Mariem Chaabouni
email: mariem.chaabouni@univ-lemans.fr

Mona Laroussi
email: mona.laroussi@univ-lille1.fr

Claudine Piau-Toffolon
email: claudine.piau-toffolon@univ-lemans.fr

Christophe Choquet
email: christophe.choquet@univ-lemans.fr

Ben Ghezala
email: henda.benghezala@ensi.rnu.tn

A context modeling approach and a tool for reusing learning scenarios

Keywords: Learning scenarios, learning context, reuse, context-based similarity, pedagogical indicators, indexing

With the evolution of teaching modalities and the high integration of the technology in the learning processes, teachers proceed to the design of learning situations in order to plan and formalize their educational experiences and share them with students and other teachers. Various academic and community initiatives of experience sharing and resulting learning scenarios repositories have emerged. This leads us to discuss the learning scenarios reuse issue, which becomes an essential practice for capitalization. Since the learning contexts are continuously changing, it could represent an obstacle to the reuse and the appropriation of learning scenarios. It therefore becomes important to consider the context dimension to assist teachers in the scenarios reuse situations. This paper deals firstly with the proposition of an approach to model learning scenarios context. Based on this modeling approach, this paper is interested in the retrieval of learning scenarios that most fit a target learning situation context by presenting a context similarity algorithm matching contextual models. The retrieval is based on contextual indexes related to scenarios. The indexing process is consolidated by the observation of the prior user-experiences of learning scenarios. An authoring tool is then presented integrating the context modeling approach and the detailed algorithm. Simulations of the implemented tool and related results are detailed within this paper.

Introduction

It becomes important to organize and capitalize the teacher's practices. This leads us to discuss the reuse issue of the learning scenarios that can be considered as the results of the formalization of these teaching practices. The reuse rate can be reduced due to the multiplicity of the scenario's formalisms, the definition of rigid scenarios, the variation of learning contexts especially when the scenarios are detailed in a very specific way for a particular context, the high variability of resources used in the scenarios and the lack of tools to assist in finding the proper scenarios for reuse. Various approaches and technics are proposed in literature helping the reuse of learning objects (LOM, 2002;[START_REF] Moura | Conceiving and Implementing a language-oriented approach for the design of automated learning scenarios[END_REF] and learning scenarios in particular [START_REF] Paquette | An ontology and a software framework for competency modeling and management[END_REF]IMS, 2003a). This paper is mainly focused on facilitating reuse by treating essentially the context aspect related to the learning scenario. It proposes an approach, addressed to teachers-designers, to assist the scenario reuse task by suggesting the scenarios that better fit a target context of learning situation. This approach is reinforced by the observation of the past learning experiences to support the pertinence of reuse. Section 2 exposes related works in the literature that discuss the learning scenarios formalisms, the reuse of these scenarios and the learning contexts. Section 3 describes the context modeling approach allowing the construction of the contextual index of a learning scenario. After that, Section 4 shows how to use this index to promote the scenarios reuse. It so describes an algorithm calculating contextual similarity between a planned context and a contextual index associated to a scenario. This algorithm returns as output the scenarios which have been indexed by the most similar contexts to the planned context in a situation of design by reuse. Then, Section 5 describes an author tool supporting the scenario design by suggesting the most appropriated scenarios to a given learning situation. Finally, the paper will discuss the obtained results.

Related works

The designations and the representations of the teacher practices have been widely treated with different views in prior works. IMS-LD (IMS, 2003a), a proposed Educational Modeling Language (EML), defines the concept of a learning process as "a time ordered series of activities to be performed by learners and teachers (role), within the context of an environment consisting of learning objects or services". We cite also the PoEML language (Perspective-oriented Educational Modeling Language) [START_REF] Caeiro-Rodrıguez | Supporting the Modeling of Flexible Educational Units, PoEML: A Separation of Concerns Approach[END_REF]) sharing a similar approach by referring to the term "educational scenario" that is "intended to support the modeling of any kind of educational unit at different aggregation levels, from simple lessons, to complete courses or curriculums".

