O estudo do limite de uma função: o que disseram os alunos?

This article presents part of the results obtained in a doctoral research that had as objective to bring new reflections related to the concept of limit of a function. There are a large number of research works with different approaches and methodologies that seek to discover the reasons for the widespread failure of students in the discipline of Differential and Integral Calculus. But there are still few who work on the college student's look at this difficulty. We will present in this text, specifically, the data of the students regarding the concept of limit with the hope that they can sensitize the teachers who teach this discipline.Este artículo presenta parte de los resultados obtenidos en una investigación de doctorado que tuvo como objetivo traer nuevas reflexiones relacionadas al concepto de límite de una función. Hay un número grande de trabajos de investigación con diferentes enfoques y metodologías que buscaron descubrir los motivos para el fracaso generalizado de los alumnos en la disciplina de Cálculo Diferencial e Integral. Pero todavía hay pocos que trabajan sobre la mirada del alumno universitario sobre esta dificultad. Presentaremos en este texto, específicamente, los datos de los alumnos referentes al concepto de límite con la esperanza de que los mismos puedan sensibilizar a los profesores que enseñan esa disciplina. Cet article présente une partie des résultats obtenus dans une recherche doctorale ayant pour objectif d'apporter de nouvelles réflexions liées au concept de limite d'une fonction. Il existe un grand nombre de travaux de recherche avec différentes approches et méthodologies qui cherchent à découvrir les raisons de l'échec généralisé des étudiants dans la discipline du calcul différentiel et intégral. Cependant il y en a encore peu qui travaillent sur le regard de l'étudiant sur cette difficulté. Nous présenterons dans ce texte, en particulier, les données des étudiants concernant le concept limite avec l'espoir qu'ils puissent sensibiliser les enseignants qui enseignent cette discipline.Este artigo apresenta parte dos resultados obtidos em uma pesquisa de doutorado que teve como objetivo trazer novas reflexões relacionadas ao conceito de limite de uma função. Há um número grande de trabalhos de investigação com diferentes abordagens e metodologias que procuraram descobrir os motivos para o fracasso generalizado dos alunos na disciplina de Cálculo Diferencial e Integral. Mas, há ainda poucos trabalham que versam sobre o olhar do aluno universitário sobre essa dificuldade. Apresentaremos nesse texto, especificamente, os dados dos alunos referentes ao conceito de limite com a esperança de que os mesmos possam sensibilizar os professores que ensinam essa disciplina

O QUE PENSAM OS PROFESSORES UNIVERSITÁRIOS SOBRE O ENSINO E A APRENDIZAGEM DO CONCEITO DE LIMITE?

Este artigo apresenta parte dos resultados obtidos em uma pesquisa de doutorado que teve como objetivo trazer novas reflexões relacionadas ao conceito de limite de uma função. Há um número grande de trabalhos de investigação com diferentes abordagens e metodologias que procuraram descobrir os motivos para o fracasso generalizado dos alunos na disciplina de Cálculo Diferencial e Integral. Mas, há ainda poucos trabalham que versam sobre o olhar do professor universitário sobre essa dificuldade. Apresentaremos nesse texto, especificamente, as “falas” deprofessores universitários referentes ao conceito de limite e seu ensino. Para tanto, procuraremos inicialmente explicitar como realizamos a leitura dessas falas. O método utilizado para a análise se aproxima da análise de conteúdo porque fizemos uma leitura repetida das respostas até encontrarmos uma maneira de explicitar o que era comum ou não, o que se repetia com frequência, as palavras mais utilizadas. Ao falarem da definição formal de limite, alguns professores utilizaram os termos vizinhança, aproximações, e mencionaram trabalhar com mais de um registro em sala de aula. Na nossa perspectiva, essa explicação não se constitui verdadeiramente em uma explicação, mas em uma “leitura” da mesma. E, então, nos perguntamos: Que visão o professor universitário teria de explicação? Como seria para ele traduzir/decodificar o simbólico para o aluno

