Revisiting the Goals and the Nature of Mathematics for All in the Context of a National Curriculum.

A movement of educational change has been developed in Portugal, aiming at giving the schools a larger autonomy in curricular decisions. In reconceiving the view about the curriculum, the concept of “competence” plays a central role while the process of innovation constitutes a major aspect. This movement is described and analysed, in particular by discussing the notion of competence and the characteristics of the process of curriculum development. A special focus is on the way in which mathematical competence for all may be interpreted and how it is related to developments in mathematics education. The analysis of obstacles emerging in a large-scale educational change may be relevant for discussion in an international context and offers some suggestions for future research and debate. 1. New trends in the Portuguese educational system The evolution and recent developments of the Portuguese educational system in the last two decades, as well as the related perspectives on the curriculum, and on the mathematics curriculum in particular, raise some issues that might be of general interest for reflection and discussion. 1.1. The context: some contradictory aspects In 1974, when we could finally restore the democracy after 48 years of a dictatorship, the extension of compulsory education up to 6 years of school – instead of the old and traditional primary school of 4 years – was a recent fact. This hardly reflected the reality in the poorest regions of the country. Illiteracy was very high among adult population. It was only in 1986 that a new general law for education fixed compulsory school attendance for all 6-15 year olds (that is, a “basic school” of nine years). In fact, we had to wait almost for the end of the twentieth century to see practically all our children and youngsters of those ages in our classrooms. At the same time, it was only after 1995 that pre-school education became a new reality, finally involving in 2000 the large majority of children of the 3-5 age level. As a result of its rapid and original development, in particular due to the fact that its basis was partly designed during a sort of “revolutionary” period, this educational system has some characteristics that may be seen as contradictory. On the one hand, we have a number of very “advanced” laws and regulations. In our system, there is a comprehensive and “inclusive” basic school of nine years for all, similar to the Scandinavian traditional organisation, and a secondary education of three years, with different branches (general, vocational, professional) all of them giving equal access to further studies. Since 1997 teachers of all school segments, from pre-school to university, must have the same academic degree at the beginning of their profession. Moreover, all teachers may use, from time to time, a sabbatical year or they can apply to a bursary in order to develop projects or to do a postgraduate course. In the second and third cycles of basic education (10-15 year olds), teachers work a maximum of 22 and a minimum of 14 class periods of 50 minutes per week, according to their age. On the other hand, all this was conceived and implemented on a tradition of a centralised and rigid school system, which was affected by lack of resources in many schools – a problem that has taken us many years to overcome. It was only in the nineties that a new law to increase the administrative autonomy of schools was adopted. Dominant public views about the curriculum tend to see it as a set of disciplines with “programmes” indicating for each subject what (and how) must be “covered” each school year. This process is actually mediated by the power of the textbooks – even if those programmes are aligned with modern international trends in most disciplines. Although there are no national exams except at the end of the secondary school, assessment is dominated by traditional written tests. Although there is an official logic of evaluating students progress throughout each cycle, the old “principle” of deciding that the student must repeat the same school year if he/she does not succeed in two or three disciplines still guides the way how many people think and act, both outside and inside the school. When focusing on mathematics education, there are also other contradictory aspects in the situation, just like in most European countries. However, Portugal probably stands in a clearer contrast. In Portugal, the community of mathematics education (teachers, teacher educators and researchers) has become quite strong in these last fifteen years. All these groups support and are involved in the Association of Teachers of Mathematics (APM), the biggest association of its kind, which was created in 1986 and has now about 6000 members. This number would be equivalent (proportionally to the population) to 24000 in Spain, more than 30000 in France or UK, and approximately 9000 in Holland! About 2000 participants attend the annual meeting organised by APM. Many Portuguese teachers and researchers began to participate in international congresses on mathematics education: in ICME-8, in 1996, they formed the third largest national representation among European countries, after Spain and UK. At the same time, a considerable number of teachers are following post-graduate studies on education, in particular on various aspects of the didactics of mathematics, and some of them are participating in projects which involve both a strong component of curricular innovation and a research dimension. Since the creation of APM, and following the experience of the MAT789 project (Abrantes, 1993), the cooperation between teachers and researchers became an interesting feature of Portuguese mathematics education – see, for example, Oliveira et al. (1997), Ponte et al. (1998) or Porfírio and Abrantes (1999). It is not surprising that curricular innovation and teachers professional development became two major areas of research. However, this community is under a strong public pressure, as a consequence of the scores in the exams at the end of secondary school or the very low position of Portugal in the rankings of the international comparative studies. Like elsewhere, as Keitel and Kilpatrick (1998) have pointed out, these rankings are frequently used without any serious consideration about what they mean or do not mean. They are used, for example, as an argument to propose not only the return to a greater emphasis on training routine skills, but also “solutions” like more exams and more comparative studies! Many teachers seem to have mixed feelings. They have sympathy with the new ideas about curriculum development, but they are also moving in a culture of school still dominated, inside and outside the school, by the old ideas and values. 1.2. Recent developments in basic education In the last four years, after one year of debate and preparation, the Ministry of Education initiated a movement towards a new curricular organisation. The starting point was the consideration that the traditional structure was not adequate to ensure significant learning experiences to all children and to avoid school failure and abandon. For the “basic education”, this movement started with a project, labelled as “flexible management of the curriculum”. This project aimed at giving the schools a larger autonomy in the decisions about the various disciplines and connections among them, as well as about new interdisciplinary components – a “project area”, an “oriented study area” and a “citizenship area”. This autonomy relates to the teaching and learning process and refers both to the activities to be developed and the time and space dedicated to each component of the curriculum. Emphasis is put on the role of the teachers and their collective structures in school, namely – at 2 and 3 levels of basic education (10-15 year olds) – the class council, this is, the group of professionals who work directly with each group of students. This movement was justified by the need to promote a new conception of the curriculum, both the intended curriculum and the implemented one. The former requires the educational authorities to express the curriculum in terms of “essential competences” and types of “educational experiences” that the school should consider for all pupils (in each cycle), in opposition to the usual programmes of content topics to be covered and corresponding methods (in each year). The latter challenges the teachers and the schools to assume a much larger responsibility in the search for the adequate decisions for the specific pupils they work with, taking into account their cultural and social environment, their educational needs and the human and material resources that exist or can be made available. In other words, under the guidance of a national curriculum expressed in general and broad terms, the process of curriculum implementation is seen like a project to be conceived and developed by the school, including more specific projects concerning each individual class. From 1997 on, schools could participate in the so-called “flexible management of the curriculum” movement by presenting their own curricular projects, under a minimum number of general rules. This participation, on a completely free basis, began with 10 schools in 1997/98, increasing in the three following years up to 184 schools all over the country. These schools constituted a sort of informal network exchanging materials and points of view, and participating in local, regional or national meetings organised by the educational authorities. 1.3. The case of mathematics Meanwhile, the Ministry of Education started to produce draft versions for discussion of the so-called “essential competences”. Some documents focussed on aspects crossing all school subjects, while others related specifically to the various disciplines.