Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Peer Instruction method in introductory math courses

Learning is not a spectator’s sport. Students do not learn much by just sitting in class listening their teachers, memorizing pre-packaged assignments and spitting out answers. The teaching-learning process has been a constant target of studies, particularly in Higher Education, in consequence of the annual increase of new students. The concern with maintaining a desired quality level in the training of these students, conjugated with the will to widen the access to all of those who finish Secondary School Education, has triggered a greater intervention from the education specialists, in partnership with the teachers of all Higher Education areas, in the analysis of this problem. Considering the particular case of Engineering, it has been witnessed a rising concern with the active learning strategies and forms of assessment. Research has demonstrated that students learn more if they are actively engaged with the material they are studying. In this presentation we describe, present and discuss the techniques and the results of Peer Instruction method in an introductory Calculus courses of an Engineering Bach

Le moment venu ou l’eveil dês editoriaux. Mutations de la littérature des années quatre-vingt vues par les revues littéraires

Les années quatre-vingt signalent un point de bascule dans et une mutation majeure dans les caractéristiques narratives de la littérature française. D’une certaine façon, elles entament la contemporanéité littéraire telle que nous la connaissons du point de vue critique. Nous insisterons sur le rôle des revues et des éditoriaux dans ce processus. Ils manifestent quelques hésitations de la critique par rapport à la littérature naissante.

Public relations in part-time : full-time service: estratégia de comunicação para o lançamento de um novo modelo de negócio ds relações públicas em Portugal

O presente trabalho visa propor uma estratégia para a construção e lançamento de um novo modelo de negócio para a atuação das Relações Públicas em Portugal, numa proposta direcionada para as micro e pequenas empresas. Entre o serviço in house e a consultadoria clássica existe um espaço não coberto em Portugal: um serviço in house partilhado. Apresenta-se aqui este projeto de serviço de Relações Públicas para aqueles para quem é incomportável assumir nos seus quadros um Técnico de Comunicação.

How to feel "in love" with Math - a MOOC experience

In the past few years we have witnessed the fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOCs). This paper presents the “Mathematics without STRESS” MOOC Project, which is a cooperation between four schools from the Polytechnic Institute of Oporto (IPP). The concepts of MOOC and their quickly growing popularity are presented and complemented by a discussion of some MOOC definitions. The process of the project development is demonstrated by focusing on used MOOC structure, as well as the several types of course materials produced. At last, is presented a short discussion about problems and challenges met throughout the project. It is also our goal to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays.

Math without stress – an open online learning project

MOOC (as an acronym for Massive Open Online Courses) are a quite new model for the delivery of online learning to students. As “Massive” and “Online”, these courses are proposed to be accessible to many more learners than would be possible through conventional teaching. As “Open” they are (frequently) free of charge and participation is not limited by the geographical situation of the learners, creating new learning opportunities in Higher Education Institutions (HEI). In this paper we describe a recently started project “Matemática 100 STRESS” (Math Without STRESS) integrated in the e-IPP project | e-Learning Unit of Porto’s Polytechnic Institute (IPP) which has created its own MOOC platform and launched its first course – Probabilities and Combinatorics – in early June/2014. In this MOOC development were involved several lecturers from four of the seven IPP schools.

Le moment venu ou l’eveil dês editoriaux. Mutations de la littérature frainçaise des années quatre-vingt vues par les revues littéraires

Les années quatre-vingt signalent un point de bascule dans et une mutation majeure dans les caractéristiques narratives de la littérature française. D’une certaine façon, elles entament la contemporanéité littéraire telle que nous la connaissons du point de vue critique. Nous insisterons sur le rôle des revues et des éditoriaux dans ce processus. Ils manifestent quelques hésitations de la critique par rapport à la littérature naissante.

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

How to feel “in love” with math – a MOOC experience

In the past few years we have witnessed the fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOCs). This paper presents the “Mathematics without STRESS” MOOC Project, which is a cooperation between four schools from the Polytechnic Institute of Oporto (IPP). The concepts of MOOC and their quickly growing popularity are presented and complemented by a discussion of some MOOC definitions. The process of the project development is demonstrated by focusing on used MOOC structure, as well as the several types of course materials produced. At last, is presented a short discussion about problems and challenges met throughout the project. It is also our goal to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays.

How to feel “in love" with math: a MOOC experience

In the past few years we have witnessed astonishing developments on distance learning tools, in particular on Open Educational Resources (OER) such as Massive Open Online Courses (MOOC). In this paper we present the “Mathematics without STRESS”, a MOOC Project, which has been a collaborative volunteer effort that brought together professors, from four schools of the Polytechnic Institute of Oporto (IPP), in Portugal. Some concepts directly associated with MOOC and their quickly growing popularity are complemented with a discussion of some particular MOOC characterizations. The design process of this project is revealed by focusing on the MOOC structure we used, as well as on the several types of course materials that were produced. At last, we undertake a short discussion about some of the problems, achievements and challenges met throughout this project development, giving a special attention to the motivational aim of this work - hoping to contribute to a change in the way of teaching and learning Mathematics is seen and practiced nowadays.

