A emergência da matemática em situações de jogo no jardim de infância e na creche

Relatório de estágio de mestrado em Educação Pré-Escolar

The effect of secular trends in the classroom furniture mismatch: support for continuous update of school furniture standards

In order to create safer schools, the Chilean authorities published a Standard regarding school furniture dimensions. The aims of this study are twofold: to verify the existence of positive secular trend within the Chilean student population and to evaluate the potential mismatch between the anthropometric characteristics and the school furniture dimensions defined by the mentioned standard. The sample consists of 3078 subjects. Eight anthropometric measures were gathered, together with six furniture dimensions from the mentioned standard. There is an average increase for some dimensions within the Chilean student population over the past two decades. Accordingly, almost 18% of the students will find the seat height to be too high. Seat depth will be considered as being too shallow for 42.8% of the students. It can be concluded that the Chilean student population has increased in stature, which supports the need to revise and update the data from the mentioned Standard. Practitioner Summary: Positive secular trend resulted in high levels of mismatch if furniture is selected according to the current Chilean Standard which uses data collected more than 20 years ago. This study shows that school furniture standards need to be updated over time.

José Anastácio da Cunha e o projeto MAT² : no trilho de uma história extraordinária

A ideia de que as Matemáticas de Portugal (e de Espanha) atravessaram, depois de um período áureo nos Descobrimentos, um longo deserto onde não foi possível florescerem Mestres, nem escolas, nem cultura científica, nem investigação de relevo foi, durante muito tempo, reiteradamente veiculada, inclusivé através de alguns dos nossos mais referenciados historiadores da Matemática, como é o caso de Gomes Teixeira ou de Rey Pastor. Mas a verdade é que o estudo da História das Matemáticas em Portugal tem, na última década, vivido um interesse crescente onde sobressaem, em particular, uma leitura menos enviesada sobre, por exemplo, o papel educativo dos Jesuítas ou a publicação das obras completas de Pedro Nunes. Está-se assim a contribuir para uma compreensão mais completa da História geral de Portugal, de que a História da Ciência e da Cultura faz parte. José Anastácio da Cunha (1744-1787) foi figura de proa no século XVIII português. Sabíamo-lo matemático que, sem nunca ter saído de Portugal, havia sido capaz de antecipar, em mais de 50 anos, os esforços de matemáticos franceses e alemães para fundar a Matemática com rigor. Sabíamo-lo também autor de uma vasta e diversificada obra de inegável importância matemática mas, igualmente, autor de textos poéticos. Agora, com o projecto que denominámos de MAT2, centramo-nos em José Anastácio da Cunha e pretendemos, se possível, ir ainda mais além. Partimos de uma descoberta, árdua mas com final feliz, em um Arquivo de família: o da Casa de Mateus. Sentimo-nos, com esta “sorte”, privilegiados e gratos por nos ter sido gentilmente concedido o acesso a um vasto conjunto de documentos únicos (diários de viagens, notas de aulas e correspondência) que incluem memórias autógrafas e inéditas de Anastácio da Cunha. Organizámo-nos, cientes do trabalho árduo que temos pela frente, multi e interdisciplinarmente englobando a Matemática (nas suas múltiplas especializações) e a História (incluindo a da Matemática) mas também contando com a Física, a Informática, os estudos militares ou a Arquivística e as Humanidades; reunimos académicos, mais e menos veteranos, com investigadores jovens e juntámos valências nacionais e estrangeiras. No presente artigo daremos conta do percurso trilhado, até agora, pelo projecto MAT2.

