Explorar e Investigar em Matemática: Uma Actividade Fundamental no Ensino e na Aprendizagem

Investigar, ensinar e aprender são actividades que podem estar presentes, de forma articulada, no ensino-aprendizagem da Matemática e na actividade profissional do professor. Para isso, é necessário conceber tarefas que possam ser o ponto de partida para investigações e explorações matemáticas dos alunos e discutir o modo como podem ser trabalhadas na sala de aula. Recorrendo a exemplos de actividades realizadas por professores de Matemática portugueses, analiso a actividade de aprendizagem suscitada por tarefas deste tipo e discuto as respectivas potencialidades. Finalmente, refiro as condições respeitantes à cultura profissional dos professores que podem favorecer uma actividade de investigação sobre a sua própria profissional, com relevo para a colaboração e a dimensão associativa.Researching, teaching and learning are activities that may be present, in coordination, teaching and learning of mathematics in the work of the teacher. Therefore, it is necessary to design tasks that may be the starting point for mathematical investigations and explorations of the students and discuss how they can be worked in the classroom. Drawing on examples of activities carried out by Portuguese teachers of mathematics by examining the activity of learning raised by such tasks and discuss their potencial. Finally, I refer to conditions relating to the professional culture of teachers who can promote the research activity on their own training, with an emphasis on collaboration and associative dimension

Chemokine-guided angiogenesis directs coronary vasculature formation in zebrafish.

Supramolecular & Biomaterials Chemistr

Interaction of free-floating planets with a star-planet pair

The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter a binary system consisting of a Jupiter-sized planet revolving around a Sun-like star. To simplify the problem we assume coplanar orbits for the bound and the free-floating planet and an initially parabolic orbit for the free-floating planet. By calculating the uncertainty exponent, a quantity that measures the dependence of the final state of the system on small changes of the initial conditions, we show that the interaction process is a fractal classical scattering. The uncertainty exponent is in the range (0.2-0.3) and is a decreasing function of time. In this way we see that the statistical approach we follow to tackle the problem is justified. The possible final outcomes of this interaction are only four, namely flyby, planet exchange, capture or disruption. We give the probability of each outcome as a function of the incoming planet's mass. We find that the probability of exchange or capture (in prograde as well as retrograde orbits and for very long times) is non-negligible, a fact that might explain the possible future observations of planetary systems with orbits that are either retrograde or tight and highly eccentric.Comment: 19 pages, 12 figure

Formation, evolution and multiplicity of brown dwarfs and giant exoplanets

This proceeding summarises the talk of the awardee of the Spanish Astronomical Society award to the the best Spanish thesis in Astronomy and Astrophysics in the two-year period 2006-2007. The thesis required a tremendous observational effort and covered many different topics related to brown dwarfs and exoplanets, such as the study of the mass function in the substellar domain of the young sigma Orionis cluster down to a few Jupiter masses, the relation between the cluster stellar and substellar populations, the accretion discs in cluster brown dwarfs, the frequency of very low-mass companions to nearby young stars at intermediate and wide separations, or the detectability of Earth-like planets in habitable zones around ultracool (L- and T-type) dwarfs in the solar neighbourhood.Comment: "Highlights of Spanish Astrophysics V", Proceedings of the VIII Scientific Meeting of the Spanish Astronomical Society (SEA) held in Santander, 7-11 July, 2008. Edited by J. Gorgas, L. J. Goicoechea, J. I. Gonzalez-Serrano, J. M. Diego. Invited oral contribution to plenary sessio

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page