Abstract
A project was commissioned by the Ministry of Education in Catalonia, in northern Spain, concerned with mathematics teaching in schools with large numbers of immigrant students. This paper describes the preliminary stage of the project and focusses on the political, socio-cultural, and educational aspects of starting such a project. It presents a number of challenges that the project team has to face.

Introduction

In recent years, there has been increasing immigration into the north-eastern region of Spain known as Catalonia (capital Barcelona) which has led to significant quantitative, and qualitative, changes in the school population. Most of the immigrant pupils come from North Africa (Magreb), but also from other countries in Africa, North and South America, Asia and East European countries. This new situation has focussed attention on the inadequacy of the educational provision in schools and classes that can be thought of as highly multicultural.

The project described here began in 1997, is funded by the Catalan Ministry of Education, and has the support of a Catalan private foundation devoted to education, Fundació Propedagògica. The project is concerned with finding more appropriate ways to teach mathematics to immigrant students both in primary and secondary schools. This paper is a report of the preliminary stage of the project highlighting the constraints, possibilities and challenges of doing research in this highly politicized social-cultural context.

The context of the project

The project will be contextualised firstly in the legal and institutional framework where it takes place, and then in the social framework.

The legal situation of foreigners in Spain is at present regulated by a law promoted in 1985, and its subsequent modifications and developments which took place in 1986, 1992, 1995 and 1996. Taking into account the fact that the previous regulations about immigration were created in 1968 and 1978, one can see that the development of these laws is a response to the "need" to control immigration and particularly the numbers of people coming from underdeveloped countries. In addition to the immigration laws, nearly every year regulations have been developed to normalize the situation of illegal immigrants, by fixing the number who would receive residence and work permission. It is also important to point out here that even if the law considers the regrouping of the family as a possibility, the practical and legal obstacles needing to be overcome to achieve it lead to the presence of many unstable, unhappy, and unstructured families.

By the end of the 1980s, both state and regional governments with educational power in Spain (as in the case of Catalonia) promoted a broad reform of the educational system. This new reform is currently being implemented. The New Educational Act, LOGSE, organises compulsory education into two stages: primary education (6-12) and compulsory secondary education (12-16). We can claim thereby that for the past decade, education to age 16 has been regarded as a right accessible to most children in the country.

The structure of the curriculum in all compulsory education is common to all fields of knowledge. Each curriculum description contains global objectives for the whole educational stage and for each field (including mathematics), general goals, three sets of contents (knowledge, skills and attitudes), final aims and teaching guidelines. The official regulations are very general, because there is an explicit intention that every school should adapt the curriculum to the actual needs of their pupils, and to its own possiblities for meeting those needs.

Generally speaking, the new system meets current educational needs much better than the previous one, although there is much to be done in the area of teaching in multicultural situations, which is one of the weakest points of the implementation of the reform. Firstly, even if the "treatment of diversity" is considered in the teaching guidelines, it is addressed in a quite naiive way. The difficulties which many teachers encounter today are far beyond their initial expectations, and they can find no solutions in the official documents. In a word, even the "good" teachers do not know how to work with culturally diverse classes. Moreover, although the changes suggested in the official documents are meaningful, old beliefs have not yet been abandoned by most of the educational community, including the administration.

In addition, in-service teacher education programs dealing with multicultural education are scarce, and consequently the teachers and schools do not yet receive enough support to carry out any teaching innovations. As a result of that, the implementation of the curriculum still takes place, for the most part, by teachers following the guidelines of the textbooks, which have become the interpreters of the new curriculum. Although there are many innovative textbooks, in general they fail to facilitate any approaches to the teaching of mathematics which take into account cultural diversity.

