37 research outputs found
Sobre o ensino superior da matemática : a geometria e os professores do 1.º ciclo : "novos desafios, velhas deficiências"
Existe, na sociedade actual, um consenso generalizado a respeito
da importância da formação (científica e pedagógica) dos professores de
Matemática. No entanto este sentimento não tem sido, em Portugal, devidamente
monotorizado nem no caso da formação científica nem no caso dos
professores do 1.º ciclo.
Apresentamos, neste artigo, um estudo que i) analisa os desafios que,
na área da Matemática e de acordo com as directivas oficiais, se colocam aos
professores do 1.º ciclo; ii) regista a formação matemática oferecida, em Portugal,
a estes profissionais e iii) avalia as competências matemáticas de um grupo de
professores e futuros professores quando nos centramos no caso dos conceitos
geométricos elementares.
Defendemos, como resultado da investigação, a necessidade urgente de se
olhar para o conteúdo matemático como verdadeiro núcleo fundamental de qualquer
programa de formação de professores do 1.º ciclo.Different vectors of the society worldwide agree on the importance
of the training (both scientifically and pedagogically) given to Mathematics
teachers.
However this belief has not been, in Portugal, followed by research on the
implementation of correspondent means neither in the case of the scientific
training of the teachers nor in the case of primary school teachers.
In this article we are presenting i) an analysis of the actual official directives
posed to these professionals; ii) some facts about the actual mathematical
training offered by the national Institutions (both Universities and Polytechnics) and finally iii) the evaluation of mathematical competencies
of a group formed by teachers and future teachers, in the case of elementary
geometrical concepts.
As a result we defend that the scientific training offered actually to these
professionals must be urgently reviewed in order to become the nucleus of
any training program to primary school teachers.Fundação para a Ciência e a Tecnologia (FCT)
Aventuras numéricas no cálculo do e
Faz-se uma análise dos erros de arredondamento no cálculo de aproximações do número de Neper com a expressão (1+1/n)^n.Fundação para a Ciência e a Tecnologi
Study on the fundamental concept of “measure” and its history
This paper exhibits a small part of a PhD degree project on the theme: “The fundamental concept of Measure: epistemological and pedagogical aspects related with the first six years of schooling”.
It aims at presenting the analyzis of the fundamental concept of measure at the so called elementary levels of schooling, in Portugal. We intend to: 1) distinguish elementary concepts and fundamental concepts; 2) explain why do we look at the mathematical concept of measurement as not only an elementary concept but, and above all, a fundamental concept in mathematics; 3) foresee implications of this distinction for teaching at the elementary level.CIEC - Centro de Investigação em Estudos da Criança, UM (UI 317 da FCT
Topics of physics in virtual experimentation
The use of information and communication technologies in education for different school levels is
becoming an usual practice. Concepts that many times are presented to the students from a static
point of view are more easily apprehended when adequate technologies are used to give them greater
dynamism.
Bearing in mind the real difficulties in the implementation of an experimental teaching of Physics, it is
possible nowadays to present to the students activities inserted in a context of new technologies that
encourage the experimentation and the sense of discovery, two essential teaching aspects of the
Experimental Sciences.
The project “Topics of Physics in Virtual Experimentation” intends to promote the virtual
experimentation in the classroom, through the exploration by the students of computational
applications and the development of small investigation projects. All the materials will be available in
the project site http:// fisicaexpvirtual.com.Fundação para a Ciência e a Tecnologia (FCT
A historical approach of the fundamental concept of measurement: Measuring “Time”, in Portuguese textbooks for 5th and 6th grades
In this article we present part of a PhD project on “The fundamental concept of Measure: epistemological and pedagogical aspects related to the first six years of schooling”.
It aims at analyzing the historical approach of the fundamental concept of Measure as presented in Portuguese mathematics textbooks for the 2nd cycle of Basic Education. In particular it intends:
1) To explain why do we look at the mathematical concept of Measurement as not only elementary but, above all, a fundamental concept in mathematics;
2) to identify a historical approach, in textbooks, inasmuch as it contributes to promotion and enrichment of learning the concept;
3) to analyse activities (problems and exercises) suggested and requiring Measurement.
Our specification of the concept of Measurement will be, in this article, “Time”
A história dos programas de matemática para a formação dos professores do 1º Ciclo do Ensino Básico em Portugal: o conceito fundamental de medida
Estamos convictas de que a preservação das memórias é, tal como o próprio Heródoto (séc. V a.
C.) defendia, a melhor forma para se compreender o presente e para se preparar o futuro.
