Departamento de Matemática (DMAT)
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- O ABC do Geometer's SketchpadPublication . Duarte, Isabel; Cavaleiro, JoãoO Geometer’s Sketchpad, sendo um software de geometria dinâmica permite-nos abordar conceitos de geometria de uma maneira inovadora.
- Accuracy of ultrasound in the diagnosis of acute cholecystitis with coexistent acute pancreatitisPublication . Pereira, J.; Afonso, A.; Constantino, J.; Matos, A.; Henriques, C.; Zago, M.; Pinheiro, L.Acute cholecystitis and pancreatitis are acute forms of cholecystolithiasis. The presence of acute cholecystitis can lead to important changes in therapy in the early course of acute pancreatitis. The aim of this study was to identify the accuracy of ultrasonography in diagnosing acute cholecystitis with coexistent acute pancreatitis.
- Accurate Spectral Estimation of Non-periodic Signals Based on Compressive SensingPublication . Duarte, Isabel M. P.; Vieira, José M. N.; Ferreira, Paulo J S G; Albuquerque, DanielIn this work we propose a method based on compressive sensing (CS) for estimating the spectrum of a signal written as a linear combination of a small number of sinusoids. In practice one deals with signals with finite-length and so the Fourier coefficients are not exactly sparse. Due to the leakage effect in the case where the frequency is not a multiple of the fundamental frequency of the DFT, the success of the traditional CS algorithms is limited. To overcome this problem our algorithm transform the DFT basis into a frame with a larger number of vectors, by inserting a small number of columns between some of the initial ones. The algorithm takes advantage of the compactness of the interpolation function that results from the ‘1 norm minimization of the Basis Pursuit (BP) and is based on the compressive sensing theory that allows us to acquire and represent sparse and compressible signals, using a much lower sampling rate than the Nyquist rate. Our method allow us to estimate the sinusoids amplitude, phase and frequency.
- Active learning during the covid-19 pandemic - A triple experimentPublication . Santos, Vanda; Hall, Andreia; Bastos, Nuno; Caridade, CMRIn recent times, the debate on active methodologies has been intensified with the emergence of strategies that can favor students' autonomy. The active, dynamic and constructive environment can positively influence the perception of teachers and students. One of the ways to achieve this is through the use of technologies that enhance learning. Due to the pandemic situation, the use of technologies was imperative and essential. Three higher education institutions were involved in an active learning project, involving diversified technologies and methodologies to enhance the learning of mathematics. In the University of Aveiro, the experiment involved all the 1st-year students enrolled in the course “Complementary Mathematics II” during the second semester of the academic year 2020-21. These are students of a master’s program for pre-service teachers, preparing to become primary school teachers and mathematics and science teachers, grades 5 and 6. At the Institute of Engineering in Coimbra, the students who attended this experiment were students of Mathematical Analysis I, from the undergraduate degree in Electrical Engineering. In the Polytechnic Institute of Viseu, the students involved in this experiment were students from the Preparation Course in Mathematics (which aims to prepare candidates over 23 who wish to apply to an undergraduate degree in Business). The methodologies used were applied during three distinct phases and according to the students’ profile, related to each course. The methodologies used were very diverse: team-based learning; flipped classroom; peer teaching; think-pair-share and exposition followed by exercise practice; problem-based learning and inquiry-based learning. The technologies were also very diversified: Desmos, Kahoot!, Quizizz, GeoGebra, Excel, OneNote, Google Docs, Zoom, Miro, Wolfram alpha, Powerpoint, calculators and videos. The use of a wide range of methodologies and technologies made it possible to teach during the lockdown imposed by the pandemic situation, and simultaneously motivated the students. In addition they provided opportunities to adapt the learning process to the diverse knowledge and learning styles of students, and increased their involvement.
- Activities with desmos and geogebra for formative and automatic feedbackPublication . Santos, V.; Bastos, NunoThe 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.
- An experience with Desmos in the study of the quadratic functionPublication . Dias, Lucília; Oliveira, Paula; Bastos, NunoAt a time when students have multiple demands in terms of technology and the resources and tools available are more and more varied, the school must respond with more attractive activities. It is, therefore, essential to provide students with digital tools accessible through the devices they are most familiar with, mobile phones and computers. By using these tools, we are creating a stimulating environment capable of engaging the students, providing them with the means to build their knowledge. In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. Desmos has a very intuitive interface where you can create sets of interactive activities and tasks that facilitate learning mathematics, in order to make it more meaningful. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education and students didn't have, at that time, a graphing calculator or any simulator in their computers. Ten activities on the quadratic function were constructed, involving various parameters so that the students, observing the changes on the graphs, were able to understand the concepts underlying this subject, namely vertical and horizontal translations of the graph, domain, range, injectivity, zeros, monotony, extremes, axis of symmetry and coordinates of the vertex of the parabola representing the graph of the quadratic function. This didactic experience was applied to two classes of 10th grade in Portuguese Educational System, involving forty-seven students, 76.7% of whom highlighted the fact that it facilitated learning in the study of functions, followed by 74.4% who considered the environment dynamic and attractive as well as the feedback given in the answers to the exercises. The use of digital tools should always be complemented with the teacher’s human component. The profile of each student is unique and specific, and the pace of learning differs from student to student. A tool like Desmos, which students are enthusiastic about using, allows monitoring of individual performance and timely and appropriate intervention by the teacher. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.