Covid-19 Dynamic Monitoring and Real-Time Spatio-Temporal Forecasting

Background: Periodically, humanity is often faced with new and emerging viruses that can be a significant global threat. It has already been over a century post—the Spanish Flu pandemic, and we are witnessing a new type of coronavirus, the SARS-CoV-2, which is responsible for Covid-19. It emerged from the city of Wuhan (China) in December 2019, and within a few months, the virus propagated itself globally now resulting more than 50 million cases with over 1 million deaths. The high infection rates coupled with dynamic population movement demands for tools, especially within a Brazilian context, that will support health managers to develop policies for controlling and combating the new virus. / Methods: In this work, we propose a tool for real-time spatio-temporal analysis using a machine learning approach. The COVID-SGIS system brings together routinely collected health data on Covid-19 distributed across public health systems in Brazil, as well as taking to under consideration the geographic and time-dependent features of Covid-19 so as to make spatio-temporal predictions. The data are sub-divided by federative unit and municipality. In our case study, we made spatio-temporal predictions of the distribution of cases and deaths in Brazil and in each federative unit. Four regression methods were investigated: linear regression, support vector machines (polynomial kernels and RBF), multilayer perceptrons, and random forests. We use the percentage RMSE and the correlation coefficient as quality metrics. / Results: For qualitative evaluation, we made spatio-temporal predictions for the period from 25 to 27 May 2020. Considering qualitatively and quantitatively the case of the State of Pernambuco and Brazil as a whole, linear regression presented the best prediction results (thematic maps with good data distribution, correlation coefficient >0.99 and RMSE (%) <4% for Pernambuco and around 5% for Brazil) with low training time: [0.00; 0.04 ms], CI 95%. / Conclusion: Spatio-temporal analysis provided a broader assessment of those in the regions where the accumulated confirmed cases of Covid-19 were concentrated. It was possible to differentiate in the thematic maps the regions with the highest concentration of cases from the regions with low concentration and regions in the transition range. This approach is fundamental to support health managers and epidemiologists to elaborate policies and plans to control the Covid-19 pandemics

COVID-SGIS: A Smart Tool for Dynamic Monitoring and Temporal Forecasting of Covid-19

Background: The global burden of the new coronavirus SARS-CoV-2 is increasing at an unprecedented rate. The current spread of Covid-19 in Brazil is problematic causing a huge public health burden to its population and national health-care service. To evaluate strategies for alleviating such problems, it is necessary to forecast the number of cases and deaths in order to aid the stakeholders in the process of making decisions against the disease. We propose a novel system for real-time forecast of the cumulative cases of Covid-19 in Brazil. / Methods: We developed the novel COVID-SGIS application for the real-time surveillance, forecast and spatial visualization of Covid-19 for Brazil. This system captures routinely reported Covid-19 information from 27 federative units from the Brazil.io database. It utilizes all Covid-19 confirmed case data that have been notified through the National Notification System, from March to May 2020. Time series ARIMA models were integrated for the forecast of cumulative number of Covid-19 cases and deaths. These include 6-days forecasts as graphical outputs for each federative unit in Brazil, separately, with its corresponding 95% CI for statistical significance. In addition, a worst and best scenarios are presented. / Results: The following federative units (out of 27) were flagged by our ARIMA models showing statistically significant increasing temporal patterns of Covid-19 cases during the specified day-to-day period: Bahia, Maranhão, Piauí, Rio Grande do Norte, Amapá, Rondônia, where their day-to-day forecasts were within the 95% CI limits. Equally, the same findings were observed for Espírito Santo, Minas Gerais, Paraná, and Santa Catarina. The overall percentage error between the forecasted values and the actual values varied between 2.56 and 6.50%. For the days when the forecasts fell outside the forecast interval, the percentage errors in relation to the worst case scenario were below 5%. / Conclusion: The proposed method for dynamic forecasting may be used to guide social policies and plan direct interventions in a cost-effective, concise, and robust manner. This novel tools can play an important role for guiding the course of action against the Covid-19 pandemic for Brazil and country neighbors in South America

Fuzzy-logic controlled genetic algorithm for the rail-freight crew-scheduling problem

AbstractThis article presents a fuzzy-logic controlled genetic algorithm designed for the solution of the crew-scheduling problem in the rail-freight industry. This problem refers to the assignment of train drivers to a number of train trips in accordance with complex industrial and governmental regulations. In practice, it is a challenging task due to the massive quantity of train trips, large geographical span and significant number of restrictions. While genetic algorithms are capable of handling large data sets, they are prone to stalled evolution and premature convergence on a local optimum, thereby obstructing further search. In order to tackle these problems, the proposed genetic algorithm contains an embedded fuzzy-logic controller that adjusts the mutation and crossover probabilities in accordance with the genetic algorithm’s performance. The computational results demonstrate a 10% reduction in the cost of the schedule generated by this hybrid technique when compared with a genetic algorithm with fixed crossover and mutation rates