Cognitive models for the concept of angle

Tese de doutoramento em FilosofiaThe instructional models taught in class were similar to the students' models. The teachers addressed angle as a basic-level category, discussed its submodels, clarified the boundaries, and established cognitive reference points. They gradually increased the use of complex metaphors and of several models. The study enriched the characterization of the first two levels of van Hiele theory and demonstrated the value of categorization theory in understanding how our comprehension of mathematics is rooted in basic human attributes pertaining to the material and social conditions of human life. The embodiment of mathematical ideas by the material world, including our bodies, needs greater emphasis in all facets of mathematics education

Transcrição das notícias sobre matemática moderna publicadas nos jornais diários de Lisboa

UIDB/04647/2020 UIDP/04647/2020 PTDC/CED-EDG/32422/2017A Coleção História e Memória do Ensino da Matemática, apoiada pelo Grupo de Trabalho sobre História e Memória do Ensino da Matemática da Associação de Professores de Matemática, pretende divulgar trabalhos científicos sobre história do ensino da Matemática, difundindo perspetivas, metodologias e temas entre investigadores da área e divulgando junto de professores e do público em geral produções nesta área. Esse livro em específico contém a transcrição de artigos sobre matemática publicados em Portugal entre 1857 e 1872. Nele consta a proposta de cada um dos quatro volumes da série e um índice. Os artigos transcritos estão separados por seus anos, entre 1857 – 1872.publishersversionpublishe

A orquestração instrumental dos recursos tecnológicos no ensino da matemática

Atualmente, os recursos tecnológicos são uma componente dos manuais escolares a par do manual do professor ou do caderno de exercícios. Alguns dos conteúdos desses recursos, em particular, das plataformas digitais estão apresentados numa forma que facilita a sua aplicação em aula mesmo por professores que não possuam muitos conhecimentos em tecnologias de informação e comunicação. Especialmente a existência de apliquetas construídas em programas de geometria dinâmica ou em programas em flash ou mesmo as questões de escolha múltipla envolvendo a verificação e avaliação de conhecimentos. Uma equipa de investigadores da Universidade Nova de Lisboa tem vindo a desenvolver um trabalho desde 2009 em que dois dos objetivos são identificar as orquestrações instrumentais que os professores utilizam quando trabalham com os recursos tecnológicos e identificar os tipos de interação entre os professores e as tarefas com recursos tecnológicos.publishersversionpublishe

Aprendizagem da matemática com recurso a materiais tecnológicos

Esta comunicação está inserida no desenvolvimento de um projecto de investigação que procura compreender a forma como os professores de matemática podem integrar o uso de materiais tecnológicos em benefício da aprendizagem dos alunos. O projecto centra-se essencialmente nos materiais electrónicos que acompanham os manuais escolares, CD-Roms, eBooks, portais, filmes e conjuntos de outras actividades que apelam ao uso do computador. Procura-se compreender o papel que estes materiais desempenham no processo de ensino aprendizagem, nomeadamente na forma como os professores se apropriam desses materiais e o uso que fazem dos mesmos na sala de aula. Procurar-se-á apresentar nesta comunicação um breve enquadramento teórico do tema em estudo indicando as principais opções assumidas pelos autores.publishersversionpublishe

Monitorização de uma abordagem tecnológica em matemática - a Academia de khan em Portugal

Este trabalho é apoiado por fundos públicos portugueses através da Fundação para a Ciência e a Tecnologia, Projeto UID/CED/02861/2016.Este texto apresenta um plano de monitorização do projeto de implementação da Plataforma da Academia de Khan em salas de aula de matemática do 1º ao 9º ano em Portugal. Com base numa parceria entre a EDUCOM, a Portugal Telecom e o Ministério da Educação português, está em curso um projeto que envolve a formação de professores na utilização da plataforma e a sua implementação com alunos de cinco escolas nos arredores de Lisboa. Apresentamos aqui os pressupostos teóricos e metodológicos subjacentes a esta monitorização, com o objectivo de caracterizar a formação dos professores envolvidos, a aprendizagem dos alunos e o papel desempenhado pela plataforma no processo de ensino e aprendizagem da matemática.publishersversionpublishe

Geography and ecology shape the phylogenetic composition of Amazonian tree communities

Aim: Amazonia hosts more tree species from numerous evolutionary lineages, both young and ancient, than any other biogeographic region. Previous studies have shown that tree lineages colonized multiple edaphic environments and dispersed widely across Amazonia, leading to a hypothesis, which we test, that lineages should not be strongly associated with either geographic regions or edaphic forest types. Location: Amazonia. Taxon: Angiosperms (Magnoliids; Monocots; Eudicots). Methods: Data for the abundance of 5082 tree species in 1989 plots were combined with a mega-phylogeny. We applied evolutionary ordination to assess how phylogenetic composition varies across Amazonia. We used variation partitioning and Moran\u27s eigenvector maps (MEM) to test and quantify the separate and joint contributions of spatial and environmental variables to explain the phylogenetic composition of plots. We tested the indicator value of lineages for geographic regions and edaphic forest types and mapped associations onto the phylogeny. Results: In the terra firme and várzea forest types, the phylogenetic composition varies by geographic region, but the igapó and white-sand forest types retain a unique evolutionary signature regardless of region. Overall, we find that soil chemistry, climate and topography explain 24% of the variation in phylogenetic composition, with 79% of that variation being spatially structured (R$^{2}$ = 19% overall for combined spatial/environmental effects). The phylogenetic composition also shows substantial spatial patterns not related to the environmental variables we quantified (R$^{2}$ = 28%). A greater number of lineages were significant indicators of geographic regions than forest types. Main Conclusion: Numerous tree lineages, including some ancient ones (>66 Ma), show strong associations with geographic regions and edaphic forest types of Amazonia. This shows that specialization in specific edaphic environments has played a long-standing role in the evolutionary assembly of Amazonian forests. Furthermore, many lineages, even those that have dispersed across Amazonia, dominate within a specific region, likely because of phylogenetically conserved niches for environmental conditions that are prevalent within regions