José Anastácio da Cunha e a criação da Casa Pia de Lisboa

As modernas ideias científicas e tecnológicas da Europa mais desenvolvida transpoem fronteiras e institucionalizam-se em Portugal com a denominada Reforma Pombalina da Universidade de Coimbra (1770-72), no reinado de D. José. Mais: não só chega a Portugal o pensamento moderno da época como, antecipando a reforma do ensino universitário no resto da Europa, o ensino universitário português faz uma aposta clara nas ciências matemáticas, físicas e naturais, bem como num ensino experimental/laboratorial. Anos mais tarde, no reinado de D. Maria, surgem outros projectos educativos e científicos igualmente modernos tais como o da criação de uma Academia Real da Marinha (1779) ou o de uma Academia Real das Ciências (1779) e idealiza-se um projeto, porventura, ainda mais revolucionário: o da criação de uma instituição de ensino – também de ciências ditas superiores – destinada, na sua génese, a orfãos e desvalidos à qual se chamou Casa Pia de Lisboa (1780), e que alguns autores reportam como sendo uma “universidade plebeia”. Com base em documentação autógrafa, ainda inédita, recentemente descoberta nos Fundos Setecentistas do Arquivo da Casa de Mateus, exploraremos o papel fundamental que José Anastácio da Cunha (1744-1787) – militar, matemático e poeta – desempenhou na concepção do Plano de Estudos para a instituição; em particular para o colégio de S. Lucas, consagrado às classes científicas.

Equations for defining the mismatch between students and school furniture: A systematic review

The present study reviews the scientific literature that describes the criteria equations for defining the mismatch between students and school furniture. This mismatch may negatively affect students' performance and comfort. Seventeen studies met the criteria of this review and twenty-one equations to test six furniture dimensions were identified. There was substantial mismatch between the relative heights of chairs and tables. Some systematic errors have been found during the application of the different equations, such as the assumption that students are sitting on chairs with a proper seat height. Only one study considered the cumulative fit. Finally, some equations are based on contradictory criteria and need to develop and evaluate new equations for these cases. Relevance to industry: Ultimately, the present work is a contribution toward improving the evaluation of school furniture and could be used to design ergonomic-oriented classroom furniture.

Analysis and selection of indicators for a sustainability assessment method for school buildings based on SBTool ‐ PT

Nowadays, the sustainability of buildings has an extreme importance. This concept goes towards the European aims of the Program Horizon 2020, which concerns about the reduction of the environmental impacts through such aspects as the energy efficiency and renewable technologies, among others. Sustainability is an extremely broad concept but, in this work, it is intended to include the concept of sustainability in buildings. Within the concept that aims the integration of environmental, social and economic levels towards the preservation of the planet and the integrity of the users, there are, currently, several types of tools of environmental certification that are applicable to the construction industry (LEED, BREEAM, DGNB, SBTool, among others). Within this context, it is highlighted the tool SBTool (Sustainable Building Tool) that is employed in several countries and can be subject to review in institutions of basic education, which are the base for the formation of the critical masses and for the development of a country. The main aim of this research is to select indicators that can be used in a methodology for sustainability assessment (SBTool) of school buildings in Portugal and in Brazil. In order to achieve it, it will also be analyzed other methodologies that already incorporate parameters directly related with the schools environment, such as BREEAM or LEED.

The importance of the category of consciousness and education for sustainability in methodologies for eco‐efficiency in school buildings

This document reports the importance of the category of consciousness and education for sustainability in the school environment. Education in school has a potential to make the benefits of the building construction visible for society and media, showing to the students, parents and communities how sustainability in built environment could improve the people life in economic, social and environment aspects. Thus, this paper addresses the main events related to sustainability, such as the Stockholm Conference, the Brundtland report, United Nations Conference on Environment and Development (UNCED) and Agenda 21, until reaching the necessity of the elaboration of Methodologies for environmental assessment of building, and later, the development of the specific methodologies according to the buildings. It is also described some examples of sustainability in schools in Germany, Finland and Italy and what kind of sustainable systems those countries are currently using.

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

The inverse along a product and its applications

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix.