With the increase of these modeling approaches, learning scenarios repositories (E-LEN, 2005; BASAR project, 2012) appeared implementing these approaches and containing a large number of scenarios. These bases are supplied to share the experience of the scenarios designers. This leads us to discuss the scenario reuse problematic that becomes an essential practice. An exploratory study of the BASAR base (Bank of hybrid, reusable an interoperable learning scenarios) (BASAR project, 2012) has revealed an important need of reuse of scenarios or activities sequences of scenarios. The study also shown a wide variation and a diversification of contexts associated with these learning scenarios. In fact, these scenarios implement different modalities like temporal, spatial, and collaborative. The designed scenarios are also targeting learners with different educational levels, technical skills or social characteristics. This variability might reduce the potential reuse of the scenarios by another designer or leads him to reuse non-adapted scenarios to its usage context.

It thus becomes important to consider the contextual dimension to assist teachers in the scenarios reuse situations. For that, we opt for a multidimensional modeling approach of the context of a learning scenario including any environmental factor that can influence the scenario progress whether educational, technical, social or others. The context of a learning situation is seen from a large perspective varying from educational and social profile of the learner or the teacher, pedagogical and affective objectives of the learning situation, used software/hardware resources, to the physical environment surrounding the execution of the scenario. Therefore, trying to use the same scenario in a different context from the original one may be not adapted to this targeted context.

The principal aim of the study presented in this paper is to define an approach to model and to analyze the context in which the scenario was implemented and to use it to build a contextual index. This will help a designer to reuse scenarios that have been indexed by closest contexts to his target context. A scenario performed in a specific context can succeed or fail with this particular case. So, the past learning experience can be useful for enhancing the indexing scenarios. In that situation, we propose to integrate this dimension of user experience in order to reflect the degree of success of a scenario in a particular context, and so benefiting from previous experiences already implemented in a given context. In order to consider the past learning experiences, it is proposed to use the observation of the learning sessions by calculating pedagogical indicators. Thus, the observation allows the teacher-designer to assess the progress of the scenario and to determine whether it was successful in a such specific context and if it has been effectively adapted to this context.

A context modeling approach of learning scenarios

Firstly, we present the approach of modeling of the learning scenario context. This modeling approach is useful to express the contextual information of a learning scenario. The main characteristics of this proposed approach, that will be more detailed thereafter, are: "multi-leveled", "scenario language-independent", and "multi-faceted" modeling of a scenario context enhanced by observation.

The forms of the scenario context vary during the phases of the engineering process of a learning scenario. This process is detailed in prior works [START_REF] Chaabouni | Indexing Learning Scenarios by the Most Adapted Contexts: An approach Based on the Observation of Scenario Progress in Session[END_REF]. So, we distinguish 3 levels of context related to a scenario as shown in Figure 1: the real usage context of the scenario during its implementation phase (ECM-LS: Effective Context Model of Learning Scenario), the contextual index of the scenario at its indexing phase (ICM-LS: Indexed Context Model of Learning Scenario) and the context of the scenario that is planned during the design phase (PCM-LS: Planned Context Model of Learning scenario). The context is formalized independently from the scenario language. So the context modeling approach is not restricted to a specific scenario's language or formalism. The contextual elements related to a learning scenario are diverse. They can be seen from didactic dimension, educational, social, technical, etc. As illustrated in the meta-model of the context in Figure 2, we opt for a multifaceted modeling ("EContext_Facet") of contextual elements ("EContext_Item"). Assessments ("EAssessment") can be assigned to the context items. The form of an assessment differs depending on the phase in which the context is instantiated and modeled. Some assessments of the context of the index may represent constraints ("isAConstraint()" operation) on the reuse of a learning scenario such as the presence of a learner pre-requisite skill or a material resource for fulfillment of the scenario. Other assessments represent characteristics ("isACharacteristic()" operation) describing the context of the scenario and which the looseness don't constrain the reuse. For example, the collaboration level indicator calculates the level of the collaboration between learners perceived in the activities "Lab work" (see Act1.2.2 in Figure 3) and "Peer Review Exercise" (see Act1.3.2 in Figure 3). For instance, the indicator needs as function inputs the traces about the number of messages sent by each learner during a chat session. This indicator can additionally inform the teacher about some identified context elements. This would inform the teacher if the "Peer Review pedagogical practice (see CE2 in Figure 4) has succeeded and if the learners have collaborated with this type of practice. So, the presented meta-model is instantiated to lead uniformed and structured context models of a scenario that are, at the same time, adapted to the community of usage. Figure 3 shows an example of a learning scenario. This example has been extracted form the BASAR base. The Figure 4 is an example of an associated ECM-LS shown both in graphical and JSON notation. "materialRessources":[ { "ref":"RESS_M_PC", "label":"PC", "id": "001-PC", "model": "HP", "processor": "Inel I5" },{ "ref":"RESS_M_SMART", "label":"Smartphone", "id": "005-SMART", "OS-system": "iOS", },{ "ref":"RESS_M_INTW", "label":"Interactive whiteboard", "id":003-INTW]} .... }} In order to use the presented contextual models enriched with indicators for indexing purposes and then for reuse, it is needed to filter/identify the elements that are relevant to indexing. This task is performed by teacher-designer who, with the system assistance, interprets the contextual model. The assistance is ensured through calculated indicators. The teacher-designer highlights the relevant elements to indexing and downgrades useless items. In order to illustrate this emphasis/downgrade, teachers attribute weights (see Weight_Index attribute in Figure 2) to the contextual elements.

