Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

Producing an explanatory proof in a 9th grade classroom

Este artigo apresenta parte de um estudo fundamentado na problemática da demonstração na matemática escolar. Descreve o modo como quatro alunos do 9.º ano exploraram uma tarefa relacionada com a descoberta de eixos de simetria em várias figuras geométricas. A demonstração, que os mesmos construíram, teve essencialmente uma função explicativa. O papel da professora na negociação do significado de demonstração e da sua necessidade é igualmente analisado. Os alunos desenvolvem primeiro uma compreensão prática sem consciência das razões que fundamentam as afirmações matemáticas e só depois uma compreensão teórica que os conduz à construção de uma demonstração.

e-learning in the classroom?

As teachers, we are challenged everyday to solve pedagogical problems and we have to fight for our students’ attention in a media rich world. I will talk about how we use ICT in Initial Teacher Training and give you some insight on what we are doing. The most important benefit of using ICT in education is that it makes us reflect on our practice. There is no doubt that our classrooms need to be updated, but we need to be critical about every peace of hardware, software or service that we bring into them. It is not only because our budgets are short, but also because e‐learning is primarily about learning, not technology. Therefore, we need to have the knowledge and skills required to act in different situations, and choose the best tool for the job. Not all subjects are suitable for e‐learning, nor do all students have the skills to organize themselves their own study times. Also not all teachers want to spend time programming or learning about instructional design and metadata. The promised land of easy use of authoring tools (e.g. eXe and Reload) that will lead to all teachers become Learning Objects authors and share these LO in Repositories, all this failed, like previously HyperCard, Toolbook and others. We need to know a little bit of many different technologies so we can mobilize this knowledge when a situation requires it: integrate e‐learning technologies in the classroom, not a flipped classroom, just simple tools. Lecture capture, mobile phones and smartphones, pocket size camcorders, VoIP, VLE, live video broadcast, screen sharing, free services for collaborative work, save, share and sync your files. Do not feel stressed to use everything, every time. Just because we have a whiteboard does not mean we have to make it the centre of the classroom. Start from where you are, with your preferred subject and the tools you master. Them go slowly and try some new tool in a non‐formal situation and with just one or two students. And you don’t need to be alone: subscribe a mailing list and share your thoughts with other teachers in a dedicated forum, even better if both are part of a community of practice, and share resources. We did that for music teachers and it was a success, in two years arriving at 1.000 members. Just do it.

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

Chitosan-alginate microparticulate delivery system for an alternative route of administration of BCG vaccine

Immunisation against M. tuberculosis with current available BCG vaccine lacks efficacy in preventing adult pulmonary tuberculosis. Targeting nasal mucosa is an attractive option for a more effective immunization. The delivery of BCG via the intranasal route involves overcoming barriers such as crossing the physical barrier imposed by the mucus layer and ciliar remotion, cellular uptake and intracellular trafficking by antigen presenting cells. Due to its biodegradable, immunogenic and mucoadhesive properties, chitosan particulate delivery systems can act both as vaccine carrier and adjuvant, improving the elicited immune response. In this study, different combinations of Chitosan/Alginate/TPP microparticles with BCG were produced as vaccine systems. The developed microparticle system successfully modulates BCG surface physicochemical properties and promotes effective intracellular uptake by human macrophage cell lines Preliminary immune responses were evaluated after s.c. and intranasal immunisation of BALB/c mice. BCG vaccination successfully stimulated the segregation of IgG2a and IgG1, where intranasal immunisation with chitosan/alginate particulate system efficiently elicited a more equilibrated cellular/humoral immune response.

Working in and on groups: an illustration of the principles of exploratory practice in an esp classroom

Neste artigo, descrevo e analiso uma actividade de trabalho em grupo desenvolvida para uma aula da disciplina de Língua Inglesa VI das turmas do 3º ano do Curso de Línguas e Secretariado do Instituto Superior de Contabilidade e Administração do Porto (ISCAP). No enquadramento teórico, abordam-se questões relacionadas com o trabalho em grupo numa aula de língua estrangeira, nomeadamente a dimensão social da sala de aula em geral e da interacção aluno-aluno em particular. Apresentam-se então os princípios da Exploratory Practice, com ênfase na possibilidade preconizada por esta abordagem de se poder transformar uma actividade de reflexão e discussão sobre o processo de ensino/aprendizagem numa unidade pedagógica. Segue-se a apresentação da proposta didáctica, respectivo plano de aula e alguns exemplos dos textos produzidos pelos alunos. O artigo termina com a apresentação de alguns comentários críticos, realçando-se a contribuição da Exploratory Practice para o desenvolvimento de uma maior consciencialização por parte dos alunos do seu processo de aprendizagem.

