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.

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.

Eastwards / westwards: which direction for gender studies in the 21st century?

Eastwards / Westwards: Which Direction for Gender Studies in the XXIst Century? is a collection of essays which focus on themes and methods that characterize current research into gender in Asian countries in general. In this collection, ideas derived from Gender Studies elsewhere in the world have been subjected to scrutiny for their utility in helping to describe and understand regional phenomena. But the concepts of Local and Global – with their discoursive productions – have not functioned as a binary opposition: localism and globalism are mutually constitutive and researchers have interrogated those spaces of interaction between the ‘self’ and the ‘other’, bearing in mind their own embeddedness in social and cultural structures and their own historical memory. Contributors to this collection provided a critical transnational perspective on some of the complex effects of the dynamics of cultural globalization, by exploring the relation between gender and development, language, historiography, education and culture. We have also given attention to the ideological and rhetorical processes through which gender identity is constructed, by comparing textual grids and patterns of expectation. Likewise, we have discussed the role of ethnography, anthropology, historiography, sociology, fiction, popular culture and colonial and post-colonial sources in (re)inventing old/new male/female identities, their conversion into concepts and circulation through time and space. This multicultural and trans-disciplinary selection of essays is totally written in English, fully edited and revised, therefore, it has a good potential for an immediate international circulation. This project may trace new paths and issues for discussion on what concerns the life, practices and narratives by and about women in Asia, as well as elsewhere in the present day global experience. Academic readership: Researchers, scholars, educators, graduate and post-graduate students, doctoral students and general non-fiction readers, with a special interest in Gender Studies, Asia, Colonial and Post-Colonial Literature, Anthropology, Cultural Studies, History, Historiography, Politics, Race, Feminism, Language, Linguistics, Power, Political and Feminist Agendas, Popular Culture, Education, Women’s Writing, Religion, Multiculturalism, Globalisation, Migration. Chapter summary: 1. “Social Gender Stereotypes and their Implication in Hindi”, Anjali Pande, Jawaharlal Nehru University, New Delhi, India. This essay looks at the subtle ways in which gender identities are constructed and reinforced in India through social norms of language use. Language itself becomes a medium for perpetuating gender stereotypes, forcing its speakers to confirm to socially defined gender roles. Using examples from a classroom discussion about a film, this essay will highlight the underlying rigid male-female stereotypes in Indian society with their more obvious expressions in language. For the urban woman in India globalisation meant increased economic equality and exposure to changed lifestyles. On an individual level it also meant redefining gender relations and changing the hierarchy in man-­woman relationships. With the economic independence there is a heightened sense of liberation in all spheres of social life, a confidence to fuzz the rigid boundaries of gender roles. With the new films and media celebrating this liberated woman, who is ready to assert her sexual needs, who is ready to explode those long held notions of morality, one would expect that the changes are not just superficial. But as it soon became obvious in the course of a classroom discussion about relationships and stereotypes related to age, the surface changes can not become part of the common vocabulary, for the obvious reason that there is still a vast gap between the screen image of this new woman and the ground reality. Social considerations define the limits of this assertiveness of women, whereas men are happy to be liberal within the larger frame of social sanctions. The educated urban woman in India speaks in favour of change and the educated urban male supports her, but one just needs to scratch the surface to see the time tested formulae of gender roles firmly in place. The way the urban woman happily balances this emerging promise of independence with her gendered social identity, makes it necessary to rethink some aspects of looking at gender in a gradually changing, traditional society like India. 2. “The Linguistic Dimension of Gender Equality”, Alissa Tolstokorova, Kiev Centre for Gender Information and Education, Ukraine. The subject-matter of this essay is gender justice in language which, as I argue, may be achieved through the development of a gender-related approach to linguistic human rights. The last decades of the 20th century, globally marked by a “gender shift” in attitudes to language policy, gave impetus to the social movement for promoting linguistic gender equality. It was initiated in Western Europe and nowadays is moving eastwards, as ideas of gender democracy progress into developing countries. But, while in western societies gender discrimination through language, or linguistic sexism, was an issue of concern for over three decades, in developing countries efforts to promote gender justice in language are only in their infancy. My argument is that to promote gender justice in language internationally it is necessary to acknowledge the rights of women and men to equal representation of their gender in language and speech and, therefore, raise a question of linguistic rights of the sexes. My understanding is that the adoption of the Universal Declaration of Linguistic Rights in 1996 provided this opportunity to address the problem of gender justice in language as a human rights issue, specifically as a gender dimension of linguistic human rights. 