Geographic patterns of tree dispersal modes in Amazonia and their ecological correlates

Aim: To investigate the geographic patterns and ecological correlates in the geographic distribution of the most common tree dispersal modes in Amazonia (endozoochory, synzoochory, anemochory and hydrochory). We examined if the proportional abundance of these dispersal modes could be explained by the availability of dispersal agents (disperser-availability hypothesis) and/or the availability of resources for constructing zoochorous fruits (resource-availability hypothesis). Time period: Tree-inventory plots established between 1934 and 2019. Major taxa studied: Trees with a diameter at breast height (DBH) ≥ 9.55 cm. Location: Amazonia, here defined as the lowland rain forests of the Amazon River basin and the Guiana Shield. Methods: We assigned dispersal modes to a total of 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests. We investigated geographic patterns in the proportional abundance of dispersal modes. We performed an abundance-weighted mean pairwise distance (MPD) test and fit generalized linear models (GLMs) to explain the geographic distribution of dispersal modes. Results: Anemochory was significantly, positively associated with mean annual wind speed, and hydrochory was significantly higher in flooded forests. Dispersal modes did not consistently show significant associations with the availability of resources for constructing zoochorous fruits. A lower dissimilarity in dispersal modes, resulting from a higher dominance of endozoochory, occurred in terra-firme forests (excluding podzols) compared to flooded forests. Main conclusions: The disperser-availability hypothesis was well supported for abiotic dispersal modes (anemochory and hydrochory). The availability of resources for constructing zoochorous fruits seems an unlikely explanation for the distribution of dispersal modes in Amazonia. The association between frugivores and the proportional abundance of zoochory requires further research, as tree recruitment not only depends on dispersal vectors but also on conditions that favour or limit seedling recruitment across forest types

Geography and ecology shape the phylogenetic composition of Amazonian tree communities

AimAmazonia hosts more tree species from numerous evolutionary lineages, both young and ancient, than any other biogeographic region. Previous studies have shown that tree lineages colonized multiple edaphic environments and dispersed widely across Amazonia, leading to a hypothesis, which we test, that lineages should not be strongly associated with either geographic regions or edaphic forest types.LocationAmazonia.TaxonAngiosperms (Magnoliids; Monocots; Eudicots).MethodsData for the abundance of 5082 tree species in 1989 plots were combined with a mega-phylogeny. We applied evolutionary ordination to assess how phylogenetic composition varies across Amazonia. We used variation partitioning and Moran's eigenvector maps (MEM) to test and quantify the separate and joint contributions of spatial and environmental variables to explain the phylogenetic composition of plots. We tested the indicator value of lineages for geographic regions and edaphic forest types and mapped associations onto the phylogeny.ResultsIn the terra firme and várzea forest types, the phylogenetic composition varies by geographic region, but the igapó and white-sand forest types retain a unique evolutionary signature regardless of region. Overall, we find that soil chemistry, climate and topography explain 24% of the variation in phylogenetic composition, with 79% of that variation being spatially structured (R2 = 19% overall for combined spatial/environmental effects). The phylogenetic composition also shows substantial spatial patterns not related to the environmental variables we quantified (R2 = 28%). A greater number of lineages were significant indicators of geographic regions than forest types.Main ConclusionNumerous tree lineages, including some ancient ones (>66 Ma), show strong associations with geographic regions and edaphic forest types of Amazonia. This shows that specialization in specific edaphic environments has played a long-standing role in the evolutionary assembly of Amazonian forests. Furthermore, many lineages, even those that have dispersed across Amazonia, dominate within a specific region, likely because of phylogenetically conserved niches for environmental conditions that are prevalent within regions

Mapping density, diversity and species-richness of the Amazon tree flora

Using 2.046 botanically-inventoried tree plots across the largest tropical forest on Earth, we mapped tree species-diversity and tree species-richness at 0.1-degree resolution, and investigated drivers for diversity and richness. Using only location, stratified by forest type, as predictor, our spatial model, to the best of our knowledge, provides the most accurate map of tree diversity in Amazonia to date, explaining approximately 70% of the tree diversity and species-richness. Large soil-forest combinations determine a significant percentage of the variation in tree species-richness and tree alpha-diversity in Amazonian forest-plots. We suggest that the size and fragmentation of these systems drive their large-scale diversity patterns and hence local diversity. A model not using location but cumulative water deficit, tree density, and temperature seasonality explains 47% of the tree species-richness in the terra-firme forest in Amazonia. Over large areas across Amazonia, residuals of this relationship are small and poorly spatially structured, suggesting that much of the residual variation may be local. The Guyana Shield area has consistently negative residuals, showing that this area has lower tree species-richness than expected by our models. We provide extensive plot meta-data, including tree density, tree alpha-diversity and tree species-richness results and gridded maps at 0.1-degree resolution