Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

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.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

A framework to operate transformations between distinct models differing in modelling concepts

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

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.

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.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

Teaching mathematics using Massive Open Online Courses

Distance learning - where students take courses (attend classes, get activities and other sort of learning materials) while being physically separated from their instructors, for larger part of the course duration - is far from being a “new event”. Since the middle of the nineteenth century, this has been done through Radio, Mail and TV, taking advantage of the full educational potential that these media resources had to offer at the time. However, in recent times we have, at our complete disposal, the “magic wonder” of communication and globalization - the Internet. Taking advantage of a whole new set of educational opportunities, with a more or less unselfish “look” to economic interests, focusing its concern on a larger and collective “welfare”, contributing to the development of a more “equitable” world, with regard to educational opportunities, the Massive Open Online Courses (MOOCs) were born and have become an important feature of the higher education in recent years. Many people have been talking about MOOCs as a potential educational revolution, which has arrived from North America, still growing and spreading, referring to its benefits and/or disadvantages. The Polytechnic Institute of Porto, also known as IPP, is a Higher Education Portuguese institution providing undergraduate and graduate studies, which has a solid history of online education and innovation through the use of technology, and it has been particularly interested and focused on MOOC developments, based on an open educational policy in order to try to implement some differentiated learning strategies to its actual students and as a way to attract future ones. Therefore, in July 2014, IPP launched the first Math MOOC on its own platform. This paper describes the requirements, the resulting design and implementation of a mathematics MOOC, which was essentially addressed to three target populations: - pre-college students or individuals wishing to update their Math skills or that need to prepare for the National Exam of Mathematics; - Higher Education students who have not attended in High School, this subject, and who feel the need to acquire basic knowledge about some of the topics covered; - High School Teachers who may use these resources with their students allowing them to develop teaching methodologies like "Flipped Classroom” (available at http://www.opened.ipp.pt/). The MOOC was developed in partnership with several professors from several schools from IPP, gathering different math competences and backgrounds to create and put to work different activities such video lectures and quizzes. We will also try to briefly discuss the advertising strategy being developed to promote this MOOC, since it is not offered through a main MOOC portal, such as Coursera or Udacity.

A framework for efficient model transformations

The reported productivity gains while using models and model transformations to develop entire systems, after almost a decade of experience applying model-driven approaches for system development, are already undeniable benefits of this approach. However, the slowness of higher-level, rule based model transformation languages hinders the applicability of this approach to industrial scales. Lower-level, and efficient, languages can be used but productivity and easy maintenance seize to exist. The abstraction penalty problem is not new, it also exists for high-level, object oriented languages but everyone is using them now. Why is not everyone using rule based model transformation languages then? In this thesis, we propose a framework, comprised of a language and its respective environment, designed to tackle the most performance critical operation of high-level model transformation languages: the pattern matching. This framework shows that it is possible to mitigate the performance penalty while still using high-level model transformation languages.

Photochemical synthesis and functional transformations of bicyclic vinyl aziridines

Aziridines, a class of organic compounds containing a three membered heterocycle with a nitrogen atom, are extremely valuable molecules in organic and medicinal chemistry. They are frequently used as versatile precursors in the synthesis of natural products, and many biologically active molecules possess the aziridine moiety. The reactivity of aziridines has been studied, for example, in ring-opening reactions with thiols. However, not much interest seems to be given to reactions of aziridines in aqueous media, despite the numberless advantages of using water as solvent in organic chemistry. The nucleophilic ring-opening reaction of aziridines in aqueous media was here explored. Following the Kaplan aziridine synthetic methodology, in which pyridinium salts undergo a photochemical transformation to give bicyclic vinyl aziridines, new aziridines were synthetized. Their nucleophilic ring-opening reaction in water under physiological conditions was investigated and a range of sulphur, nitrogen, carbon and oxygen nucleophiles tested. Thiols, anilines and azide proved to be good nucleophiles to react with the aziridines, giving the ring-opening product in moderate to good yields. The best results were obtained with thiols, more specifically with cysteine-derived nucleophiles. Preliminary results show that these bicyclic vinyl aziridines can modify calcitonin, a peptide containing two cysteine amino acids residues, grating them the potential to be used in bioconjugation as ligands to cysteine-containing proteins, or even as enzyme inhibitors of, for example, cysteine proteases. Additionally, exploratory investigations suggest that the separation of both enantiomers of the bicyclic vinyl aziridine can be performed by taking advantage of an enzymatic methodology for the resolution of racemic secondary alcohols. Both enantiomers would be highly valuable as precursors in the synthesis of enantiomerically pure molecules, as no other method is currently reported for their separation.