As the description of the network inclusion reminds us, most of the scientific literature and discourse focuses on the notion of inclusion with regard to the inclusion of people with disabilities. The focus on disability would tend to make us forget that inclusion, beyond the consideration of people in situations of mental or physical disability, encompasses all marginalizing situations (Richardson & al. , 2011 ; Rix & al., 2013).

This fringe of the population in need of compensatory aid overlaps in many countries with the fringe of people who are very socially deprived, or rejected by part of the population because they do not fit into the subjectively "established" norms (Garnier & al., 2020). People with a migrant background, especially from recent waves of immigration in Europe, are particularly affected by these phenomena of exclusion or difficulties in being included in a particularly tense socio-economic landscape.

In this migratory context, many families seek refuge in countries whose standard of living seems to be conducive to their inclusion (Sleeter, 2007). Within these families, children are particularly vulnerable and schooling is a way for them to discover a social and cultural environment other than their own. Of course, this is not self-evident. In welcoming families to schooling for their children, primary school headmasters play an important role. Indeed, this first contact will give a more or less positive sign to the family on how their child will be taken care of by the school community.

As part of my research in education and training sciences on the professional identity of primary school headmasters in France, I was particularly interested in the way in which it took into account these families and children who are often suffering, far from their country of origin. It is in the context of the fight against inequality, a major problem in the French education system, that their day-to-day action caught my attention.

This study is based on a qualitative approach and the corpus was built up by going to meet them and interviewing them. The interest was to bring to life a certain number of variables which I hypothesised played an essential role in the management of the school and the leadership of the teaching team. At this stage, it should be remembered that the head teacher in France is not a hierarchical superior but a colleague in charge of the school. This is a function and not a status.

So I interviewed headmasters working in various types of schools. They worked in rural areas as well as in highly urbanised areas, in small schools or large establishments, in socio-culturally advantaged or very disadvantaged areas... In all, about sixty meetings were held, which allowed us to gather speeches on the daily activity of headmasters, the advantages and difficulties of the profession.

Through their narrative, it is both their representations of the function that have emerged but also elements of their daily practice. Varied practices since only a tiny percentage (less than 10ù of them) has a charge totally dedicated to the administration of the school. The others are always in charge of classes, this time depending on the size of the school. The stories collected were analysed in the form of a thematic analysis (Bardin, 2013).

And the categories were determined by the initial hypotheses but also by what the interviewees could add. The presentation presented in the framework of ECER 2021 will focus more specifically on how, depending on their work context and experience, school headmasters participate on a daily basis in the fight against exclusionary inequalities

This research in education and training sciences falls within the field of sociology of education. I became interested in the professionalism of school headmasters and sought to understand how their personal and professional background coloured their daily work as a headmaster. It is a qualitative approach that has been undertaken. In fact, the corpus is made up of some sixty interviews conducted with both male and female primary school headmasters. In order to have a representative sample, directors of all ages and seniority were interviewed. The region chosen to conduct the survey covered all categories of primary schools: geographical diversity, social diversity, socio-economic diversity and diversity in school size. The contact was made directly outside of any action to the hierarchy and they volunteered to answer the questions asked. The interviews lasted between one and three and a half hours. The interviewees were questioned about their daily life as headteachers and not about their classroom practice (90% had a greater or lesser class load). The interview guide constructed and used revolved around predefined themes. Relationships with pupils, colleagues, hierarchy, parents and the town hall were therefore envisaged. Representations concerning their role and status were discussed. And with regard to their daily tasks, what they found easy or difficult in managing the school and leading the teaching team, including the care of pupils with special educational needs. All interviews were transcribedin their entirety. Based on the transcript, a thematic breakdown was made to define categories and build a typology with regard to the changes and reforms imposed by the Ministry. Hypotheses were a guiding thread in the creation of the categories, using independent and dependent variables to finalise the results and allow for interpretation. But it was also the information gathered during the interviews that opened up other avenues of reflection and other hypotheses with reference to the work of Glaser and Strauss (1967).

Research has shown the importance of the role of parents in children's success and how the representations that teachers make of families are sometimes unfavourable to this success (Périer, 2005; Monceau, 2014). For headteachers, therefore, welcoming families from ethnically diverse backgrounds is an essential lever. The challenge is to share the school's objectives and to give everyone a place that contributes to their child's success. This is what the directors we met are trying to do. The analysis of the corpus allows us to say that the intensity of commitment to diversity management by managers is quite variable. On the one hand, there are simple responses, often seemingly in response to institutional demand, such as actions announced in the school project, but there are also real commitments. Most of the time, these commitments are based on personal convictions and values to be defended. It is above all a civic commitment. This willingness to fight against discrimination and to participate in the implementation of a truly inclusive school refers to political commitments, associative commitments or an expression of religious belief. Variables such as age or seniority in the profession have no influence. For these headmasters, it is rather a question of developing skills such as living together while respecting differences. What is also noteworthy is that the unwilling discourse most often emanates from managers who are blasé or even tired of institutional demands, with inclusion being taken as an additional demand. Places where teaching is more difficult, such as priority education areas, which concentrate a population living in precarious conditions, are mostly places where headteachers are strongly committed to an inclusive approach.

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