Facebook vs moodle : Surveying university students on the use of learning management systems to support learning activities outside the classroom

CISTI'2015 - 10ª Conferência Ibérica de Sistemas e Tecnologias de Informação, 17 a 20 de junho de 2015, Águeda, Aveiro, Portugal.

Correcção automática de respostas de texto livre para a aplicação UNI_NET-Classroom

Ao longo dos tempos foi possível constatar que uma grande parte do tempo dos professores é gasta na componente de avaliação. Por esse facto, há já algumas décadas que a correcção automática de texto livre é alvo de investigação. Sendo a correcção de exercícios efectuada pelo computador permite que o professor dedique o seu tempo em tarefas que melhorem a aprendizagem dos alunos. Para além disso, cada vez mais as novas tecnologias permitem o uso de ferramentas com bastante utilidade no ensino, pois para além de facilitarem a exposição do conhecimento também permitem uma maior retenção da informação. Logo, associar ferramentas de gestão de sala de aula à correcção automática de respostas de texto livre é um desafio bastante interessante. O objectivo desta dissertação foi a realização de um estudo relativamente à área de avaliação assistida por computador em que este trabalho se insere. Inicialmente, foram analisados alguns correctores ortográficos para seleccionar aquele que seria integrado no módulo proposto. De seguida, foram estudadas as técnicas mais relevantes e as ferramentas que mais se enquadram no âmbito deste trabalho. Neste contexto, a ideia foi partir da existência de uma ferramenta de gestão de sala de aula e desenvolver um módulo para a correcção de exercícios. A aplicação UNI_NET-Classroom, que foi a ferramenta para a qual o módulo foi desenvolvido, já continha um componente de gestão de exercícios que apenas efectuava a correcção para as respostas de escolha múltipla. Com este trabalho pretendeu-se acrescentar mais uma funcionalidade a esse componente, cujo intuito é dar apoio ao professor através da correcção de exercícios e sugestão da cotação a atribuir. Por último, foram realizadas várias experiências sobre o módulo desenvolvido, de forma a ser possível retirar algumas conclusões para o presente trabalho. A conclusão mais importante foi que as ferramentas de correcção automática são uma mais-valia para os professores e escolas.

Constructing and Using Multimodal Narratives to Research in Science Education: Contributions Based on Practical Classroom

This study deals with the problem of how to collect genuine and useful data about science classroom practices, and preserving the complex and holistic nature of teaching and learning. Additionally, we were looking for an instrument that would allow comparability and verifiability for teaching and research purposes. Given the multimodality of teaching and learning processes, we developed the multimodal narrative (MN), which describes what happens during a task and incorporates data such as examples of students’ work.

How short and light can a simple pendulum be for classroom use?

We compare the period of oscillation of an ideal simple pendulum with the period of a more 'real' pendulum constituted of a rigid sphere and a rigid slender rod. We determine the relative error in the calculation of the local acceleration of gravity if the period of the ideal pendulum is use?d instead of the period of this real pendulum. © 2014 IOP Publishing Ltd..

Performance assessment in the portuguese public administration

Apresentação realizada na Conferência "Changing Public Sevice in a Changing World" realizada em Budapeste a 24 de Abril de 2009

The portuguese public administration organization

Apresentação realizada no INA por ocasião da visita de uma delegação da República da Sérvia a Portugal.

Evaluation of portuguese public administration - institutions, managers and workers

Apresentação realizada a uma delegação da Administração pública da Bulgária, que visitou o INA em 2 de Dezembro de 2008.

Evaluation of training of public managers in the context of portuguese public administration

Comunicação apresentada na 32ª conferência anual do European Group of Public Administration (EGPA), em Toulouse.