quark loop and the W and t loops having negligible impact).

Physical layer aware network architecture for the future internet

In this article, physical layer awareness in access, core, and metro networks is addressed, and a Physical Layer Aware Network Architecture Framework for the Future Internet is presented and discussed, as proposed within the framework of the European ICT Project 4WARD. Current limitations and shortcomings of the Internet architecture are driving research trends at a global scale toward a novel, secure, and flexible architecture. This Future Internet architecture must allow for the co-existence and cooperation of multiple networks on common platforms, through the virtualization of network resources. Possible solutions embrace a full range of technologies, from fiber backbones to wireless access networks. The virtualization of physical networking resources will enhance the possibility of handling different profiles, while providing the impression of mutual isolation. This abstraction strategy implies the use of well elaborated mechanisms in order to deal with channel impairments and requirements, in both wireless (access) and optical (core) environments.

Fly by data link: feasibility of a relative navigation solution for aviation relying on a future L-band data link

Trabalho final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações