Frações (parte I)

A temática das frações é provavelmente o assunto mais delicado no que diz respeito ao ensino da matemática inicial. Por terem múltiplas aplicações, contextos e sentidos, as frações pedem um ensino altamente especializado e esmerado. Há que modelar de forma cuidadosa o conceito de fração, fasear e ordenar os nós conceptuais ao longo dos anos e dosear o caráter abstrato/concreto dos exemplos e atividades. Muito se testou, teorizou e escreveu sobre esta temática. Este trabalho consiste num resumo alargado sobre o ensino das frações, documentado em literatura especializada e ilustrado através de exemplos concretos retirados de manuais do Singapore Math, um dos mais cotados métodos de ensino do mundo.

Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: calculo mental: um estudo sobre as estratégias utilizadas por alunos do 1.º e do 2.º ciclo do ensino básico

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Débora, qual foi o livro que trouxeste hoje? A potencialidade dos livros na educação pré-escolar

Relatório da UC Seminário de Apoio à Prática Profissional Supervisionada Mestrado em Educação Pré-Escolar

Desenvolvimento do sistema de controlo de um braço robotizado e respetiva interface com o utilizador

A robótica tem evoluído de forma significativa nos últimos anos e passa a ser indispensável em várias aplicações nas áreas da engenharia, aeronáutica, medicina, entre outras. O estado da arte do presente trabalho está dividido em duas partes, uma que aborda vários aspetos relacionados com a robótica e outra com os aspetos da fundamentação matemática por de trás da robótica, porque para controlar o robô é necessário implementar expressões matemáticas para o poder controlar. Neste trabalho é apresentado um sistema de controlo do braço robótico MENTOR e o desenvolvimento de uma interface para o utilizador. Para o controlo do braço robótico foi necessário calcular a cinemática direta e inversa, para que se possa obter os ângulos das juntas para uma dada posição ou qual é a posição final do braço robótico para um valor das juntas. O sistema é bastante flexível e foi desenvolvido para ser utilizado essencialmente para aprendizagem de robótica, podendo no entanto ser utilizado em outras aplicações.

A divisão no 4º ano de escolaridade

Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Professions and inter-disciplinary teamwork in socially embedded bureaucracies: Synthesis and hypotheses on the impact of informal and formal organization

In order to maximize their productivity, inter-disciplinary multi-occupation teams of professionals need to maximize inter-occupational cooperation in team decision making. Cooperation, however, is challenged by status anxiety over organizational careers and identity politics among team members who differ by ethnicity-race, gender, religion, nativity, citizenship status, etc. The purpose of this paper is to develop hypotheses about how informal and formal features of bureaucracy influence the level of inter-occupation cooperation achieved by socially diverse, multi-occupation work teams of professionals in bureaucratic work organizations. The 18 hypotheses, which are developed with the heuristic empirical case of National Science Foundation-sponsored university school partnerships in math and science curriculum innovation in the United States, culminate in the argument that cooperation can be realized as a synthesis of tensions between informal and formal features of bureaucracy in the form of participatory, high performance work systems.

Práticas de avaliação formativa na aula de matemática: um estudo no 2º ciclo

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré- Escolar e nos 1º e 2º Ciclo do Ensino Básico

A new horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

A new horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

A New horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

Behind video lectures in a MOOC

The year 2012 was the “boom year” in MOOC and all its outstanding growth until now, made us move forward in designing the first MOOC in our Institution (and the third in our country, Portugal). Most MOOC are video lectured based and the learning analytic process to these ones is just taking its first steps. Designing a video-lecture seems, at a first glance, very easy: one can just record a live lesson or lecture and turn it, directly, into a video-lecture (even here one may experience some “sound” and “camera” problems); but developing some engaging, appealing video-lecture, that motivates students to embrace knowledge and that really contributes to the teaching/learning process, it is not an easy task. Therefore questions like: “What kind of information can induce knowledge construction, in a video-lecture?”, “How can a professor interact in a video-lecture when he is not really there?”, “What are the video-lectures attributes that contribute the most to viewer’s engagement?”, “What seems to be the maximum “time-resistance” of a viewer?”, and many others, raised in our minds when designing video-lectures to a Mathematics MOOC from the scratch. We believe this technological resource can be a powerful tool to enhance students' learning process. Students that were born in digital/image era, respond and react slightly different to outside stimulus, than their teachers/professors ever did or do. In this article we will describe just how we have tried to overcome some of the difficulties and challenges we tackled when producing our own video-math-lectures and in what way, we feel, videos can contribute to the teaching and learning process at higher education level.

Matemática 100 stress: um projeto aberto no IPP

A Era Tecnológica em que nos vemos inseridos, cujos avanços acontecem a uma velocidade vertiginosa exige, por parte das Instituições de Ensino Superior (IES) uma atitude proactiva no sentido de utilização dos muitos recursos disponíveis. Por outro lado, os elementos próprios da sociedade da informação – flexibilidade, formação ao longo da vida, acessibilidade à informação, mobilidade, entre muito outros – atuam como fortes impulsionadores externos para que as IES procurem e analisem novas modalidades formativas. Perante a mobilidade crescente, que se tem revelado massiva, a aprendizagem tende a ser cada vez mais individualizada, visual e prática. A conjugação de várias formas/tipologias de transmissão de conhecimento, de métodos didáticos e mesmo de ambientes e situações de aprendizagem induzem uma melhor adaptação do estudante, que poderá procurar aqueles que melhor vão ao encontro das suas expetativas, isto é, favorecem um processo de ensino-aprendizagem eficiente na perspetiva da forma de aprender de cada um. A definição de políticas estratégicas relacionadas com novas modalidades de ensino/formação tem sido uma preocupação constante na nossa instituição, nomeadamente no domínio do ensino à distância, seja ele e-Learning, b-Learning ou, mais recentemente, “open-Learning”, onde se inserem os MOOC – Massive Open Online Courses (não esquecendo a vertente m-Learning), de acordo com as várias tendências europeias (OECD, 2007) (Comissão Europeia, 2014) e com os objetivos da “Europa 2020”. Neste sentido surge o Projeto Matemática 100 STRESS, integrado no projeto e-IPP | Unidade de e-Learning do Politécnico do Porto que criou a sua plataforma MOOC, abrindo em junho de 2014 o seu primeiro curso – Probabilidades e Combinatória. Pretendemos dar a conhecer este Projeto, e em particular este curso, que envolveu vários docentes de diferentes unidades orgânicas do IPP.

The role of molecular imaging in modern drug development

Drug development represents a highly complex, inefficient and costly process. Over the past decade, the widespread use of nuclear imaging, owing to its functional and molecular nature, has proven to be a determinant in improving the efficiency in selecting the candidate drugs that should either be abandoned or moved forward into clinical trials. This helps not only with the development of safer and effective drugs but also with the shortening of time-to-market. The modern concept and future trends concerning molecular imaging will assumedly be hybrid or multimodality imaging, including combinations between high sensitivity and functional (molecular) modalities with high spatial resolution and morphological techniques.

Immediate effects of hip mobilization with movement in patients with hip osteoarthritis: A randomised controlled trial

Background Mobilization with movement (MWM) has been shown to reduce pain, increase range of motion (ROM) and physical function in a range of different musculoskeletal disorders. Despite this evidence, there is a lack of studies evaluating the effects of MWM for hip osteoarthritis (OA). Objectives To determine the immediate effects of MWM on pain, ROM and functional performance in patients with hip OA. Design Randomized controlled trial with immediate follow-up. Method Forty consenting patients (mean age 78 ± 6 years; 54% female) satisfied the eligibility criteria. All participants completed the study. Two forms of MWM techniques (n = 20) or a simulated MWM (sham) (n = 20) were applied. Primary outcomes: pain recorded by numerical rating scale (NRS). Secondary outcomes: hip flexion and internal rotation ROM, and physical performance (timed up and go, sit to stand, and 40 m self placed walk test) were assessed before and after the intervention. Results For the MWM group, pain decreased by 2 points on the NRS, hip flexion increased by 12.2°, internal rotation by 4.4°, and functional tests were also improved with clinically relevant effects following the MWM. There were no significant changes in the sham group for any outcome variable. Conclusions Pain, hip flexion ROM and physical performance immediately improved after the application of MWM in elderly patients suffering hip OA. The observed immediate changes were of clinical relevance. Future studies are required to determine the long-term effects of this intervention.

A filter inexact-restoration method for nonlinear programming

A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669, 2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer (Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.