The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.

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

Statmedia 3 : activitats on-line individualitzades d'estadística i matemàtiques als ensenyaments de Ciències Experimentals i Socials

El projecte Statmedia 3 ha consolidat definitivament la proposta de les assignatures Bioestadística de Biologia, Anàlisi de dades de Ciències Ambientals i d’Estadística Matemàtica de la Diplomatura renovant una part del material creat amb Statmedia 2. S’han inclòs a més Matemàtiques d’Ambientals i Introducció a la Probabilitat del Grau d’Estadística. L’anterior MQD abastava només pràctiques mentre que aquest projecte permet una oferta diversa d’activitats individualitzades. La individualització consisteix en que cada estudiant rep una proposta de cas personalitzada amb dades diferents. Les activitats poden ser programades presencialment o no, però la clau de l’èxit de l’activitat és que l’alumne obtingui reconeixement del seu treball en l’avaluació continuada. La valoració que fan als alumnes de Statmedia és molt bo, i observem que es produeix una millora en els resultats acadèmics. Statmedia 3 ha implicat un important esforç en la vessant informàtica del projecte, la barreja de tecnologies que utilitzem son punteres: Ajax, servlets i applets Java... Hem posat a punt un assistent on-line per dissenyar documents i planificar activitats que facilita la tasca dels professors. La nostre participació en primera línea del procés de convergència a l’EEES ens ha permès anticipar alguns canvis, i s’ha traduït en que el claustre del Departament d’Estadística assumís que Statmedia és una metodologia essencial dels seus plans docents. El projecte continua en un quart projecte MQD consecutiu, on desplegarem la nova tecnologia implementada. L’objectiu principal serà dotar a les assignatures dels 7 graus on participa el departament d’activitats individualitzades en forma de casos pràctics, problemes i proves diverses. La col·lecció de material emmagatzemada en la nostra biblioteca, forjada després de quasi deu anys de treball continuat, juntament amb l’experiència acumulada de com utilitzar Statmedia de la forma més eficient han començat a ser explotades en els nous graus aquest mateix curs 2009-2010.

O processo de construção de objetos de aprendizagem em cálculo diferencial e integral durante uma atividade de design

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O estágio supervisionado: uma influência na constituição dos saberes e do professor de matemática na formação inicial

Este estudo teve por objetivo principal investigar o Estágio Supervisionado do Curso de Licenciatura em Matemática da UFPa, cuja hipótese se baseou na ideia de que o estágio supervisionado quando ocorre de maneira colaborativa, proporciona significados positivos aos sujeitos que se constituem professores. Metodologicamente, esta pesquisa se caracteriza por ser de abordagem qualitativa, e que tem como foco de observação, as atividades curriculares correspondentes ao Estágio Supervisionado e os elementos formativos que emergem da parceria professor escolar e estagiário no decorrer dessas atividades. O estudo envolveu três alunos do curso de Licenciatura em Matemática da referida Universidade, especificamente do Campus de Marabá (CAMAR), durante as atividades de estágio. O material para análise foi coletado por meio de entrevistas semi-estruturadas e de relatórios de estágio resultantes das ações realizadas durante o estágio no Campus de Marabá (CAMAR) e nas escolas da rede pública de ensino. O estudo enfatizou os elementos formativos que emergem das atividades de estágio, especialmente, da relação colaborativa entre professor escolar e estagiário, os quais podem contribuir com a formação inicial e com o desenvolvimento profissional do sujeito que está se constituindo professor, tendo em vista a formação de um professor de matemática diferenciado. Os resultados da pesquisa mostraram que o estágio quando bem direcionado e quando os professores escolares são colaborativos nas ações pedagógicas dos estagiários no contexto escolar, reforça ou faz emergir nos estagiários o desejo de assumir a profissão professor, com práticas pedagógicas diferenciadas.

Luz, câmera, flashes: uma compreensão sobre a disciplina de prática de ensino de matemática a distância

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A geometria euclidiana na licenciatura em matemática do ponto de vista de professores formadores

Pós-graduação em Educação Matemática - IGCE

Futuros Matemáticos e suas concepções sobre o conhecimento matemático e seu ensino

Taking referential theoretical conceptions of mathematical knowledge present in some of the main mathematics philosophical currents and considering that the teacher´s practice is influenced by his conception of mathematical knowledge, this research aims to understand the conceptions of mathematical knowledge and its teaching and learning teaching of future mathematicians. It follows a qualitative approach (case study) in which the data were collected by semi-structured interviews and document analysis. This investigation has pointed out that Mathematics together with Mathematics Teaching (or part of this: on the didactic and pedagogical knowledge of how to teach) could be important to formation of the future mathematician, who will probably teach in a college or university.

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

Why Mathematics is essential in Biomedical Sciences degree?

Improvement of mathematical education and motivation of students in the mathematics" area is needed. What can be done? We introduce some ideas to generate the student"s interest for mathematics, because they often present difficulties in appreciating the relevance of mathematics and its role in the health sciences. We consider that a cornerstone in the strategy to attract the students" interest is linking the mathematics with real biomedical situations. We proceed in the following manner: We first present a real biomedical situation to produce interest and to generate curiosity. Second, we ask thought-provoking questions to students as: Which is the biomedical problem presented? Which is my knowledge on this situation? What could I do to solve this biomedical situation? Do I need some new mathematical concepts and procedures? Thereupon, the teacher explains the mathematical concepts necessary to solve the case presented, providing definitions, properties and tools for graphical display and/or mathematical calculations. In this learning methodology, ICTs were cornerstones for reaching the proposed competences. Furthermore, ICTs can also be used in the evaluative task in its two possible aspects: formative and for obtaining a qualification. Comments from students about this new mathematics teaching method indicate that the use of real biomedical case studies kept the lessons in mathematics interesting.

How to teach mathematics with MOODLE

The aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.

Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.