After treating how we can represent the context of a learning scenario and how to build a contextual index of a scenario based on the observation of the progress of the scenario and its context, we present then how to use this contextual index to assist the reuse of the associated scenarios. So, the next section describes an algorithm calculating contextual similarities between learning scenarios.

Context-based similarity algorithm for learning scenario reuse

We have a set of Learning Scenarios LS ={LSi / i=(1..N)}. Each LSi is associated to one or more contextual indexes ICM ={ICMj / j=(1..M)}. In a ICMj index, each context element (i.e. pedagogical_learner_profile/competences, collaborative_modality, etc.) is associated with an evaluation represented as a weighted vector IC. So, let ICMj be a set of weighted vectors of different context elements valuations ICMj={ICk / k=(1..n)}. ICk takes as values the weights assigned by the teacher during the indexing phase. In addition, each ICMj is associated with a Success Rate (SRj) reflecting the success of the concerned scenario LSi in this indexed context ICMj. In a situation where designers want to reuse existing scenarios, they express the planned contexts in which they expect to execute their scenarios. This planned context is presented by PC vectors. The algorithm, detailed below, calculates the similarity between the Planned Context Model (PCM) and each contextual index (ICMj) associated with different stored learning scenarios (LSi). The algorithm is based on the weighted DICE similarity [START_REF] Jousselme | Distances in evidence theory: Comprehensive survey and generalizations[END_REF].

Input

Similarity(IC k ,PC l )= SR ! × ! !! ! × !! ! ! 1.3.2.
Calculation of similarities Average in the tree to retrieve global similarity value: Similarity(ICM i ,PCM) 1.4. If Similarity(ICM i ,PCM) >= MinTh then Add LS i corresponding to ICM i to the L list 2. Return L List

An authoring tool to assist the reuse of adapted learning scenarios

The identified levels of the scenario context and the presented similarity algorithm have been implemented and integrated into an authoring tool named "CAPtuRe-tool" (Context-based APproach to assist educational scenarios Reuse) addressed to teachers-designers. This tool is principally conceived to assist the teacher-designer in the scenario reuse task. Firstly, the tool helps designers in retrieving the most relevant scenarios to a planned learning situation, and so to enhance the learning scenario reuse. The teacher informs its planned context (PCM-LS) in which the scenario will be implemented through the form (see "Inform my context" part of Figure 5). The form shows the multidimensionality of the context model. This planned context is also enriched by data from other sources such as universities databases, location sensors, etc. After executing the similarity algorithm, the tool identifies and suggests interactively the existing scenarios having been indexed by the most similar contexts ICM-LS to the planned context (see "Reuse scenarios" part of Figure 5). The CAPtuRe-tool is integrated with the "Scenario Basar" tool enabling the design of learning scenarios.

