Luís Descalço

On Automatic Rees Matrix Semigroups

Abstract We consider a Rees matrix semigroup S = M[U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that pU 1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.

SUBSEMIGROUPS OF THE BICYCLIC MONOID

In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determine the regular, simple and bisimple subsemigroups of B. Finally we describe algorithms for obtaining the parameters from the generating set.

Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

We study generalized Greens equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B.

Ensino personalizado: o MOODLE como ferramenta na busca da Aprendizagem Significativa

A educacao personalizada so e possivel apos a identificacao das dificuldades dos alunos que os impedem de terem os subsuncores necessarios para captarem e aprenderem os conteudos que lhes sao ministrados. Com o uso das Tecnologias de Informacao e Comunicacao (TICs) e dos Ambientes Virtuais de Aprendizagem (AVAs), nesse artigo o MOODLE, sao identificados os pontos fortes e fracos de cada aluno, relacionados nesse caso a disciplina de Lingua Portuguesa do 6o ano do Ensino Fundamental. Apos essa identificacao, sao indicados conteudos personalizados visando sanar as possiveis dificuldades de cada individuo. Constatou-se que atraves da indicacao de Objetos de Aprendizagem (OAs) que levem em consideracao o ritmo e a base de conhecimento individual, pode-se obter melhores resultados para a aprendizagem. Isso ocorre pois o aluno consegue ancorar os novos conteudos a partir dos seus proprios subsuncores atingindo-se assim a almejada Aprendizagem Significativa.

LEARNING TRAJECTORIES WITH BAYESIAN STUDENT MODEL FOR AUTONOMOUS STUDY IN FLIPPED LEARNING

As a complementary tool for learning Calculus, we have been using SIACUA, a computer system designed to help autonomous learning, which is based on the use of parameterized questions with detailed solutions, also parameterized, with a Bayesian user model for feedback. This system has proven to be effective in keeping the students working during the classes’ period, as the recent data usage we present in this article shows. A difficulty in flipped learning is to guarantee that students study before the classes. We address this issue by trying to provide the best possible conditions for this autonomous work to occur. Hence, we propose an expansion of SIACUA, by combining it with the model MOTRAC, a model for creating learning objects and learning trajectories for meaningful learning, based on Meaningful Learning Theory and Cognitive Load Theory, to achieve good guidance, together with the already existing Bayesian feedback, in a flipped learning set, with active learning occurring in the classes. In the proposed learning set we also use an assessment computer system: PmatE. System PmatE is being used from 1989, mainly in the yearly science competitions, that nowadays join in our University, in the three days of the competitions, about ten thousand students, from all ages, from basic to secondary schools. To achieve some extrinsic motivation, and to further guarantee the students study before the classes, we use system PmatE, which imports contents from SIACUA, for assessment in the end of each class. Past experiences show two main advantages of using two completely different computer systems, one for learning and another one for assessment are: (i) students are more motivated to use the learning system because they know its contents or similar are going to be used for assessment; (ii) students are not afraid of answering questions in the learning system because they know that the diagnosis on this system is not going to be used for assessment and so it is a useful and safe feedback.

Using parameterized calculus questions for learning and assessment

We have implemented a Web application reusing questions from two computer systems, true/false questions from PmatE (Projeto Matemática Ensino) and multiple choice questions from Megua (Mathematics Exercise Generator, University of Aveiro). Our application implements a Bayesian user model for diagnosing student knowledge in the topics covered. In this article we propose the use of this system for both learning and assessment in a calculus course, encouraging the students to work during the semester without increasing the work load for teachers.