É nosso propósito compreender a evolução dos programas de formação dos professores do 1.º
Ciclo do Ensino Básico, em Portugal, nomeadamente no que respeita ao conhecimento
matemático e perceber que dimensão é atribuída ao conceito fundamental de Medida. Neste
artigo reportar-nos-emos, em particular, a uma fonte primária histórica sobre a uniformização
dos pesos e medidas: o Mappa do Systema decimal em Nomenclatura Portugueza (1812-1814)
The fundamental concept of measure in elementary mathematics textbooks
In this article we present the work in progress at a PhD degree in Estudos da Criança, Área de
Conhecimento de Matemática Elementar, Universidade do Minho (Portugal). The focus on this
paper is the analysis of the fundamental concept of “measure” as seen in Portuguese textbooks
directed to the first six years of schooling. The concept of “measure” plays an important role in the
construction of mathematical knowledge, in particular at the elementary stages of education. Our
main aims are: (1) to define a set of criteria based on both scientific and methodological aspects
(related to the concept of measurement) to be applied on the analysis of mathematics textbooks; (2) to identify criteria for developing didactical material for coherently teaching the concept of measure during the first six years of schooling; (3) to apply our results to programs for both initial training for teachers and “recycling” teaching careers
Francisco Gomes Teixeira: o conceito de reta tangente no Curso de Analyse Infinitesimal
Francisco Gomes Teixeira destacou
-
se como matemático mas também como pedagogo.
O seu
“
Curso
”
foi utilizado como livro de texto durante vários anos nas Universidades
do Porto e de Coimbra e é um exemplo na forma como deve ser composto e revisto um
livro de
texto. Neste artigo analisaremos a parte relativa ao tratamento dado por
Gomes Teixeira ao conceito
de reta tangente,
explicitando as lições pedagógicas que se
podem retirar desse tratamento.FEDER através do “Programa Operacional
Factores de Competitividade
–
COMPETE” e por fundos Portugueses através
da FCT
FEDER através do “Programa Operacional
Factores de Competitividade – COMPETE” e por fundos Portugueses através
da FCT –“Fundação para a Ciência e Tecnologia”, incluída no Projeto PEst – C/MAT/UI0013/201
Reflection upon a "Method for Studying Maths", by José Monteiro da Rocha (1734-1819)
This was a workshop designed to acquaint the participants with a broad spectrum of mathematical ideas and viewpoints presented in a manuscript written, in the 18th century, by the Portuguese priest (and very influential scholar during the reform of the University of Coimbra) José Monteiro da Rocha, as an introduction to a mathematics course.
Based on both Monteiro da Rocha’s life and on his own comments on the teaching and learning of mathematics in Portugal, we have strong reasons to date this unpublished manuscript around 1760. At that time, the study of mathematics as well as the study of other areas, was at such a low level that some scholars were quite concerned with the learning content as well as the methods of learning; as a consequence we can find some important suggestions for dealing with these problems. An example of this is Luís António de Verney’s “Verdadeiro Método de Estudar” (“True Method of Studying”), published in 1750 which acquired quite a large circulation and, even nowadays, is used as a source of research. Less known than Verney’s work, and other similar texts produced all over Europe at that time, is the above cited manuscript by Monteiro da Rocha. In this work he echoed his concern with the teaching and learning of mathematics, emphasysing the lack of teachers of mathematics while, in his own words, “waking up his nationals from the lethargic state [in which they were living]”. In particular he suggested “writing in vulgar language” (i.e. Portuguese instead of Latin) for spreading mathematical knowledge among Portuguese citizens and he stimulated the national pride by reporting on the example of Portugal’s “glorious maritime discoveries”.
In the present workshop:
i) We presented a brief summary on the life and works of José Monteiro da Rocha, referring, in particular, to his activity in designing and writing the rules for the big reform of the University of Coimbra (1772) where, for the first time, a Faculty of Mathematics was created in Portugal. We also referred to his activity as a professor of the same university and his relationships with the academics of Real Academia das Ciências de Lisboa; we will also report on the international spreading of some of his works on Astronomy.
ii) We referred to the ideas/models presented in other textbooks of Monteiro da Rocha’s times.
iii) We proposed the analysis of some specific parts of the above cited introduction, by reading them from an English version of the original manuscript distributed to the participants.
iv) We lead a follow-up discussion/reflection on
- The actuality of da Rocha’s ideas, for example on his understanding of what is mathematical knowledge;
- The development/history of the models for presenting/introducing mathematics textbooks;
- The historical-didactical facts that we can learn/apply, at the present time where there is an acknowledged decrease of interest in studying mathematics.Fundação para a Ciência e Tecnologi (FCT
The teaching of the concept of tangent line using original sources
FEDER Funds through "Programa Operacional Factores de Competitividade
COMPETE" and by Portuguese Funds through FCT-
"Fundação para a Ciência e a Tecnologia", within the
project PEst-C/MAT/UI0013/201