The use of learning management platforms in school context - a national study

This report results from a national study carried out under the Project “Educational application of learning management platforms”, supported and funded by the Computers, Networks, and Internet in Schools department of the Portuguese Ministry of Education- General Directorate for Innovation and Educational Development. This report has been developed by the ICT Competence Centre of the Faculty of Sciences- University of Lisbon, during the school year 2007/2008

Jacobi multipliers and Hamel''s formalism

In this work we establish the relation between the Jacobi last multiplier, which is a geometrical tool in the solution of problems in mechanics and that provides Lagrangian descriptions and constants of motion for second-order ordinary differential equations, and nonholonomic Lagrangian mechanics where the dynamics is determined by Hamel''s equations. © 2021 IOP Publishing Ltd

Isotopic data from the Pomarinho enclave swarm (SW Iberian Chain)

Mafic microgranular enclaves are a common feature of calc-alkaline granitoids (e.g. tonalites and granodiorites) in active continental margins and collisional orogens. They correspond to dark-coloured globules that, although widespread throughout the host rock, usually constitute only a small proportion of the whole volume of the intrusion. When the enclaves occur strongly concentrated in a restricted area, they form an enclave swarm (e.g. Tobish et al. 1997). At Pomarinho, the Granialpa quarry is a privileged exposure of a cluster of dark igneous enclaves that has been targeted for geochemical and geophysical studies (GeoRadar and AMS). The Pomarinho swarm is located in the SW edge of Évora granitoid (Carvalhosa, 1983), in the Portuguese sector of the Ossa-Morena Zone (Iberian Variscides). The enclaves have tonalitic and granodioritic compositions, whereas the host correspond to a very homogeneous light-coloured granodiorite. Preliminary geochemical information, based on major and trace elements (Moita et al., 2011), suggests that the enclaves and the host rock are probably derived from co-genetic magmas. Rb-Sr isotope data now obtained in four enclaves and three host-rock samples yield an isochron corresponding to 335±14Ma (MSWD=0.96), which fits into the spectrum of ages of the Variscan granitoids in the region. Additionally, the homogeneity of both 87Sr/86Sr335 (0.704758 to 0.705133) and εNd335 (-0.10 to 1.13) values corroborates the hypothesis of derivation of the enclaves and the host granodiorite from a common primitive melt through magmatic differentiation. Low 87Sr/86Sr335 and high εNd335 values suggest that ultimately the parental melt is related to a mantle source, with no or only small contribution of metasedimentary crustal materials

Teachers' and students' views and attitudes towards a new mathematics curriculum: A case study

The education system in Portugal is in the midst of a period of intensive reform. This paper describes the findings of a qualitative case study focusing on the views and attitudes of teachers and students participating in a pilot curriculum development programme stressing active methodologies and group work, conducted by the Ministry of Education In particular it discusses their views and attitudes about mathematics, mathematics teaching and curriculum innovation. The teachers were found to struggle with a contradiction: whilst they approved the new orientations, which were seen as adequate and innovative, they complained strongly about the design and implementation of the programme Students had a generally positive attitude towards mathematics, although there were differences among them. The 7th graders were satisfied with their mathematics classes and with the new curriculum. The 10th graders did not consider the changes as significant in themselves, but expressed concern for their academic progress

Learning mathematics and competences: Bringing together three theoretical perspectives

The symposium aims to bring into analysis and discussion a possibility of articulating and integrating theoretical concepts from Activity Theory, Situated Learning and Critical Mathematics Education in order to contribute to understanding learning in practices where mathematics and technology seem to be relevant

A Survey on q-Polynomials and their Orthogonality Properties

In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW)) for almost any complex value of the parameters and for all non-negative integers degrees. We state the degenerate version of Favard's theorem, which is one of the keys of the paper, that allow us to extend the orthogonality properties valid up to some integer degree N to Sobolev type orthogonality properties. We also present, following an analogous process that applied in [16], tables with the factorization and the discrete Sobolev-type orthogonality property for those families which satisfy a finite orthogonality property, i.e. it consists in sum of finite number of masspoints, such as q-Racah (qR), q-Hahn (qH), dual q-Hahn (dqH), and q-Krawtchouk polynomials (qK), among others. -- [16] R. S. Costas-Santos and J. F. Sanchez-Lara. Extensions of discrete classical orthogonal polynomials beyond the orthogonality. J. Comp. Appl. Math., 225(2) (2009), 440-451Comment: 3 Figures, 3 tables, in a 22 pages manuscrip