Math without stress: an open online learning project

MOOC (as an acronym for Massive Open Online Courses) are a quite new model for the delivery of online learning to students. As “Massive” and “Online”, these courses are proposed to be accessible to many more learners than would be possible through conventional teaching. As “Open” they are (frequently) free of charge and participation is not limited by the geographical situation of the learners, creating new learning opportunities in Higher Education Institutions (HEI). In this paper we describe a recently started project “Matemática 100 STRESS” (Math Without STRESS) integrated in the e-IPP project | e-Learning Unit of Porto’s Polytechnic Institute (IPP) which has created its own MOOC platform and launched its first course – Probabilities and Combinatorics – in early June/2014. In this MOOC development were involved several lecturers from four of the seven IPP schools.

Innovations in technology: a friendly math project and the learning analytics “challenge”

Currently the world around us "reboots" every minute and “staying at the forefront” seems to be a very arduous task. The continuous and “speeded” progress of society requires, from all the actors, a dynamic and efficient attitude both in terms progress monitoring and moving adaptation. With regard to education, no matter how updated we are in relation to the contents, the didactic strategies and technological resources, we are inevitably compelled to adapt to new paradigms and rethink the traditional teaching methods. It is in this context that the contribution of e-learning platforms arises. Here teachers and students have at their disposal new ways to enhance the teaching and learning process, and these platforms are seen, at the present time, as significant virtual teaching and learning supporting environments. This paper presents a Project and attempts to illustrate the potential that new technologies present as a “backing” tool in different stages of teaching and learning at different levels and areas of knowledge, particularly in Mathematics. We intend to promote a constructive discussion moment, exposing our actual perception - that the use of the Learning Management System Moodle, by Higher Education teachers, as supplementary teaching-learning environment for virtual classroom sessions can contribute for greater efficiency and effectiveness of teaching practice and to improve student achievement. Regarding the Learning analytics experience we will present a few results obtained with some assessment Learning Analytics tools, where we profoundly felt that the assessment of students’ performance in online learning environments is a challenging and demanding task.

The development and implementation of math projects in a HEI: expectations, objectives, experiences and analysis

An overwhelming problem in Math Curriculums in Higher Education Institutions (HEI), we are daily facing in the last decade, is the substantial differences in Math background of our students. When you try to transmit, engage and teach subjects/contents that your “audience” is unable to respond to and/or even understand what we are trying to convey, it is somehow frustrating. In this sense, the Math projects and other didactic strategies, developed through Learning Management System Moodle, which include an array of activities that combine higher order thinking skills with math subjects and technology, for students of HE, appear as remedial but important, proactive and innovative measures in order to face and try to overcome these considerable problems. In this paper we will present some of these strategies, developed in some organic units of the Polytechnic Institute of Porto (IPP). But, how “fruitful” are the endless number of hours teachers spent in developing and implementing these platforms? Do students react to them as we would expect? Do they embrace this opportunity to overcome their difficulties? How do they use/interact individually with LMS platforms? Can this environment that provides the teacher with many interesting tools to improve the teaching – learning process, encourages students to reinforce their abilities and knowledge? In what way do they use each available material – videos, interactive tasks, texts, among others? What is the best way to assess student’s performance in these online learning environments? Learning Analytics tools provides us a huge amount of data, but how can we extract “good” and helpful information from them? These and many other questions still remain unanswered but we look forward to get some help in, at least, “get some drafts” for them because we feel that this “learning analysis”, that tackles the path from the objectives to the actual results, is perhaps the only way we have to move forward in the “best” learning and teaching direction.

Viva@Matemática project: a different way to see math

Viva@Mat is a project developed by four Math teachers from the School of Industrial Studies and Management (ESEIG) that was born with the fundamental objective of engaging ESEIG students with different math backgrounds in Math challenging activities. Some of these activities were transformed into real palpable materials and others into small interactive ones, being the great majority of them proposed by ESEIG’ students themselves. This small project rapidly grew into something we didn’t expect – it did flow over the walls of our institution to the general involving community – specifically to pre-university schools through the Viva@Math Exhibits – Orange, Blue and Green (the fourth, the Purple one is still in development). Nowadays, Viva@Math Exhibits – the public face of the Project – are itinerant and have been travelling between several, and different institutions (pre-university schools, preparatory schools, libraries, among others), around ESEIG and IPP area of influence and having registered visitors/participants of all ages. In this article we will describe the Viva@Math Project, its different activities that are categorized in some “great groups” like Numerical Trivia, Logic Activities and Mental Calculation, Puzzles, Geometric Curiosities, Magic Tricks, among others, designed to challenge students to use the underlying logical-mathematical reasoning to any ordinary and everyday activity. We will give specific and concrete examples of some of the activities developed and, also, reproduce of the general stimulating feedback the Project receives from the enrolled “actors” (teachers, students and their relatives, institutions, among others). We feel that this Project has become a small “bridge” between the pre-university schools and Higher Education Institutions (HEI), in trying to shorten the “gap” between the institutions of different levels of education and bring them to work together.

Desarrollo de un sistema de e-Learning para Nintendo DS

El proyecto trata de crear un software que dinámicamente nos proporcione exámenes o pruebas dependiendo de nuestro nivel de conocimientos actual. Estos exámenes se cargarán a través de un fichero XML configurable, lo que nos permitirá poner a prueba nuestros conocimientos en el tema que deseemos. El software se desarrollará en Nintendo DS, para aprovechar las prestaciones que nos ofrece de serie: doble pantalla, pantalla táctil, portabilidad.