Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Gold electrode modified by self-assembled monolayers of thiols to determine DNA sequences hybridization

The process of immobilization of biological molecules is one of the most important steps in the construction of a biosensor. In the case of DNA, the way it exposes its bases can result in electrochemical signals to acceptable levels. The use of self-assembled monolayer that allows a connection to the gold thiol group and DNA binding to an aldehydic ligand resulted in the possibility of determining DNA hybridization. Immobilized single strand of DNA (ssDNA) from calf thymus pre-formed from alkanethiol film was formed by incubating a solution of 2-aminoethanothiol (Cys) followed by glutaraldehyde (Glu). Cyclic voltammetry (CV) was used to characterize the self-assembled monolayer on the gold electrode and, also, to study the immobilization of ssDNA probe and hybridization with the complementary sequence (target ssDNA). The ssDNA probe presents a well-defined oxidation peak at +0.158 V. When the hybridization occurs, this peak disappears which confirms the efficacy of the annealing and the DNA double helix performing without the presence of electroactive indicators. The use of SAM resulted in a stable immobilization of the ssDNA probe, enabling the hybridization detection without labels. This study represents a promising approach for molecular biosensor with sensible and reproducible results.

Desenvolvendo o pensamento algébrico no 2.º ciclo do ensino básico: o sentido dos símbolos e da generalização

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º Ciclos do Ensino Básico

New quasi-orthogonal BCH-derived sequences for CDMA applications

European Transactions on Telecommunications, vol. 18

An overview of the higher level classification of Pucciniomycotina based on combined analyses of nuclear large and small subunit rDNA sequences

Mycologia, Vol. 98, nº6

XII Iberian-Italian Congress of Financial and Actuarial Mathematics

"The purpose of the XII Iberian-Italian Congress of Financial and Actuarial Mathematics is to provide a meeting point for researchers in Financial Economics from different countries and research backgrounds in universities, government or financial institutions. In fact, the Congress which is currently taking place in Lisbon has been organized to encourage communication and debate among the participants as well as to reinforce the bonds between us.The current edition of the Congress is characterized by the quality and diversity of the papers that have been submitted with special attention to the International Financial Crisis and measures of risk in different financial markets. However, as the Congress Program indicates, there are also parallel sessions about traditional topics in finance such as asset pricing, insurance, corporate finance, etc.Although this Congress has always been organized alternately between Spain and Italy, this year we have the great pleasure of celebrating it in Portugal which will be included as a permanent partner." [prefácio]

A stratigraphic framework for the Miocene from the lower Tagus Basin (Lisbon, Setúbal Península, Portugal) Depositional sequences, biostratigraphy and isotopic ages

Rev. Soc. Geol. España, 12(1), ano 1999

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

The impact of an online mathematics education project (MATACTIVA) on higher education students

The Online Mathematics Education Project (MatActiva) is an exciting new initiative which aims to support and enhance mathematics education. The project is led by the Institute of Accounting and Administration of Porto (ISCAP), part of the Polytechnic Institute of Porto (IPP). It provides innovative resources and carefully constructed materials around themes such as Elementary Mathematics, Calculus, Algebra, Statistics and Financial Mathematics to help support and inspire students and teachers of mathematics. The goal is to increase mathematical understanding, confidence and enjoyment, enrich the mathematical experience of each person, and promote creative and imaginative approaches to mathematics. Furthermore the project can be used to deliver engaging and effective mathematics instruction through the flipped classroom model. This paper also presents the findings of a large survey, whose propose was to study the student’s reaction to the project.

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

Rapid Evolution of the Sequences and Gene Repertoires

Proteins secreted to the extracellular environment or to the periphery of the cell envelope, the secretome, play essential roles in foraging, antagonistic and mutualistic interactions. We hypothesize that arms races, genetic conflicts and varying selective pressures should lead to the rapid change of sequences and gene repertoires of the secretome. The analysis of 42 bacterial pan-genomes shows that secreted, and especially extracellular proteins, are predominantly encoded in the accessory genome, i.e. among genes not ubiquitous within the clade. Genes encoding outer membrane proteins might engage more frequently in intra-chromosomal gene conversion because they are more often in multi-genic families. The gene sequences encoding the secretome evolve faster than the rest of the genome and in particular at non-synonymous positions. Cell wall proteins in Firmicutes evolve particularly fast when compared with outer membrane proteins of Proteobacteria. Virulence factors are over-represented in the secretome, notably in outer membrane proteins, but cell localization explains more of the variance in substitution rates and gene repertoires than sequence homology to known virulence factors. Accordingly, the repertoires and sequences of the genes encoding the secretome change fast in the clades of obligatory and facultative pathogens and also in the clades of mutualists and free-living bacteria. Our study shows that cell localization shapes genome evolution. In agreement with our hypothesis, the repertoires and the sequences of genes encoding secreted proteins evolve fast. The particularly rapid change of extracellular proteins suggests that these public goods are key players in bacterial adaptation.

FATAL GROUP A STREPTOCOCCAL TOXIC SHOCK-LIKE SYNDROME IN A CHILD WITH VARICELLA: REPORT OF THE FIRST WELL DOCUMENTED CASE WITH DETECTION OF THE GENETIC SEQUENCES THAT CODE FOR EXOTOXINS SPE A AND B, IN SÃO PAULO, BRAZIL

A previously healthy seven-year-old boy was admitted to the intensive care unit because of toxaemia associated with varicella. He rapidly developed shock and multisystem organ failure associated with the appearance of a deep-seated soft tissue infection and, despite aggressive treatment, died on hospital day 4. An M-non-typable, spe A and spe B positive Group A Streptococcus was cultured from a deep soft tissue aspirate. The criteria for defining Streptococcal toxic shock-like syndrome were fulfilled. The authors discuss the clinical and pathophysiological aspects of this disease as well as some unusual clinical findings related to this case.

Molecular analysis of the dengue virus type 1 and 2 in Brazil based on sequences of the genomic envelope-nonstructural protein 1 junction region

The genomic sequences of the Envelope-Non-Structural protein 1 junction region (E/NS1) of 84 DEN-1 and 22 DEN-2 isolates from Brazil were determined. Most of these strains were isolated in the period from 1995 to 2001 in endemic and regions of recent dengue transmission in São Paulo State. Sequence data for DEN-1 and DEN-2 utilized in phylogenetic and split decomposition analyses also include sequences deposited in GenBank from different regions of Brazil and of the world. Phylogenetic analyses were done using both maximum likelihood and Bayesian approaches. Results for both DEN-1 and DEN-2 data are ambiguous, and support for most tree bipartitions are generally poor, suggesting that E/NS1 region does not contain enough information for recovering phylogenetic relationships among DEN-1 and DEN-2 sequences used in this study. The network graph generated in the split decomposition analysis of DEN-1 does not show evidence of grouping sequences according to country, region and clades. While the network for DEN-2 also shows ambiguities among DEN-2 sequences, it suggests that Brazilian sequences may belong to distinct subtypes of genotype III.

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.