Geochronology and Isotope Geochemistry of Felsic Marginal Facies of the Reguengos de Monsaraz Pluton (OMZ)

No sector sueste do maciço de Reguengos de Monsaraz (Zona de Ossa-Morena), ocorrem rochas félsicas quer em continuidade espacial com as litologias principais do plutonito quer em pequenos corpos aparentemente separados. Neste trabalho, estudou-se o granito marginal da zona de Arraieiras, bem como o tonalito da zona do ribeiro dos Gagos. Datações U-Pb (em zircão e monazite) revelam que estas litologias são, no essencial, contemporâneas entre si, bem como relativamente às fácies mais comuns do maciço de Reguengos, e que os processos de instalação magmática deverão ter decorrido há 337-338 Ma. Do ponto de vista geoquímico, o granito de Arraieiras parece ter uma relação genética forte com o resto do plutonito, através de processos de mistura de líquidos (de origens mantélica e de anatexia de metassedimentos) e diferenciação magmática, a que se terão seguido fenómenos locais de assimilação do encaixante no nível de instalação final. O paradoxo de haver rochas mais máficas do que o granito com assinaturas isotópicas mais “crustais” poderá ser explicado pela intervenção final destes processos de assimilação. Quanto ao tonalito de Gagos, as suas características geoquímicas, e em particular as razões isotópicas de Sr e Nd, requerem uma origem distinta, com contribuição de fonte infracrustal.Felsic rocks occur in the SE sector of the Reguengos de Monsaraz massif either as a border zone of the pluton or as small satellite bodies. In this work, the Arraieiras granite (from the border zone) and the Gagos tonalite (from a satellite body) were studied for geochronology and geochemistry. The obtained zircon and monazite U-Pb ages show that the two felsic lithologies and the main units of the Reguengos pluton are essentially contemporaneous to each other and that magma emplacement took place at 337-338 Ma. Geochemical features of the Arraieiras granite suggest that it has a strong genetic link with the other lithologies of the pluton, through magma mixing (from mantle and metasedimentary sources) and differentiation processes; in a late evolutionary stage, at the final emplacement level, assimilation of country rock material also took place. The paradox of some more mafic rocks displaying isotope signatures more “crustal” than those revealed by the Arraieiras granite is probably a consequence of late assimilation events. In contrast, the Gagos tonalite, according to the Sr and Nd isotope fingerprints, seems to be related to a different sequence of processes and, in particular, it requires the contribution of an infracrustal source

New U-Pb zircon age constraints for the emplacement of the Reguengos de Monsaraz Massif (Ossa Morena Zone)