3. “The Rebirth of an Old Language: Issues of Gender Equality in Kazakhstan”, Maria Helena Guimarães, Polytechnic Institute of Porto, Portugal. The existing language situation in Kazakhstan, while peaceful, is not without some tension. We propose to analyze here some questions we consider relevant in the frame of cultural globalization and gender equality, such as: free from Russian imperialism, could Kazakhstan become an easy prey of Turkey’s “imperialist dream”? Could these traditionally Muslim people be soon facing the end of religious tolerance and gender equality, becoming this new old language an easy instrument for the infiltration in the country of fundamentalism (it has already crossed the boarders of Uzbekistan), leading to a gradual deterioration of its rich multicultural relations? The present structure of the language is still very fragile: there are three main dialects and many academics defend the re-introduction of the Latin alphabet, thus enlarging the possibility of cultural “contamination” by making the transmission of fundamentalist ideas still easier through neighbour countries like Azerbaijan, Uzbekistan and Turkmenistan (their languages belong to the same sub-group of Common Turkic), where the Latin alphabet is already in use, and where the ground for such ideas shown itself very fruitful. 4. “Construction of Womanhood in the Bengali Language of Bangladesh”, Raasheed Mahmood; University of New South Wales, Sydney. The present essay attempts to explore the role of gender-based language differences and of certain markers that reveal the status accorded to women in Bangladesh. Discrimination against women, in its various forms, is endemic in communities and countries around the world, cutting across class, race, age, and religious and national boundaries. One cannot understand the problems of gender discrimination solely by referring to the relationship of power or authority between men and women. Rather one needs to consider the problem by relating it to the specific social formation in which the image of masculinity and femininity is constructed and reconstructed. Following such line of reasoning this essay will examine the nature of gender bias in the Bengali language of Bangladesh, holding the conviction that as a product of social reality language reflects the socio-cultural behaviour of the community who speaks it. This essay will also attempt to shed some light on the processes through which gender based language differences produce actual consequences for women, who become exposed to low self-esteem, depression and systematic exclusion from public discourse. 5. “Marriage in China as an expression of a changing society”, Elisabetta Rosado David, University of Porto, Portugal, and Università Ca’Foscari, Venezia, Italy. In 29 April 2001, the new Marriage Law was promulgated in China. The first law on marriage was proclaimed in 1950 with the objective of freeing women from the feudal matrimonial system. With the second law, in 1981, values and conditions that had been distorted by the Cultural Revolution were recovered. Twenty years later, a new reform was started, intending to update marriage in the view of the social and cultural changes that occurred with Deng Xiaoping’s “open policy”. But the legal reform is only the starting point for this case-study. The rituals that are followed in the wedding ceremony are often hard to understand and very difficult to standardize, especially because China is a vast country, densely populated and characterized by several ethnic minorities. Two key words emerge from this issue: syncretism and continuity. On this basis, we can understand tradition in a better way, and analyse whether or not marriage, as every social manifestation, has evolved in harmony with Chinese culture. 6. “The Other Woman in the Portuguese Colonial Empire: The Case of Portuguese India”, Maria de Deus Manso, University of Évora, Portugal. This essay researches the social, cultural and symbolic history of local women in the Portuguese Indian colonial enclaves. The normative Portuguese overseas history has not paid any attention to the “indigenous” female populations in colonial Portuguese territories, albeit the large social importance of these social segments largely used in matrimonial and even catholic missionary strategies. The first attempt to open fresh windows in the history of this new field was the publication of Charles Boxer’s referential study about Women in lberian Overseas Expansion, edited in Portugal only after the Revolution of 1975. After this research we can only quote some other fragmentary efforts. In fact, research about the social, cultural, religious, political and symbolic situation of women in the Portuguese colonial territories, from the XVI to the XX century, is still a minor historiographic field. In this essay we discuss this problem and we study colonial representations of women in the Portuguese Indian enclaves, mainly in the territory of Goa, using case studies methodologies. 7. “Heading East this Time: Critical Readings on Gender in Southeast Asia”, Clara Sarmento, Polytechnic Institute of Porto, Portugal. This essay intends to discuss some critical readings of fictional and theoretical texts on gender condition in Southeast Asian countries. Nowadays, many texts about women in Southeast Asia apply concepts of power in unusual areas. Traditional forms of gender hegemony have been replaced by other powerful, if somewhat more covert, forms. We will discuss some universal values concerning conventional female roles as well as the strategies used to recognize women in political fields traditionally characterized by male dominance. Female empowerment will mean different things at different times in history, as a result of culture, local geography and individual circumstances. Empowerment needs to be perceived as an individual attitude, but it also has to be facilitated at the macro­level by society and the State. Gender is very much at the heart of all these dynamics, strongly related to specificities of historical, cultural, ethnic and class situatedness, requiring an interdisciplinary transnational approach.

