Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

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

In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Numerical Uncertainty and Its Implications

Copyright © 2014 António F. Rodrigues, Nuno O. Martins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property António F. Rodrigues, Nuno O. Martins. All Copyright © 2014 are guarded by law and by SCIRP as a guardian.

A relação entre a álgebra acadêmica e a álgebra escolar em um curso de licenciatura em matemática: concepções de alunos e professores

Pós-graduação em Educação - FCT

O pensamento algébrico e a descoberta de padrões na formação de professores

Este texto incide sobre o tema do pensamento algébrico nos primeiros anos de escolaridade ao nível da formação contínua de professores. Na abordagem apresentada o tema dos padrões surge como contexto estruturante para o desenvolvimento do pensamento algébrico. Começa-se por fazer um enquadramento dos referenciais teóricos que fundamentam a adoção de uma proposta didática desenvolvida nesse âmbito, recorrendo em seguida a um estudo empírico que foi desenvolvido, do qual se relata aqui uma parte centrada nas práticas de sala de aula de uma professora do primeiro ciclo em formação, de modo a poder confirmar a eficácia da proposta no ensino e desenvolvimento do pensamento algébrico dos alunos. Os resultados permitem concluir que a professora interiorizou e projetou na sua prática os aspetos essenciais que conduziram ao desenvolvimento do pensamento algébrico nos alunos. O texto termina com algumas conclusões e implicações para a formação de professores.

Fibras óticas de plástico em redes de acesso

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Eletrónica e Telecomunicações

Auditoria energética à indústria têxtil do Ave

A Indústria Têxtil do Ave S.A. (ITA) dedica-se, desde 1948, à produção de componentes têxteis para pneus em forma de fio torcido (corda) e tela. Estes componentes são quimicamente activados e impregnados em estufas, possibilitando assim a posterior adesão ao pneu. A máquina de impregnar corda Single End é composta pelos grupos de estiragem, por um recipiente contendo a solução química e por 4 estufas em série. A máquina de impregnar tela Zell é composta pelos grupos de estiragem, pelos acumuladores de saída e entrada, pelos recipientes com as soluções químicas e por um grupo de 7 estufas em série. O aquecimento das estufas é feito através da queima de gás natural. O presente trabalho teve como objectivo a realização de uma auditoria energética à ITA com um especial destaque às máquinas de impregnar corda (Single End) e tela (Zell). As correntes de entrada que contribuem para a potência térmica de impregnação são a combustão do gás natural, o ar de combustão, o ar fresco, o artigo em verde e as soluções químicas. As correntes de saída correspondem aos gases de combustão e exaustão, ao artigo impregnado e às perdas térmicas. A auditoria à máquina Single End mostrou que a potência térmica de impregnação é de 413,1 kW. Dessa potência térmica, 77,2% correspondem à combustão do gás natural, 6,7% ao ar de combustão, 15% ao ar fresco, 0,7% às cordas em verde e 0,4% à solução química. Da potência térmica de saída, 88,4% correspondem aos gases de combustão e exaustão, 3,2% às cordas impregnadas e 8,4% às perdas térmicas. Da auditoria à máquina Zell observou-se que a potência térmica de impregnação é de 5630,7 kW. Dessa potência, 73,3% corresponde à combustão do gás natural, 1,6% ao ar de combustão, 24,5% ao ar fresco, 0,3% à tela em verde e 0,3% às soluções químicas. Da potência térmica de saída, 65,2% correspondem aos gases de combustão e exaustão, 3,1% à tela impregnada e 31,7% às perdas térmicas. Foram sugeridas como medidas de optimização a redução dos caudais de exaustão das estufas e o aumento de temperatura do ar fresco. O aumento da temperatura do ar fresco da máquina de impregnar Single End para 50 ºC, usando ar quente dos torcedores, leva a uma poupança de 0,22 €/h, com um período de retorno do investimento de 13 anos e 4 meses enquanto o aumento para 120 ºC, usando o calor dos gases de combustão e exaustão, reduz os custos em 0,88 €/h, sendo o período de retorno para esse investimento de 2 anos e 6 meses. Na máquina de impregnar Zell, uma redução de 15% no caudal de exaustão numa das estufas leva a ganhos de 3,43 €/h. O aumento de temperatura do ar fresco para 45 ºC, usando o calor de gases de combustão e exaustão, leva a uma poupança de 9,93 €/h sendo o período de retorno para cada uma das duas sugestões de investimento de 5 meses e 9 meses.

Helical Twisting of Electrospun Liquid Crystalline Cellulose Micro- and Nanofibers

Helically twisted fibers can be produced by electrospinning liquid-crystalline cellulose solutions. Fiber topographies are studied by atomic force microscopy, scanning electron microscopy (see figure) and polarized optical microscopy. The fibers have a nearly universal pitch-to-diameter ratio and comprise both right- and left-handed helices.

Modeling for control design of a multi-reach water canal

This article addresses the problem of obtaining reduced complexity models of multi-reach water delivery canals that are suitable for robust and linear parameter varying (LPV) control design. In the first stage, by applying a method known from the literature, a finite dimensional rational transfer function of a priori defined order is obtained for each canal reach by linearizing the Saint-Venant equations. Then, by using block diagrams algebra, these different models are combined with linearized gate models in order to obtain the overall canal model. In what concerns the control design objectives, this approach has the advantages of providing a model with prescribed order and to quantify the high frequency uncertainty due to model approximation. A case study with a 3-reach canal is presented, and the resulting model is compared with experimental data. © 2014 IEEE.

Modeling for control design of a multi-reach water canal

This article addresses the problem of obtaining reduced complexity models of multi-reach water delivery canals that are suitable for robust and linear parameter varying (LPV) control design. In the first stage, by applying a method known from the literature, a finite dimensional rational transfer function of a priori defined order is obtained for each canal reach by linearizing the Saint-Venant equations. Then, by using block diagrams algebra, these different models are combined with linearized gate models in order to obtain the overall canal model. In what concerns the control design objectives, this approach has the advantages of providing a model with prescribed order and to quantify the high frequency uncertainty due to model approximation. A case study with a 3-reach canal is presented, and the resulting model is compared with experimental data. © 2014 IEEE.

Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid