MATHEMATICS TEACHING IN EDUCATION AND TRAINING COURSES
H. Rocha

Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia (PORTUGAL)

Education and Training Courses have been specifically designed to the high number of young people in a situation of school dropout and in transition to working life, particularly those who enter the labor market early with insufficient levels of schooling and professional training. Mathematics is one of the curriculum components of these courses, for its contribution to the exercise of citizenship in a democratic society. Being an important part of the cultural legacy of our society is too often seen by students as a source of exclusion. It is known that young people who enter these courses often had an experience of underachievement in the discipline, what justifies that motivating students is at once the great challenge faced by the teacher. The program suggests taking a more concrete and linked to reality approach, allowing students to learn to recognize the mathematics in the world around them and using technology to promote that learning. However, it is the teacher who is responsible for managing its implementation, shaping the learning situations and integrating them in a coherent and articulated way in the specific course that students attend. In what concerns to assessment, the program also takes into account the usual characteristics of the students. Thus, the assessment includes a strong appreciation of students’ work, its presentation and discussion and further improvement of that work. The directions given to the teacher diverge from the traditional option of the evaluation test, providing guidelines to the form that each evaluation can take depending on the contents in study. However, once again, the teacher's role in curriculum management is not neglected, being valued the adequacy of proposals to the characteristics of the students.
The study presented here had as its main goal to analyze and understand the choices made by the teacher during the different stages of his practice, giving attention to the dilemmas he faced and to the reasons he took into account when making decisions.

The study adopts a qualitative and interpretative methodological approach, undertaking one teacher case study. Data collection included semi-structured interviews, classroom observation and document collection. Data analysis was based on the evidence gathered in the light of the problem under study.

The conclusions of the study point to the important role of technology and suggest that the reduction of prerequisites, the intention of taking into account the students’ interests and the desire of improving students culture is central in what concerns to task selection; while the active involvement of students characterized the implementation of the classes. The dilemmas faced by the teacher focus mainly on the relative importance and on the demanding level that he should give to each content, as well as the articulation that he should promote between formal and intuitive knowledge. In what concerns to assessment, the results achieved highlight the impact that students ideas can have on teacher’s practice, conducting to the inclusion of tests as an assessment element, against the teacher’s intentions.

keywords: education and training courses, mathematics, innovation, technology.

This paper showcases MDSheet, a framework aimed at improving the engineering of spreadsheets. This framework is model-driven, and has been fully integrated under a spreadsheet system. Also, its practical interest has been demonstrated by several empirical studies.

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Nas últimas décadas, os estudos sobre o desempenho de vigas de betão armado (BA) reforçadas com materiais compósitos de matriz polimérica têm aumentado. Porém, muitas dúvidas e questões persistem, fazendo realçar algumas lacunas sobre o conhecimento adquirido. Um desses aspetos reside na forma de modelar a ligação entre o compósito e o betão. É também sabido que a modelação da abertura de fendas no betão (discreta ou distribuída numa banda) influência o desempenho da ligação entre os materiais colados.
Nesse sentido, apresentam-se, neste trabalho, os resultados numéricos obtidos da modelação numérica não-linear a 3D de vigas de BA sujeitas a flexão de 4 pontos. Os resultados numéricos são confrontados com os experimentais e os diferentes parâmetros que influenciam a ligação analisados e discutidos.

Given graphs G and H, and a coloring of the edges of G with k colors, a monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H. Let f_{k}(n,H) be the smallest number t such that any graph G of order n and any coloring of its edges with k colors, admits a monochromatic H-decomposition with at most t parts. Here we study the function f_{k}(n,K_r) for k≥ 2 and r≥ 3.

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The paleontological richness of Morocco has been scientifically known since at least the early 20th century. The region of the Middle Atlas, more specifically the Boulemane area, has been however only sparsely studied since the 1960s when it provided vertebrate fossils from the Middle Jurassic. In September 2013, a Moroccan-Portuguese expedition to the village of Taghrout, Boulemane, made excavations in a Pleistocene fossil site that once was a small high-altitude sedimentary basin, uncharted in previous geological maps. The excavations yielded bone material from large mammals, the most common findings are elephants ascribed to Elephas, but artiodactyls, turtles, and in-situ Acheulean tools were also collected. This represents a new and important paleontological and archeological site. In addition to the discoveries of Taghrout, the expedition also retrieved Quaternary vertebrate material from a nearby cave and found new Jurassic localities, with arcosaur bones and dinosaur footprints, in El Mers.

Motivated by the need to describe bear-bull market regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes, threshold and delay, given by a stochastic differential equation. When the difference between the regimes is simply given by a different set of real valued parameters for the drift and diffusion coefficients, with changes between regimes depending only on these parameters, we show that if the delay is known there are consistent estimators for the threshold as long we know how to classify a given observation of the process as belonging to one of the two regimes. When the drift and diffusion coefficients are of geometric Brownian motion type we obtain a model with parameters that can be estimated in a satisfactory way, a model that allows differentiating regimes in some of the NYSE 21 stocks analyzed and also, that gives very satisfactory results when compared to the usual Black–Scholes model for pricing call options.

Transactional memory (TM) is an increasingly popular technique for synchronising threads in multi-threaded programs. To address both correctness and performance-related issues of TM programs, one needs to monitor and analyse their execution. However, monitoring concurrent programs (including TM programs) may have a non-negligible impact on their behaviour, which may hamper the objectives of the intended analysis. In this paper, we propose several approaches for monitoring TM programs and study their impact on the behaviour of the monitored programs. The considered approaches range from specialised lightweight monitoring to generic heavyweight monitoring. The implemented monitoring tools are publicly available to the scientific community, and the implementation techniques used for lightweight monitoring of TM programs may be used as an inspiration for developing other specialised lightweight monitors.

We study Mellin pseudodifferential operators (shortly, Mellin PDO's) with symbols in the algebra \(\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))\) of slowly oscillating functions of limited smoothness introduced in [K09]. We show that if \(\mathfrak{a}\in\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))\) does not degenerate on the ``boundary" of \(\mathbb{R}_+\times\mathbb{R}\) in a certain sense, then the Mellin PDO \(\operatorname{Op}(\mathfrak{a})\) is Fredholm on the space \(L^p\) for \(p\in(1,\infty)\) and each its regularizer is of the form \(\operatorname{Op}(\mathfrak{b})+K\) where \(K\) is a compact operator on \(L^p\) and \(\mathfrak{b}\) is a certain explicitly constructed function in the same algebra \(\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))\) such that \(\mathfrak{b}=1/\mathfrak{a}\) on the ``boundary" of \(\mathbb{R}_+\times\mathbb{R}\). This result complements the known Fredholm criterion from [K09] for Mellin PDO's with symbols in the closure of \(\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))\) and extends the corresponding result by V.S. Rabinovich (see [R98]) on Mellin PDO's with slowly oscillating symbols in \(C^\infty(\mathbb{R}_+\times\mathbb{R})\).

Let $X$ be a finite or infinite chain and let $\O(X)$ be the monoid of all endomorphisms of $X$.
In this paper, we describe the largest regular subsemigroup of $\O(X)$ and Green's relations on $\O(X)$.
In fact, more generally, if $Y$ is a nonempty subset of $X$ and $\O(X,Y)$ is the subsemigroup of $\O(X)$ of all elements with range contained in $Y$,
we characterize the largest regular subsemigroup of $\O(X,Y)$ and Green's relations on $\O(X,Y)$.
Moreover, for finite chains, we determine when two semigroups of the type $\O(X,Y)$ are isomorphic and calculate their ranks.