Existência de minimizantes relaxados e fenómeno de Lavrentiev

Doutoramento em MatemáticaNeste trabalho prova-se a existência de minimizantes relaxados em problemas de controlo óptimo não convexos usando técnicas de compactificação. Faz-se a extensão do exemplo de Manià a dimensão dois, obtendo-se uma classe de problemas variacionais em 2D que apresentam Fenómeno de Lavrentiev. Prova-se que o fenómeno persiste a certas perturbações, obtendo- -se assim uma classe de funcionais cujos Lagrangianos são coercivos e convexos em relação ao gradiente. Adicionalmente, apresentam-se exemplos de problemas do cálculo das variações com diferentes condições de fronteira, e em diferentes tipos de domínios (incluindo domínios com fronteira fractal), que exibem Fenómeno de Lavrentiev.The existence of relaxed minimizers of nonconvex optimal control problems is proved in this work using compactification techniques. The example of Manià is extended to two dimensions, thus obtaining 2D examples which exhibit the Lavrentiev Phenomenon. The persistence of the phenomenon for certain perturbations on the integrands is proved, thus arriving to a class of functionals whose Lagrangians are coercive and convex with respect to gradient, and which exhibit the Lavrentiev Phenomenon. Examples for the problems of the calculus of variations with different types of boundary conditions and different types of domains (including domains of fractal boundary), which exhibit the Lavrentiev Phenomenon, are also constructed

Using bayesian networks and parameterized questions in independent study

The teaching paradigm is changing from a traditional model of teachers as suppliers of knowledge and toward a model of teachers as advisers who carefully observe students, identify their learning needs, and help them in their independent study. In this new paradigm, computers and communication technology can be effective, not only as means for knowledge transmission, but also as tools for automatically providing feedback and diagnosis in the learning process. We present an approach integrating parameterized questions from two computer systems (Megua and PmatE), combined with a Web application (Siacua) implementing a Bayesian user model, using already many hundreds of questions from each of the two systems. Our approach allows the students a certain level of independence and provides some orientation in their independent study, by giving feedback about answers to questions and also about the general progress in the study subject. This progress is shown in the form of progress bars computed by Bayesian networks where nodes represent “concepts” and knowledge evidences. Teachers use Megua for creating and organizing their own database of (parameterized) questions, make them available for students, and for seeing the progress of each student or class in every topic being studied

Parameterized exercises in SMC

The authoring of parameterized exercises has been a useful activity both for teachers, who could take advantage of databases of parameterized exercises for preparing study materials, but also for students that learn by producing new problems. This has been verified during the realization of MSc dissertations written by High School teachers that, as students again, have written about the positive aspects of their experience in the production of parameterized exercises. Parameterized exercises can also be used in online systems as a secondary study tool for STEM students (such as SIACUA system [2]). With these goals in mind, we have been developing a package named MEGUA to handle databases of parameterized exercises in the SageMath platform for mathematics. During the use of this system we gathered several requests from users claiming a better system. In this paper we present a redefined tool as well as some first opinions on the new facilities. Originally, this package had the old SageMath Notebook [4] as a front-end which has been presented in ICERI 2013 [3]. A new version of this package has been developed for the new platform named “Sage Math Cloud” (SMC) running in a secure and centralized web platform creating, for each new project, a virtual Linux machine with shell command access. In online systems (or cloud), a supervisor could follow student work and help to solve their problems (at distance) since it can see the student work in progress (no need to send emails with attachments)

Computer-assisted independent study in multivariate calculus

Learning mathematics requires students to work in an independent way which is particularly challenging for such an abstract subject. Advancements in technology and, taking the student as the focus of his own learning, led to a change of paradigm in the design and development of educational contents. In this paper we describe the first experience with an interactive feedback and assessment tool (Siacua), based on parameterized math exercises, and explain how we use it to motivate student independent study in a multivariate calculus environment. We have defined an index about the subject, trying to make it consensual enough for being used in other courses about multivariate calculus. Then we have created a concept map, selected some existing parameterized true/false questions from PmatE project and classified them using our concept map, for being reused in our system. For complementing the course we have created about one hundred parameterized multiple choice question templates in system Megua and generated about one thousand instances for using in Siacua. Results based on data collected by this tool and also based on an informal survey are presented. This first experience allows us to conclude our approach has an important impact on student motivation and contributes to the success on learning multivariate calculus

