Preparação das discussões matemáticas no ensino da Álgebra: o caso da professora Ana

As discussões matemáticas podem ser uma atividade importante para promover a aprendizagem dos alunos, criando oportunidades para a partilha, justificação e argumentação de ideias matemáticas resultantes do seu trabalho com tarefas. No entanto, a sua realização constitui um desafio exigente para o professor, tanto na sua preparação como na sua condução tendo em vista a aprendizagem dos alunos. Nesta comunicação, procuramos compreender as práticas de discussão de Ana, professora do 3.º ciclo do Ensino Básico (EB), na preparação da discussão coletiva no trabalho com a Álgebra, em articulação com o seu conhecimento didático. Os resultados mostram que a professora, apoiada no seu conhecimento da Matemática, da prática letiva e dos alunos e da aprendizagem, identifica (antes e durante a aula) as ideias matemáticas que pretende que os alunos discutam a partir do seu trabalho com tarefas selecionadas para o efeito. Antecipa, também, possíveis estratégias de resolução e pensa como pode levar os alunos atingir os objetivos definidos. Na aula, e perante o trabalho dos alunos, reconhece as ideias mais importantes para discutir e estabelece uma ordem de apresentação tendo em vista promover a generalização dessas ideias

Path Integral Approach to Strongly Nonlinear Composite

We study strongly nonlinear disordered media using a functional method. We solve exactly the problem of a nonlinear impurity in a linear host and we obtain a Bruggeman-like formula for the effective nonlinear susceptibility. This formula reduces to the usual Bruggeman effective medium approximation in the linear case and has the following features: (i) It reproduces the weak contrast expansion to the second order and (ii) the effective medium exponent near the percolation threshold are $s=1$, $t=1+\kappa$, where $\kappa$ is the nonlinearity exponent. Finally, we give analytical expressions for previously numerically calculated quantities.Comment: 4 pages, 1 figure, to appear in Phys. Rev.

Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a new conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide new examples of realizable two-point correlation functions and suggest a set of analytical basis functions. Moreover, we devise an efficient and isotropy- preserving construction algorithm, namely, the Lattice-Point algorithm to generate realizations of materials from their two- point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions.Comment: 37 pages, 26 figure

Detecção de Cucumber mosaic virus em alface no estado do Pará.

A alface (Lactuca sativa L.) é uma planta anual, originária de clima temperado, pertencente à família Asteracea, e certamente uma das hortaliças mais populares e consumidas no Brasil e no mundo. Diversas viroses podem causar danos à cultura da alface. O objetivo deste trabalho foi detectar a presença do Cucumber mosaic virus (CMV) na cultura da alface, utilizando o teste RT-PCR. Foram coletadas 50 amostras de alface aparentemente sem sintomas característicos de viroses no município de Ananindeua-PA e na horta da UFRA campus Belém-PA. O ácido nucléico total foi extraído a partir de folhas de alface. Para a detecção do CMV por meio do RT-PCR utilizou-se um par de iniciadores denominados CMV-CPR e CMV-CPF que permitem a amplificação do fragmento de cerca de 700 pb do DNA do gene da capa proteica. O CMV foi detectado em três amostras analisadas. Este foi o primeiro relato de CMV em alface no estado do Pará

Integration of Dirac-Jacobi structures

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.Comment: 10 pages. Brief changes in the introduction. References update

Probabilistic models of information retrieval based on measuring the divergence from randomness

We introduce and create a framework for deriving probabilistic models of Information Retrieval. The models are nonparametric models of IR obtained in the language model approach. We derive term-weighting models by measuring the divergence of the actual term distribution from that obtained under a random process. Among the random processes we study the binomial distribution and Bose--Einstein statistics. We define two types of term frequency normalization for tuning term weights in the document--query matching process. The first normalization assumes that documents have the same length and measures the information gain with the observed term once it has been accepted as a good descriptor of the observed document. The second normalization is related to the document length and to other statistics. These two normalization methods are applied to the basic models in succession to obtain weighting formulae. Results show that our framework produces different nonparametric models forming baseline alternatives to the standard tf-idf model

Intraepidermal Epidermotropic Metastatic Melanoma: a Clinical and Histopathological Mimicker of Melanoma in Situ Occurring in Multiplicity

The distinction between primary melanoma and melanoma metastatic to the skin has major prognostic implications. We report a case of a 67-year-old male with a diagnosis of a superficial spreading melanoma (stage IB) rendered 6 years earlier who presented clinically with an atypical nevus on his left thigh. Histopathological examination showed an intraepidermal melanocytic proliferation that was interpreted as melanoma in situ. Subsequently, 45 additional pigmented macules appeared in crops over a 9-month period. Clinically and dermoscopically, these lesions were extremely polymorphic. Histopathological findings were compatible with melanoma in situ, as each lesion consisted of a wholly intraepidermal proliferation of markedly atypical melanocytes arranged singly and in nests. A complete gastrointestinal study showed multiple pigmented metastatic lesions throughout the stomach and small bowel, which supported a diagnosis of metastatic melanoma with gastrointestinal and epidermotropic skin involvement. Monosomy of chromosome 9 and a BRAF V600E mutation were detected in the primary tumor sample and in macro-dissected secondary lesions. No CDKN2A or CDK4 germline mutations were found. Intraepidermal epidermotropic metastases of melanoma have been rarely described in literature. In this case, histopathology alone was insufficient to distinguish metastatic melanoma from multiple in situ melanomas. The recognition of epidermotropic metastases should be based on the correlation between clinical, dermoscopic, histopathological and molecular findings

Teachers’ development of professional knowledge through action research and the facilitation of this by teacher educators

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