Language and trade: the (new) route of portuguese in the 21st century

Globalisation has eliminated frontiers and in the case of Europe helped the crossing of borders and changed forever the concept of social (and I would also say individual) geography: the rest of the world is out there; we can pretend not to see it, but we cannot avoid it. Moreover, Europe is undergoing a serious crisis, also economic, and new markets and business partners are welcome. In this context, cultural bonds like a common language can open new investment paths and give rise to successful stories. In this paper we intend to present an example of how low linguistic distance can lead to good business, even if a) in the internationalization process of the companies’ language is often forgotten as a management element and b) consumers of language products (like User Guides) are also not stimulating investment in language by the companies. Through the results of 2 studies carried out in 2010 and 2011 we will show how a pluricentric language like Portuguese is managed in multinational companies (MC) and Small and medium Enterprises (SMEs). The second study is based on an online survey questioning the effectiveness, efficiency and general quality of User Guides and the reaction of consumers to language. Results show that although playing a role in the internationalization process of companies in the same linguistic space, language is opportunistically used. On the other hand, Portuguese and Brazilian consumers show a very functional perception of the Portuguese language...

De intruso a tutor: impactos da formação em contexto PNEP

Este trabalho decorre de uma experiência de formação contínua de âmbito nacional, durante um ano letivo, relacionada com o ensino do português no 1º Ciclo no contexto do Programa Nacional de Ensino do Português (PNEP). Para se compreender o impacto da formação e do seu modelo, analisaram-se as produções escritas (do género narrativo e epistolar) dos alunos do 1º ao 4º ano de escolaridade, os resultados das Provas de Aferição de Língua Portuguesa do 4º ano, os inquéritos de avaliação dos formandos à própria formação, da competência da Comissão Nacional de Acompanhamento (CNA) e, ainda, as reflexões dos portefólios produzidos pelos formandos ao longo da formação. Em génese, pretende-se aferir de que modo esta formação interferiu nas aprendizagens e no desenvolvimento de competências dos alunos no domínio da língua materna, nomeadamente ao nível da escrita. Nessa perspetiva, são comparados dois grupos de alunos do mesmo agrupamento, do distrito de Lisboa, sendo o grupo experimental constituído pelos alunos cujos professores frequentaram a ação de formação PNEP e o grupo de controlo formado por alunos cujos professores nunca frequentaram a referida ação. Todavia, podendo o PNEP ser considerado como uma formação inovadora, porque se desenvolve em contexto, procura-se também saber como se sentiram os professores ao longo desta formação, bem como que repercussões e mais-valias obtiveram para as suas práticas pedagógicas e para a resolução real dos problemas vividos na sala de aula. Por fim, cruzando todos os dados de que se dispõe, aspira-se compreender o papel e o contributo da figura do formador no contexto PNEP, o que poderá conduzir a uma nova abordagem de formação, mais consentânea com o conceito de “mentoria”, e seus processos, do que com os pressupostos iniciais assentes numa lógica de “tutoria”. - This study originates from a one year education experience, nation wide, in the wake of the PNEP (Programa Nacional de Ensino do Português, in its maiden form) program. The aim is to understand how the model herein impacts first to fourth year primary school children’s learning and writing skills, how it influences the fourth year’s final exam results, and how it