Os estágios curriculares e o seu impacto na empregabilidade dos licenciados

Em Portugal, de acordo com os dados do Instituto Nacional de Estatística (INE), a taxa de desemprego entre os jovens, no primeiro trimestre de 2013, foi de 42,1 por cento. Embora esta taxa seja inferior entre os licenciados é, no entanto, preocupante, uma vez que tem vindo a aumentar concomitantemente com a visibilidade social do desemprego neste grupo de jovens. Desta forma, poderá contribuir, a prazo, para diminuir a população escolar e o número de candidatos ao ensino superior, dificultando o necessário aumento da qualificação dos jovens, com prejuízos ao nível do desenvolvimento do país

Quality of multiple choice questions in a numerical and statistical methods course

The quality control of written examination is very important in the teaching and learning process of any course. In educational assessment contexts, Item Response Theory (IRT) has been applied to measure the quality of a test in areas of knowledge like medicine, psychology, and social sciences, and its interest has been growing in other topics as well. Based on statistical models for the probability of an individual answering a question correctly, IRT can be addressed to measure examiners’ ability in an assessment test and to estimate difficulty and discrimination levels of each item in the test. In this work, IRT is applied to Numerical and Statistical Methods course to measure the quality of tests based on Multiple Choice Questions (MCQ). The present study focuses on three school years, namely 2015, 2016 and 2017, more specifically on the 1st semester of the 2nd year of the degree course. It has involved more than 300 students in each year, and it points out questions (also called items) from some chapters of the program that were evaluated through MCQ. Emphasis is given on the range of item difficulty and item discrimination parameters, estimated by IRT methodology, for each question in those exams. We show where each partial exam explores ability levels: at a passing point or at more demanding levels. After the application of IRT to each test, which was composed of eight questions, we got 48 item difficulty and item discrimination parameters. The application of standard boxplots shows few atypical responses from students in terms of extremal values of difficulty and discrimination, which corresponds to MCQ that deserve further attention. We have concluded that the vast majority of questions are well posed considering that they are designed to focus on the cut-off point (passing/not passing). A proposed reflection, about the learned benefits from ‘good’ outliers and possible causes for those ‘bad’ items, suggests future improvements to classes, study materials and exams.publishe

Yes, we can: internships providing leverages in the labour market

Facing unprecedented challenges to deal with the problem of graduate unemployment, Higher Education Institutions (HEIs) are increasingly concerned with the professional insertion of their graduates in the labour market and with the design of institutional mechanisms that facilitate students’ transition from higher education to work. This has been achieved, inter alia, through the creation of study programmes with internships, or several other forms of cooperative education between HEIs and employing institutions. Benefits of internships are extensively reported in the majority of studies dealing with the professional integration of graduates. There is a general consensus that internships can be regarded as an institutional mechanism that facilitates students’ transition from higher education to work. However, there seems to be a gap between the intended results and the actual impact of internships on employability, which needs to be better understood. Moreover, existing research tends to be largely based on the perceptions of the main stakeholders involved – students, HEIs, and employing institutions – rather than on actual post-graduation career outcomes. This paper aims to assess the importance of internships for the employability of graduate students. Three inter-related dimensions are explored. Firstly, the extent to which the introduction of internships in study programmes contributes to the decrease of graduate unemployment rates is analysed. Second, the extent to which the different features of internships, namely those associated with their length and structure, contribute to lower graduate unemployment rates is assessed. Thirdly, the internship approaches, which seem to allow greater job preparedness, namely those related to interns’ supervision entailing close collaboration between universities and employers, are discussed. Our empirical data consists of a unique database comprising 1,168 Portuguese first cycle degrees, with study programmes approved from 2006 to 2009 and published in the Official Gazette. These results are crosschecked with the perspectives of the main stakeholders involved in internships, regarding their motivations; required efforts; and expected outcomes. Empirically, this is based on the content analysis of semi-structured individual interviews to units’ coordinators and also focus groups conducted with the coordinators of study programmes; academic internship supervisors; and former interns

Computadores no apoio ao estudo autónomo e avaliação em Matemática

Sem resumo disponível.publishe

Exercise templates with Sage Math

Students can benefit from the study of a detailed answer of an exercise after trying to solve it in traditional pen-and-paper way as has been verified in literature. This basic fact was the incentive to the creation of a new package, for the growing community of users of Sage Math, that allows an author to add, change and delete parameterized exercise templates, with detailed answer, from one or more personal databases, as well as producing new exercises in a booklet style or exam form