Figure 5. Interface of managing planned context and scenario retrieval in the CAPtuRe-tool Parallel to the design, the teacher plans the observation through selecting and specifying the indicators to be calculated during the execution of the scenario. These indicators help the teacher to observe the context and to perceive the success of the scenario in this specific context.

Results and conclusion

During the setting up of the exposed approach, and in order to highlight the need of reuse, a first phase of controlled experiments has been performed with teachers placed in design situations without having a tool assisting the scenarios reuse task. Results have been collected through an online survey diffused for BASAR designers. In this usage case, the survey demonstrates that, during the design phase, 80% of teachers did not reuse existing scenarios from any scenario's repository and 92.3% did not reuse scenarios from the BASAR base especially. The main reason of the non-reuse is "after research, I didn't find the appropriate scenario" with a percentage of 51.1%. In addition, 57.1% of participants confirm a need of reuse, with, on the other hand, 42.9% expressing that they did not feel the necessity of reusing scenarios. This analysis reveals the importance of reuse and confirms the need of assisting teachers-designers in the scenarios reuse task.

Then, in order to validate contextual model data and the presented similarity algorithm, we firstly start by the analysis of the existing BASAR scenarios (currently 106 scenarios) and the extraction of the associated context of each one. We complement these contextual data through the establishment of a survey addressed to BASAR designers. This survey allowed us to collect complementary context information in which the scenarios were effectively executed, and which is not available in the existing scenarios (learners and teacher's competences and specialties, environmental and technical constraints required for the scenario execution, geographic location of learners and teachers, etc.). Therefore, we construct, from the collected data, the associated contextual indexes (ICM-LS) to enrich existing BASAR scenarios. We proceed then to different simulations of planned contexts (PCM-LS) through the implemented tool.

To conclude, we have firstly proposed in this paper a representation formalism of a learning scenario context in different phases (Planned time -execution time -indexing and capitalizing time) and the main characteristics of the adopted approach. Based on this representation, we have then defined an approach of indexing a learning scenario with its contextual dimension. The idea is to consider the user experience to index the scenario with contexts having been the most adapted to this scenario. This is performed by observing the scenario progress through pedagogical indicators calculating and analyzing the success of the scenario in a given context. An algorithm of context-based similarity is then illustrated calculating the similarities between a planned context in a learning situation and contextual indexes associated with learning scenarios. In order to concretize the proposed approach and the context-based similarity algorithm, the tool "CAPtuRe-tool" has been presented. In a situation of pedagogical design by reuse, this tool suggests the scenario that can be the most adapted to the context of the learning situation. Finally, results are discussed through the simulations of usages of the implemented tool in controlled experiments performed by a group of teachers-designers.

Figure 1 .

 1 Figure 1. Positioning of a scenario, its context levels and related pedagogical indicators

Figure 2 .

 2 Figure 2. Meta-Model of the context of a learning scenario

Figure 3 .

 3 Figure 3. Example of a Learning Scenario (LS)

Figure 4 .

 4 Figure 4. Example of an Effective Context Model of a Learning Scenario (ECM-LS)

  -A set of N learning scenarios: LS -A set of M index instances and associated Success Rates: ICM, SR -A Planned Context: PCM -Min similarity Threshold: MinTh Output -A list L of the most relevant scenarios corresponding to the planned context PCM, and insuring a minimum similarity threshold MinTh Procedure 1. For each ICM i 1.1. Match correspondent elements and establish links between IC k vectors and PC l vectors valuations 1.2. In the PC l vectors, verify the presence of all index constraints (elements with the w=1 in IC k vectors) 1.3. If all index constraints are satisfied 1.3.1. For each matched IC k vectors and PC l vectors 1.3.1.1. Apply Dice similarity formula, reinforced by the success rate SR k associated to the given index:


Julie Falcon
email: julie.falcon@unil.ch

Pierre Bataille

Equalization or reproduction ? Long-term trends in the intergenerational transmission of advantages in higher education in France

, the inuence of social background on social destination does not necessarily declines linearly with educational level. Altogether, these ndings question the greater meritocratic nature of the labour market among the highly educated and call for more research to be undertaken on the inuence of non-meritocratic assets related to social background on the recruitment process and occupational career development.