Concerning the social framework in which the project takes place, the immigration context in Spain until the seventies was that of a country where most of the foreigners were tourists, a fact which made our citizens able to claim that they were tolerant of foreigners. The relatively small number of working immigrants of that decade have already "stabilized" within the society, and their children are already well integrated. The working immigrants of the eighties have not yet stabilized and the process of their integration is still going on; thus they keep strong not only their languages but also their life-styles. Since the beginning of the nineties, the illegal entrance of immigrants has become an accepted fact. This fact, together with the economic and structural crisis, and the concentration of the immigrant working population in certain areas of the country, no longer creates the illusion that our society is a tolerant society, when the individuals concerned feel that their integrity or their status is at risk.

At the beginning of the project, and probably as a partial result of the facts described above, we are acutely aware of one crucial social issue. Many parents of Catalan children have removed them from the schools that have "too many" immigrant children. Besides that, the schools that have committed themselves in the past to working seriously for immigrant and cultural minorities have attracted even more of these children. Consequently many of the schools which initially did good work with a culturally diverse population of students have become "ghetto" schools. However, it must also be said that in some towns the educational administration has taken a strong position to address this situation, by for example changing the rules for school registration, so that the first criterion for allocating a child to a certain school is no longer the place where the child lives.

Negotiating the aims of the project

If we consider the three approaches to ethnomathematics research as outlined by Bishop (1995): anthropological approach, historical approach, and social psychological approach, our starting point was to consider the project from its third meaning. We are not dealing with how research can help rebuild a country after many years of colonialism; neither are we dealing with how the different cultures have contributed to the history of mathematics; but we are dealing with the mathematics education of culturally diverse students who live in the same country.

We have to deal with students whose parents belong to a culture different from the one that hosts them, but we regard the students themselves as being at a certain point on a continuum between their parents’ culture and the host culture. Therefore we believe that the main educational approach should be to help them create their own psychological and social identities. In line with this belief, we want our research and its implications to take into account the students’ out-of-school knowledge, including their values, beliefs and expectations. But the question for us is how to take this knowledge into account? We see no point, for example, in trying to teach aspects of the Moslem history of mathematics when the students make explicit in class that they want to become fully integrated Catalan adults. (Even if they are faithful Moslems, some students change their names to disguise their family and cultural origins.)

A further point is that the research team strongly believes that such an inclusive approach to both content and methodology in mathematics classroom, will be beneficial not only to children who are "culturally different" but also to the children of the Catalan communities, because it will make them aware of learning in a non-ethnocentric context, which has respect for other cultures and which also enlarges their understanding of mathematics as a cultural product.

Even if the project was the result of a request from the administration, the team’s understanding of the multicultural fact in schools goes far beyond that of the educational administration. The team has negotiated strongly, and continues to do so, to change what initially was a policy-driven "research" project into a research project with no inverted commas. The team does not see cultural differences as a "problem to be solved" nor as a "diversity to be treated" but as a potentiality, to help ALL students to learn from the contrasting experiences and out-of-school knowledge of their peers.

As the result of the negotiation the aims of the project include, among others:

• To know more about the "out-of-school knowledge" connected with mathematics that immigrant students have, and how this knowledge can be linked with the curriculum content and its development in class.
• To uncover the values immigrant students associate with school and out-of-school mathematics and how these can help or interfere with the teaching of mathematics.
• To develop both proposals and practical examples of how to adapt the school curriculum to the multicultural situation of the classroom.
• To help make teachers aware of the different cultural backgrounds immigrant students have and their implications for the teaching of mathematics from a non-ethnocentric point of view which could help both immigrant and Catalan students.
• To promote and synthesise research in the field which could shed light on the previous points.

The research team

Having received the request to address an issue which is mainly connected with schools, the author, as a researcher and university lecturer, argued for the necessity of having a team which included different members of the educational community, to work in the project. The result of this negotiation resulted in a collaborative team, whose other members are two secondary mathematics teachers (Núria Planas and Xavier Vilella) a primary teacher (Montse Fontdevila) and a psychologist (Montserrat Benlloch). Núria is a research student and teaches in a secondary school in a very socially-deprived area of Barcelona, which has both immigrant and very poor Catalan pupils. She has got a partial release from her teaching hours to devote time to the project. Xavier normally teaches in a secondary school in an agricultural area near Barcelona, where cultural diversity occurs but is not necessarily linked to poor Catalan pupils. He has been given one year’s leave to devote to the project. Montse, the primary teacher, has also partial leave, and is an expert on producing materials and on in-service teachers training. Montserrat, the psychologist, is teaching at the University of Vic, a city that has a strong commitment towards solving the problem of Catalan parents removing their children from the schools which have immigrant students. As part of her job she can work as a researcher and also with her in-practice pre-service students teachers in the schools in Vic.