- An Experimental Study of the Ant Colony System for the Period Vehicle Routing ProblemPublication . Matos, Ana Cristina; Oliveira, Rui CarvalhoIn this paper, a new Ant System approach to the Period Vehicle Routing Problem (PVRP) is presented. In PVRP, visit days have to be assigned to customers in order to find efficient routes over the period. We suggest a new technique for defining the initial solution and a novel strategy to update the pheromone trails that is especially suited for solving large scale problems. An illustrative example for a waste collection system involving 202 localities in the municipality of Viseu, Portugal, demonstrates the effectiveness of the model.
- Análise de agrupamentos consensuaisPublication . Sousa, Lúcia; Sousa, FernandaO trabalho apresentado foca o problema do consenso de agrupamentos, um agrupamento que combina os diferentes agrupamentos individuais, refletindo as principais estruturas em classes neles inerentes, numa perspetiva de obter um agrupamento de maior qualidade. São discutidos dois tipos de abordagens a este problema: a baseada em mecanismos de votação e a que recorre às noções de Informação Mútua e híper grafos. É apresentado um estudo comparativo destas abordagens, considerando a sua aplicação a conjuntos de dados simulados com diferentes características, no que respeita ao número de classes, sua cardinalidade, homogeneidade e separabilidade.
- Approaches to suggest potential agreements: Perspectives of mediation with incomplete informationPublication . Sarabando, Paula; Dias, Luís; Vetschera, RudolfIn bilateral Negotiation Analysis, the literature often co nsiders the case of complete information. In this context, since the negotiators know the value functions of both parties, it is not difficult to calculate the Pareto frontier and the Pareto efficient soluti ons for the negotiation. Thus rational negotiators can reach agreement on this frontier. However, these approaches are not applied in practice when the parties do not have complete information. The research question of our work is “It is possible to help negotiators achieving an efficient soluti on if they do not have complete information regarding the different parameters of the model?”. We propos e to obtain information regarding the preferences of negotiators during the negotiation process , in order to be able to propose alternatives close to the Pareto frontier. During this work we will presen t three approaches to help a mediator proposing a better solution than the compromise the negotia tors have reached or are close to reach.
- Are Consumers Aware of Sustainability Aspects Related to Edible Insects? Results from a Study Involving 14 CountriesPublication . Guiné, Raquel P. F.; Florença, Sofia De Guiné E; Anjos, Ofélia; Boustani, Nada M.; Chuck-Hernández, Cristina; Sarić, Marijana Matek; Ferreira, Manuela; Costa, Cristina Amaro Da; Bartkiene, Elena; Cardoso, Ana Paula; Tarcea, Monica; Correia, Paula; Campos, Sofia; Papageorgiou, Maria; Camino, Daniel Abarquero; Korzeniowska, Malgorzata; Černelič-Bizjak, Maša; Kruma, Zanda; Damarli, Emel; Ferreira, Vanessa; Djekic, IlijaIn recent years, edible insects have been suggested as an alternative food that is more sustainable compared with other sources of animal protein. However, knowledge about the sustainability aspects associated with this source of food may play a role in convincing consumers to adopt insects as part of their diet. In this context, the present study investigated the level of knowledge about the sustainability of edible insects in a group of people originating from 14 countries, with some naturally entomophagous and others not. To measure the knowledge, 11 items were selected and the scores obtained were tested with statistical tools (t-test for independent samples, analysis of variance—ANOVA) to search for differences according to sociodemographic and socioeconomic characteristics, geographical origin, and consumption habits of edible insects. The obtained results showed that, in general, knowledge is moderate, with the values of the average scores for the 11 items investigated ranging from 0.23 ± 0.99 to 0.66 ± 1.02, on a scale ranging from –2 (=very low knowledge) to 2 (=very high knowledge). The highest scores were found for items relating to the lower use of animal feed and lower emission of greenhouse gases required for the production of insects compared with beef. When investigating the differences between groups of participants, significant differences were generally found, revealing a trend for higher knowledge among males and young adults, for participants residing in urban areas and in countries such as Spain, Mexico, and Poland, and for participants with higher education levels and higher incomes. When testing the influence of consumption variables on the level of knowledge, the results showed a higher knowledge for participants who had already consumed insects or are willing to consume them. Finally, it was observed that higher knowledge was found for participants whose motivation to consume insects related to curiosity, a wish to preserve the planet, the gastronomic characteristics of insects, and their nutritional value. In conclusion, these results clearly indicate a very marked influence of a number of variables on the knowledge about the sustainability of edible insects, and this may be helpful to delineate strategies to effectively raise knowledge and eventually increase the willingness to consider insects as a more sustainable alternative to partially replace other protein foods, even in countries where this is a not a traditional practice.