Presentation of the Portuguese educational system
Before entering the university the students have a non-compulsory pre-school education (years 3 to 5), a compulsory Basic education (years 6 to 14) and a compulsory Secondary education (years 15 to 18).
The pre-school education is intended for children aged from 3 years till the entry into compulsory education and is optional; it is often given in garden-schools, public or private. Garden public-schools are free.
Compulsory Education - Basic Education
Basic education corresponds to the first nine years of compulsory education, from 6 to 15 years old, and is organized into three sequential cycles.
In 1. Cycle, education is comprehensive and aims to develop basic skills in Portuguese Language, Mathematics, Environmental Studies and Expressions. With the implementation of full-time school, by extending the hours of operation for a minimum of eight hours a day, the schools promote curriculum enrichment activities, including the compulsory teaching of English, study support for all students, the activity physical fitness and sports, the teaching of music and other artistic expressions and other foreign languages.
The cycle operates in a regime of only one teacher, using specialist teachers in certain areas.
In 2nd Cycle, the teaching is organized by disciplines and interdisciplinary areas of study.
In 3rd Cycle, the teaching is organized by subject. The main objectives of this cycle are the development of knowledge and skills necessary for entry into employment or further study.
The 2nd and 3rd cycles operate on a multi-teacher regime, with specialist teachers in different subject areas or disciplines.
In Basic education it is compulsory to learn two foreign languages, including English, French, German and Spanish.
Throughout Basic school students are subject to internal summative assessment, in addition, at the end of 3rd Cycle, students are subjected to external summative assessment by national testing in the disciplines of mathematics and Portuguese (form 2012 there will be external assessment in the 6th and 9th grades).
Students who successfully complete the 3rd Cycle are assigned a degree of basic education.
Public education is free.
Mathematics syllabus for Basic Education (version of 2007) - in Portuguese
Documents that complement the syllabus and support its implementation - in Portuguese
Compulsory Education - Secondary Education
To access any course of secondary school students must have completed Basic schooling or have equivalent qualification. Only recently Secondary Education was considered to be compulsory.
Secondary education is organized into different forms, either targeted for further studies or to the world of work. The curriculum of secondary level is a benchmark of three academic years and includes four types of courses:
Scientific-humanistic courses, designed primarily to further studies at tertiary level;
Mathematics syllabus for years 10-12 for Science and Economics areas: "Mathematics A" - in Portuguese
Mathematics syllabus for years 10-11 for Social Sciences and Languages areas: "Mathematics Applied to the Social Sciences" - in Portuguese
Technological courses, aimed at students wishing to enter the labor market, allowing also the continuation of studies on technological specialized or higher education;
Mathematics syllabus for years 10-12: "Mathematics B" - in Portuguese
Specialized artistic courses, to ensure artistic training in specialized areas of visual arts, audiovisual, dance and music, allowing entry into the world of work or further education courses in post - secondary non-tertiary, or even in higher education;
Mathematics syllabus for years 11-12: "Mathematics" - in Portuguese
Vocational courses intended to provide entry into the world of work, providing also further education courses in post - secondary non-tertiary or higher education. Modules are organized by different areas of training.
Mathematical modules for years 10, 11 and 12: "Mathematics" - in Portuguese
To complete any course of high school students are subject to an internal summative assessment. In addition to this assessment, students of the scientific-humanistic courses are also subjected to an external summative assessment through the implementation of national examinations in certain subjects prescribed by law.
Students who have completed this level of education are assigned a secondary education diploma. The technological, artistic and skilled professionals provide even a vocational qualification at UE-level 3.
In public education, students have to pay a small annual fee.
Education and Training for Youth and Adults
Education and training of young people and adults offers a second chance to individuals who left school early or who are at risk of leaving, and those who had no opportunity to go there when young, and also those looking for the school matters of professional or personal development from the perspective of lifelong learning.
In order to provide new ways to learn and progress came to the "New Opportunities" which he defines as a key objective to extend the minimum training reference to the 12. Th grade and whose strategy rests on two pillars:
Raise the basic training of the workforce;
Making vocational education a real option for young people.
The different forms of education and training of young people and adults to acquire a permit school certification and / or professional qualifications as well as further studies at post-secondary non-tertiary or higher education.
Education and training of young people and adults take the following forms:
System for Recognition, Validation and Certification of Competences (RVCC) acquired throughout life, through formal, informal and non-formal education, allowing students to obtain a dual academic and professional certification. The training received allows access to better jobs and better perspective of lifelong education. This system takes place in the New Opportunities Centres, spread throughout the country;
Education and Training (CEF) for students aged 15 and over;
Education and Training (EFA) and Modular Training for students over 18 years;
"Short-term Actions S @ ber +" for students over 18 years;
Recurrent education in primary and secondary education for students aged 15 or over 18 years for the primary and secondary, respectively;
National System of Learning, the responsibility of the Office of Employment and Vocational Training for young people aged 15 years.
Mathematics syllabus for Education and Training (CEF): "Applied Mathematics" - in Portuguese
Mathematics for Education and Training (EFA): "Mathematics for Life" - in Portuguese
Papers about the situation in Portugal:
Alexandra Gomes, Elfrida Ralha, Keith Hirst - Undergraduate Mathematics for Primary School Teachers - The situation in Portugal - Proceedings of the 2nd International Conference on the Teaching of Mathematics (at the undergraduate level), University of Crete, 1 – 6 July 2002
João Pedro Ponte - Investigations and explorations in the mathematics classroom - ZDM Mathematics Education (2007) 39:419–430
João Pedro Ponte - (2008). A investigação em educação matemática em Portugal: Realizações e perspectivas. In R. Luengo-González, B. Gómez-Alfonso, M. Camacho-Machín & L. B. Nieto (Eds.), Investigación en educación matemática XII (pp. 55-78). Badajoz: SEIEM.
João Pedro Ponte - (2005). A formação do professor de Matemática: Passado, presente e futuro. In L. Santos, A. P. Canavarro & J. Brocardo (Eds.), Educação matemática: Caminhos e encruzilhadas (pp. 267-284). Lisboa: APM.
Jose? Manuel Matos - Changing representations and practices in school mathematics: the case of Modern Math in Portugal - in Bjarnado?ttir, K. Furinghetti, F., & Schubring, G. (Eds.) (2009). “Dig where you stand”. Proceedings of the conference “On-going research in the History of Mathematics Education”.
Ana Paula Canavarro, Isabel Rocha - Professional development of mathematics teachers: Challenges from a national in-service teacher education program in Portugal - ICME-11, 2008.
Jaime Carvalho e Silva
Universidade de Coimbra, Portugal