With such a team we consider that not only do we have the support and the expertise from the university level but also knowledge and expertise from school practitioners. However, as all the members of the team consider themselves as "outsiders" to the immigrant situation, we are now trying to involve in the project a primary teacher who has been trained in Catalonia, but who comes from Morocco, the country from where most of the immigrant students come. It is also our intention for the future to try to involve in the project some adults from the different communities, and also to extend the number of collaborating teachers.

Research procedures

The research procedures being followed by the team are similar to those used by Abreu (1995) and Presmeg (1997), and consist of the following:

• Collecting examples of classroom situations and incidents that exemplify cultural conflicts.
• Interviewing teachers to find more about their understanding and beliefs of cultural conflicts in mathematics classrooms, with examples of classroom situations and incidents being the motivation for the discussion during the interview.
• Observing students systematically during mathematics lessons to identify their potentialities as well as weaknesses regarding mathematical content.
• Interviewing students to investigate mathematical possibilities in their environment and their expectations about their learning mathematics.
• Documenting social practices that immigrant and Catalan students could understand as social activities involving mathematical knowledge.
• Creating classroom activities which are rich both from the point of view of research and learning, and which could be used as models for other teaching situations.
• Creating classroom activities that could lead the students to project their values and beliefs to identify diferent cultural practices.
• Documenting procedures which could be used by other teachers in other situations.

Constraints and possibilities for action

When first defining the project the research team made some assumptions, maybe too optimistically, regarding the contribution we could expect to receive from the educational administration. Throughout the negotiation of the project’s aims and the resources to develop it, we have realized the existence of various constraints that we are unable to affect. In particular we have found that it is impossible:

• to change any aspects of the intended curriculum,
• to have release time for any other teachers to collaborate in the project,
• to involve adults of the different communities in the actual teaching in the classroom to help with communicating with students who have language difficulties,
• to allow teachers to teach in any other language different from Catalan, the oficial language of the schools, even though the students understand Castilian (Spanish) much better,
• to get any global data regarding the level of attainment of both immigrant and Catalan pupils,
• to obtain any information about the previous school history of the pupils before coming to our country.

Conscious of the constraints surrounding the project, the team is however clear that there are several possibilities for action to achieve the goals of the project and to implement its implications for teaching, such as:

• to hear the opinion of the different communities about the research project and their understanding of the educational situation,
• to involve someone from the different communities to work with the research team,
• to find ways to overcome the language barrier in the classroom, in particular to analyse the effects of letting the pupils work in small groups using their home or preferred language,
• to work with some schools and analyse comparatively the data they have about the level of attainment and difficultites that both immigrant and Catalan pupils have.
• to influence the implemented curriculum by offering models of rich activities which take into account the out-of-school knowledge and the practices of the different communities and which build on the students’ potentialities,
• to participate in the in-service teacher education programs, and to promote reflection among the teachers’ professional associations, to educate the awareness of the teaching community about the multicultural situation, to change their perceptions of difference, to present them with strategies which would allow them to know more about their students’ previous knowledge and potentialities, and to give them clues as to how to change the social dynamics of the classroom.

Observations and immediate challenges

During the first year’s work we have observed many aspects of the situation, most of which have convinced us that it is important to keep working on the project. In particular, we have data which documents that the understanding of the multicultural situation by teachers is far from what we believe it should be. For many of the most sensitive and sensible teachers we have interviewed, the cultural differences are reduced to language differences, and they believe that once the language barrier is overcome, if one ignores the colour of the skin, there are no more differences among the students.