is reflected on practitioners’ (teachers undergoing the PNEP) performance evaluation inquires, and on concept development within their portfolios. In genesis, we seek to analyse whether the PNEP changed the way children attending primary school learn and master Portuguese, particularly its written expression. To do so, the study focus on two different publics, whereby an experimental group was build around a set of classes whose teachers had completed the PNEP education and training program, and a control group, set around a similar sample, but where teachers had no PNEP education or training at all. In addition, because PNEP might be considered as an advanced education model, we also wanted to disclosure how it adds to schoolteachers’ education techniques, and how it would help them solve daily ordinary problems within the classroom. Last but not the least, the study reveals that PNEP can change Portuguese standard education perspectives, changing classic tutorial methodologies towards a, more responsive, mentoring approach.

O teatro de marionetas e o desenvolvimento da oralidade no 2º ciclo do ensino básico

Dissertação apresentada à Escola Superior de Educação de Lisboa para a obtenção do grau de mestre em Educação Artística - Especialização em Teatro na Educação

Reported missing - learners in SLA/EFL research

Versão integral da revista no link do editor

La enseñanza de la gramática en primaria y secundaria: algunas reflexiones y propuestas

En el presente artículo pretendemos trazar algunas líneas generales destacadas por la investigación a propósito de la instrucción gramatical y su relación con el dominio del uso de la lengua. Hacemos referencia a algunas ideas del debate generado en el mundo anglosajón y francófono y en España. Nos centramos en algunas aportaciones realizadas en España en relación a aspectos como la metodología en el aula o los procesos de aprendizaje.

Os padrões e a resolução de problemas no 1º ciclo do ensino básico: potencialidades para o ensino-aprendizagem da matemática

Mestrado (PES II), Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico, 27 de Junho de 2014, Universidade dos Açores (Relatório de Estágio).

Concepções dos professores face à inclusão de alunos com NEE no ensino regular

Dissertação apresentada à Escola Superior de Educação de Lisboa para a obtenção de grau de mestre em Ciências da Educação -Especialidade Educação Especial

An Interface to Retrieve Personal Memories Using an Iconic Visual Language

Relevant past events can be remembered when visualizing related pictures. The main difficulty is how to find these photos in a large personal collection. Query definition and image annotation are key issues to overcome this problem. The former is relevant due to the diversity of the clues provided by our memory when recovering a past moment and the later because images need to be annotated with information regarding those clues to be retrieved. Consequently, tools to recover past memories should deal carefully with these two tasks. This paper describes a user interface designed to explore pictures from personal memories. Users can query the media collection in several ways and for this reason an iconic visual language to define queries is proposed. Automatic and semi-automatic annotation is also performed using the image content and the audio information obtained when users show their images to others. The paper also presents the user interface evaluation based on tests with 58 participants.

Desenvolvimento lexical: perspectivas e práticas de professores no 1.º ciclo do ensino básico

Dissertação apresentada à Escola Superior de Educação de Lisboa para a obtenção de grau de Mestre em Didática da Língua Portuguesa no 1.º e 2.º Ciclos do Ensino Básico

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.