The Reguengos de Monsaraz massif is located in the Portuguese sector of the Ossa Morena Zone (ZOM), one of the major geotectonic units of the Iberian Variscan Belt. It intruded Lower Paleozoic metasediments, strongly affected by deformation and metamorphism during the Varis-can orogeny. Pluton emplacement was responsible for the development of a contact metamor-phism aureole in the surrounding country rocks. Based on regional constraints, the intrusion was included in the group of the late-post-tectonic granitoids. The pluton shows an inversely zoned pattern and consists of tonalitic to granodioritic rocks with abundant mafic microgranular enclaves, occupying most of the presently exposed intrusion area and minor bodies of gabbro-diorites in the east and centre. Field, petrographical and geo-chemical data reveal that mixing / mingling between mantle- and crustally-derived magmas and fractional crystallization played a major role in the genesis and evolution of these granitoids 1. Early attempts to date the Reguengos de Monsaraz intrusion, using Rb-Sr isotopic data for a feldspar-amphibole pair from one granodiorite sample, yielded an age of 297.5 ± 2.9 Ma. This age was interpreted as a cooling age and provided a minimum estimate for the timing of mag-matic crystallization. In order to better constrain the age and emplacement sequence of the mas-sif, five samples representing the different magmatic units (gabbro diorites, tonalites and mafic microgranular enclaves) were selected for determination of U-Pb zircon ages by isotope dilution techniques. The zircon populations from two samples of the gabbro diorites (one from the central sector and the other from the easternmost body) yielded overlapping 206Pb/238U average ages of 337.4 1.1 Ma and 338.6 ± 0.7 Ma, respectively. Similar ages were obtained in two samples from the main tonalite-granodiorite facies (337.3 ± 2.3 Ma; 337.8 ± 0.7 Ma). Finally, the zircons from the microgranular enclave yielded a 206Pb/238U average age of 336.5 ± 0.5 Ma. A slightly younger age was obtained in two fractions of titanite from the enclave (333.6 ± 2.5 Ma), suggesting either resetting of their original magmatic ages or late stage crystallization. The new U-Pb age data support a coeval emplacement for all the members of this suite, at ap-proximately 337-338 Ma. Such a close space-time association between mafic and felsic grani-toids is consistent with the proposed mixing model. According to recent studies, this sector of the OMZ was affected by three Variscan deforma-tion events 2. The earlier deformation phases (D1 and D2) occurred in Late Devonian ( 380-360 Ma) and Early Carboniferous times ( 360-345 Ma), whilst the latter (D3) has a Pennsylva-nian age (305-295 Ma). Based on the available geochronological information, the emplacement of the Reguengos de Monsaraz magmas took place at a time of tectonic quiescence between D2 and D3. The relatively young Rb-Sr age recorded in the feldspar-amphibole pair may therefore reflect the effects of the last tectonothermal event, also documented by the replacement of horn-blende crystals by actinolite

Sr isotopic signatures of Portuguese bottled mineral waters, their relationships with the geological setting and potential use for product authentication

The Sr isotopic ratios of nine bottled natural mineral waters from Portugal were measured in the Laboratory of Isotope Geology of the University of Aveiro (LGIUA). The results obtained show that the Sr isotopic variability of these waters is strongly correlated with the age and mineralogical composition of the aquifer source rocks. The lowest 87Sr/86Sr ratios are found in water samples from the Monchique aquifer (87Sr/86Sr = 0,70447), located in Late Cretaceous alkaline magmatic rocks of mantle origin. The Vimeiro waters are hosted in carbonate and evaporite formations of Jurassic age and have 87Sr/86Sr values of 0,70808, whereas the waters sourced in Cenozoic siliciclastic sediments tend to exhibit higher 87Sr/86Sr ratios, close to the rainwater value (São Silvestre; 87Sr/86Sr = 0,71078). Finally, the waters coming from granitic and/or metamorphic terrains of the Iberian Variscan basement (Vitalis, Luso, Carvalhelhos, Fastio, Serra da Estrela) display the most radiogenic Sr isotopic signatures (87Sr/86Sr > 0,7136). In the modern commercial context, the differences encountered provide a powerful tool for fingerprinting the mineral water origin and may be used for purposes of mineral water authentication. The use of 87Sr/86Sr ratios may also be extended to studies on the provenance of some foods and beverages, taking into account the influence of the geological / pedological factor on the Sr isotopic composition recorded by the plants

Uma boa prática de integração do Moodle nas escolas

Documento produzido no âmbito do Projecto “Utilização educativa de plataformas de aprendizagem” desenvolvido pelo Centro de Competência RTE/PTE da Faculdade de Ciências da Universidade de Lisboa e financiado pela Equipa RTE/PTE da Direcção Geral de Inova- ção e Desenvolvimento Curricular.Não vamos começar com "Era uma vez" mas pretende-se contar uma história, contextualizada num dado momento no tempo e no espaço, mas que revela, na verdade, a capacidade de poder situarse em vários espaços (escolares) e em diferentes "tempos", passados, presentes ou futuro... A “boa-prática”, ou antes, “a-experiência-prática-que-vive-e-viveudificuldades- mas-onde-se-têm-vindo-a-conseguir-bons-resultados” que a seguir se apresenta foi estruturada com base no relato do um elemento do conselho executivo do Agrupamento de Escolas de Ribamar, no concelho da Lourinhã. As frases que aparecem em itálico são, na verdade, o discurso directo dessa professora