Explorar e Investigar em Matemática: Uma Actividade Fundamental no Ensino e na Aprendizagem

Investigar, ensinar e aprender são actividades que podem estar presentes, de forma articulada, no ensino-aprendizagem da Matemática e na actividade profissional do professor. Para isso, é necessário conceber tarefas que possam ser o ponto de partida para investigações e explorações matemáticas dos alunos e discutir o modo como podem ser trabalhadas na sala de aula. Recorrendo a exemplos de actividades realizadas por professores de Matemática portugueses, analiso a actividade de aprendizagem suscitada por tarefas deste tipo e discuto as respectivas potencialidades. Finalmente, refiro as condições respeitantes à cultura profissional dos professores que podem favorecer uma actividade de investigação sobre a sua própria profissional, com relevo para a colaboração e a dimensão associativa.Researching, teaching and learning are activities that may be present, in coordination, teaching and learning of mathematics in the work of the teacher. Therefore, it is necessary to design tasks that may be the starting point for mathematical investigations and explorations of the students and discuss how they can be worked in the classroom. Drawing on examples of activities carried out by Portuguese teachers of mathematics by examining the activity of learning raised by such tasks and discuss their potencial. Finally, I refer to conditions relating to the professional culture of teachers who can promote the research activity on their own training, with an emphasis on collaboration and associative dimension

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

Refined histopathological predictors of BRCA1 and BRCA2 mutation status: A large-scale analysis of breast cancer characteristics from the BCAC, CIMBA, and ENIGMA consortia

Introduction: The distribution of histopathological features of invasive breast tumors in BRCA1 or BRCA2 germline mutation carriers differs from that of individuals with no known mutation. Histopathological features thus have utility for mutation prediction, including statistical modeling to assess pathogenicity of BRCA1 or BRCA2 variants of uncertain clinical significance. We analyzed large pathology datasets accrued by the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA) and the Breast Cancer Association Consortium (BCAC) to reassess histopathological predictors of BRCA1 and BRCA2 mutation status, and provide robust likelihood ratio (LR) estimates for statistical modeling. Methods: Selection criteria for study/center inclusion were estrogen receptor (ER) status or grade data available for invasive breast cancer diagnosed younger than 70 years. The dataset included 4,477 BRCA1 mutation carriers, 2,565 BRCA2 mutation carriers, and 47,565 BCAC breast cancer cases. Country-stratified estimates of the

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as

Assessing associations between the AURKAHMMR-TPX2-TUBG1 functional module and breast cancer risk in BRCA1/2 mutation carriers

While interplay between BRCA1 and AURKA-RHAMM-TPX2-TUBG1 regulates mammary epithelial polarization, common genetic variation in HMMR (gene product RHAMM) may be associated with risk of breast cancer in BRCA1 mutation carriers. Following on these observations, we further assessed the link between the AURKA-HMMR-TPX2-TUBG1 functional module and risk of breast cancer in BRCA1 or BRCA2 mutation carriers. Forty-one single nucleotide polymorphisms (SNPs) were genotyped in 15,252 BRCA1 and 8,211 BRCA2 mutation carriers and subsequently analyzed using a retrospective likelihood appr

Genome-Wide Association Study in BRCA1 Mutation Carriers Identifies Novel Loci Associated with Breast and Ovarian Cancer Risk

BRCA1-associated breast and ovarian cancer risks can be modified by common genetic variants. To identify further cancer risk-modifying loci, we performed a multi-stage GWAS of 11,705 BRCA1 carriers (of whom 5,920 were diagnosed with breast and 1,839 were diagnosed with ovarian cancer), with a further replication in an additional sample of 2,646 BRCA1 carriers. We identified a novel breast cancer risk modifier locus at 1q32 for BRCA1 carriers (rs2290854, P = 2.7×10-8, HR = 1.14, 95% CI: 1.09-1.20). In addition, we identified two novel ovarian cancer risk modifier loci: 17q21.31 (rs17631303, P = 1.4×10-8, HR = 1.27, 95% CI: 1.17-1.38) and 4q32.3 (rs4691139, P = 3.4×10-8, HR = 1.20, 95% CI: 1.17-1.38). The 4q32.3 locus was not associated with ovarian cancer risk in the general population or BRCA2 carriers, suggesting a BRCA1-specific associat

The polarized image of a synchrotron-emitting ring of gas orbiting a black hole

High Energy Astrophysic