Another observation concerns important differences between primary and secondary schools regarding their immigrant students. In primary schools the immigrant children are mostly of a second generation (but still legally considered immigrants) and therefore have had all their schooling here. In secondary schools there are many students who have just arrived in our country (many of them illegally) and who therefore received most of their schooling abroad. Moreover, there is another important distinction between primary and secondary schools, due to the characteristics of their teachers. Primary school teachers are more concerned about individuals than secondary teachers who are more concerned about content. All these facts mean that the way we address the two communities of teachers must be different.

Differences between the characteristics of schools in relatively small towns and big urban areas have also been observed. The cultural conflict in schools receiving immigrant children in big urban areas is associated with social conflicts and economical deprivation, while in rural areas or small towns, the cultural conflict is only that.

The above points have to do with general aspects and do not only refer to the teaching of mathematics. Regarding the curricular mathematical content, we have observed that the actual mathematical content is far away from the students’ interests, and in some cases, students’ needs. Therefore all the efforts we have made to know more about out-of-school and social practices involving mathematical knowledge promise to be worthwhile. Also regarding the mathematical content, we have observed, to a certain surprise, that what is taught in mathematics lessons in Catalonia is very close to what is taught in the students’ countries of origin. This fact reaffirms the need to know more about students’ needs and interests and to promote changes not only in the mathematical content, but also in the way it is to be taught, and in the social dynamics of the classroom and of the school.

If we had to say which has been the most significant observation after this year’s work we would certainly say that it is about differences in the social dynamics of the educational situation. When talking about differences in a social situation one means differences from the "normality", where this is defined according to the assumptions and expectations of the individuals concerned. Thus, teachers find immigrant students to be "different" from what they expect their pupils to be. Immigrant students find their teachers "different", as they do the dynamics of the classroom and the school they are in. The interactions among students and between students and teachers are also culturally "different" as are the relationships between parents and the school system. We strongly believe that if we want any educational act to be positive both for the individuals and their communities it is crucial to make explicit to everybody the social dynamics of these "differences", and to begin to consider them as a source of richness, rather than problems, in the educational context.

Together our observations during the first year have shown us that there are some real and immediate challenges which we face. These include:

• to achieve a full acceptance of the project by the educational politicians, by convincing them that our project is not only "politically correct" but a real social need,
• encouraging the involvement of school principals and inspectors; in a word, "selling" our project to those who see it as a threat to the well-established tradition, and convincing them that the education of children within a multicultural framework is, at the present time, a priority,
• seeking support from groups of teachers within schools and overcoming teacher-researcher conflicts, and, in particular, teachers’ reluctance to participate in the project,
• gaining the trust of students, and establishing the credibility of the research team with immigrant parents and with significant members of the different communities, in order to extend the ownership of the project from the research team to the communities involved,
• overcoming practical matters for gathering and interpreting information, especially language barriers, by involving a language specialist who could help the team not only with translation, but also with the interpretation of the different language structures which can interfere with the teaching of mathematics in Catalan.

References

Abreu, G. (1995) ‘A Matemática na Vida Versus na Escola: Uma Questâo de Cogniçâo Situada ou de Identidades Sociais?’ in Psicologia: Teoria e Pesquisa. May-August 1995, Vol. 11, No. 2, pps 085-093.

Bishop, A. J. (1995) ‘Mathematics education between technology and ethnomathematics: Should it be common? Does it make sense?’ Plenary address at the 47^th annual conference of the International Commission for the Study and Improvement of Mathematics Education, Berlin.

Presmeg, N. C. (1997), ‘A semiotic framework for linking cultural practice and clasroom mathematics’ In J.A. Dossey, J.O. Swafford, M. Parmatie and A.E. Dossey (Eds.), Proc. of the XIX Annual Meeting of the North American Chapter of PME, Vol. 1, pps 151-156. Columbus, Ohio: ERIC SMEAC.