School governance and academic excellence: the representations of distinguished students in an annual award of excellence

Within a research project on «academic excellence in the state school», this paper is a contribution to the sociological reflection on the cultural and organisational characteristics of the school and its relationship with the academic success of students. The data we present stem from a case study underway at a secondary school in the north of Portugal, referring to the universe of students that since 2003 have distinguished themselves for achieving grades equal to or greater than 18 (on a scale of 0 to 20) and have thus been included in the school’s Framework of Excellence. From a contextual approach to this educational practice, we focused on the cultural characteristics of the school/subject as analytical support for the study of school and non-school dimensions in their mutual connections. To this end, we used the information from document analysis and data collected from a questionnaire survey administered to more than two-thirds of the students included in the above-mentioned Framework of Excellence. Subsequently, we will use the data from this survey to understand the extent to which academic excellence is perceived as an indivisible social construction of the school’s political and organisational matrix, particularly in terms of the educational and teaching guidelines adopted by the management body. We will conclude by questioning the meaning of the school’s management policies regarding the emphasis on educational outcomes, with particular focus on the representations of excellent students in the processes of school leadership, teaching organisation, school merit and justice.

O ensino da matemática e a avaliação externa de escolas: um estudo com professores do 1.º e 2.º ciclos

Os processos e práticas de educação e formação portugueses estão cada vez mais integrados em agendas globalmente estruturadas, cujo eixo de influência se situa no quadro comum das políticas da União Europeia e de organismos transnacionais como a OCDE (Pacheco, 2009). A avaliação tem vindo a assumir, nas últimas décadas, um papel central, extrapolando a sua importância para além do campo da educação (Afonso, 2010). O destaque atribuído à avaliação das escolas decorre de duas tendências que marcam a generalidade dos países europeus: a descentralização de meios e a definição de objetivos nacionais e de patamares de resultados escolares (Eurydice, 2011). Utilizando a análise político-económica da globalização na educação e fazendo também uma abordagem crítica às políticas de partilha (Takayama, 2013), pretendese analisar a mediação das pressões das políticas curriculares de homogeneização e estandardização dos resultados (Afonso, 2012; Santiago, Donaldson, Looney & Nusche, 2012) e a sua influência nos professores de Matemática. O presente estudo quantitativo envolve a realização de um inquérito por questionário aos professores do 1.º e 2.º ciclos de Matemática do Ensino Básico, onde se averigua de que forma o modelo de avaliação externa de escolas, implementado em Portugal desde 2006, tem colaborado para a elaboração de consequências concretas nos standards de avaliação, e na preponderância dos testes sumativos na disciplina de Matemática, considerando as mudanças curriculares e pedagógicas.

School health promotion and teacher professional identity

PURPOSE – Health and education are inextricably linked. Health promotion sits somewhat uncomfortably within schools, often remaining a marginal aspect of teachers’ work. The purpose of this paper is to examine the compatibility of an HP-initiative with teacher professional identity. DESIGN/METHODOLOGY/APPROACH – A qualitative research design was adopted consisting of semi-structured interviews. In total, 49 teachers in two school districts in the Auvergne region in central France were interviewed in depth post having completed three years’ involvement in a health promoting schools initiative called “Learning to Live Better Together” (“Apprendre a Mieux Vivre Ensemble”). FINDINGS – Teachers in the study had a broad conceptualisation of their role in health promotion. In keeping with international trends, there was more success at classroom than at whole school level. While generally teachers can be reluctant to engage with health promotion, the teachers in this study identified having little difficulty in understanding their professional identity as health promoters and identified strong compatibility with the HP-initiative. PRACTICAL IMPLICATIONS – Teachers generally viewed professional development in health promotion in a positive light when its underlying values were commensurate with their own and when the context was seen as compatible with the school mission. The promotion of health in schools needs to be sensitive to professional identity and be tailored specifically to blend more successfully with current teacher identity and practice. ORIGINALITY/VALUE – The promotion of health in schools needs to be sensitive to professional identity and be tailored specifically to blend more successfully with current teacher identity and practice.

Girls out of school. State, culture and education in poor rural Lao People's Democratic Republic

Tese de Doutoramento em Sociologia