Activities with desmos and geogebra for formative and automatic feedback

The study developed here was carried out within the scope of a National Meeting “19.º MatViseu” with secondary school mathematics teachers in a workshop entitled Desmos and GeoGebra: activities with automatic feedback and formative”. The objectives were to articulate the mathematics curriculum and essential learning program, and to explore activities that use some of the strengths of Desmos and GeoGebra to provide feedback to students and develop some activities with feedback appropriate to the level of education they teach. This National Meeting was organized with plenary sessions (invited speakers) and parallel sessions (workshops). In-service teacher training is an essential element to help them to adapt to different curricula and new methods and resources in their professional careers. This study aims to understand how the use of these two platforms can allow a different approach in their classes. The research methodology adopted consists of a case study, relating to a group of teachers who worked autonomous in this workshop. Essentially, a qualitative approach was adopted through the interpretation of data collected through observation, interaction in these platforms and a brief questionary. We can conclude that using the GeoGebra platform requires prior preparation, essentially with GeoGebraScript and with the Desmos platform it was easier to work with the Computation Layer language, although GeoGebraScript and Computation Layer language are new for most of them. Thus, it is recommended that in future training, the creation of strategies and dynamics of preparation for work in the GeoGebraScript and in the Desmos language, to carry out a complete work. However, it is important to keep in mind that the GeoGebra platform was known to most of the participants, but Desmos was not and that the sample is not significant to draw general conclusions.publishe

Global Alfven Wave Heating of the Magnetosphere of Young Stars

Excitation of a Global Alfven wave (GAW) is proposed as a viable mechanism to explain plasma heating in the magnetosphere of young stars. The wave and basic plasma parameters are compatible with the requirement that the dissipation length of GAWs be comparable to the distance between the shocked region at the star's surface and the truncation region in the accretion disk. A two-fluid magnetohydrodynamic plasma model is used in the analysis. A current carrying filament along magnetic field lines acts as a waveguide for the GAW. The current in the filament is driven by plasma waves along the magnetic field lines and/or by plasma crossing magnetic field lines in the truncated region of the disk of the accreting plasma. The conversion of a small fraction of the kinetic energy into GAW energy is sufficient to heat the plasma filament to observed temperatures.Comment: Submitted to ApJ, aheatf.tex, 2 figure

Ten-year follow-up of a giant prolactinoma

Giant prolactinomas are rare pituitary tumours of which management can be a challenge. A 28-year-old man presented with headaches, visual impairment and behavioural changes. Clinically, the patient was found to have hypogonadism and bitemporal hemianopsia. A MRI demonstrated a pituitary tumour 76 mm in diameter and blood tests revealed a serum prolactin of 158 700 µU/mL (reference range 58-254). Initially, a craniotomy was performed. Immunohistochemistry of the tumour identified a prolactinoma with a high proliferative index and the patient was started on treatment with a dopamine agonist. A year later, neurological symptoms worsened due to regrowth of the lesion's cystic component, and so further surgery was performed. After 10 years of treatment with dopamine agonists, the prolactin levels decreased by 96.8%, there was an effective reduction in tumour size, and the neurological signs and symptoms resolved

Expansion-Free Cavity Evolution: Some exact Analytical Models

We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.Comment: 9 pages, Revtex. Typos corrected. Published in Int. J. Mod. Phys.