Introduction

When Bourdieu and Passeron published their seminal book Les Héritiers in 1964, they revealed that "a senior executive"s son [was] eighty times more likely to enter a university than a farm worker"s son, and forty times more likely than an industrial worker"s son 1 " (Bourdieu and Passeron 1964 :11).

After the post-WWII educational reforms and in the context of the rst expansion of the educational system, the demonstration of the persisting salience of inequality in educational opportunity had farreaching consequences on French society. Further educational reforms were thus implemented in the following decades. One of the most recent striking metamorphoses of the French educational system has 1 University of Lausanne, NCCR LIVES, Switzerland 2 Université Libre de Bruxelles, METICES, Belgique been the second "democratisation" wave, which was initiated in 1985 with the political target to get 80% of an age class to reach the Baccalauréat 2 level by 2000. Although this target has not been reached, the share of Baccalauréat holders increased from 30% to more than 60% between 1985 and 2006 in France [START_REF] Ichou | Do All Roads Lead to Inequality ? Trends in French Upper Secondary School Analysed with Four Longitudinal Surveys[END_REF]. Moreover, access to tertiary education has opened up to students from traditionally underrepresented social backgrounds [START_REF] Poullaouec | Retours sur la seconde explosion scolaire[END_REF], even though the educational career patterns of these second "democratisation" children diers from that of most of graduates with a higher social background [START_REF] Hugrée | Le CAPES ou rien ?[END_REF]. Thus, more than fty years after the publication of Les Héritiers the French educational landscape has been totally modied. The extent to which these

Research background

The role of education on intergenerational social mobility Comparative social mobility research has identied two main mechanisms through which education can increase social uidity [START_REF] Breen | Explaining Change in Social Fluidity : Educational Equalization and Educational Expansion in Twentieth-Century Sweden[END_REF].

First, the so-called equalization eect suggests that the decreasing association between social origin and educational attainment can foster social uidity. If inequality in educational attainment decreases, then social background should have a weaker inuence on individuals' allocation on the labour market. Second, the so-called compositional eect maintains that the inuence of social background on labour market outcome is weaker within higher levels of education, as labour market allocation would be more meritocratic among higher education graduates [START_REF] Hout | More Universalism, Less Structural Mobility : The American Occupational Structure in the 1980s[END_REF]. Given that an increasing share of the population is coming to hold a higher education degree as the education system expands, the overall level of social uidity is expected to correspondingly increase.

Empirical evidence widely supports the existence of these two mechanisms. An educational equalization trend has been documented in many Western countries [START_REF] Ballarino | Persistent Inequalities : Expansion of Education and Class Inequalities in Italy and Spain[END_REF][START_REF] Breen | Nonpersistent Inequality in Educational Attainment : Evidence from Eight European Countries[END_REF][START_REF] Breen | Long-Term Trends in Educational Inequality in Europe : Class Inequalities and Gender Dierences[END_REF]Shavit, Arum, and Gamoran 2007). Scholars have furthermore observed the existence of a lower association between social origin and social destination among higher education graduates in many nations [START_REF] Breen | Educational Expansion and Social Mobility in the 20th Century[END_REF][START_REF] Breen | Social Mobility and Education : A Comparative Analysis of Period and Cohort Trends in Britain and Germany[END_REF][START_REF] Falcon | Social Mobility in 20th Century Switzerland[END_REF][START_REF] Pfeer | How Has Educational Expansion Shaped Social Mobility Trends in the United States ?[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF]). However, despite these indications of evolution, education still remains the main vector of social reproduction : between half and three-quarters of intergenerational socio-economic association is mediated by education in Western countries (Ballarino and Bernardi 2016 :257 ; see also : Blau and Duncan 1967). Several mechanisms have been put forward to explain this phenomenon. According to the Maximally Maintained Inequality hypothesis [START_REF] Raftery | Maximally Maintained Inequality : Expansion, Reform, and Opportunity in Irish Education, 1921-75[END_REF], unless access to the highest educational level becomes universal, educational inequalities will remain maximally maintained, as privileged families will always take advantage of social class dierentials in educational attainment. The Eectively Maintained Inequality hypothesis [START_REF] Lucas | Eectively Maintained Inequality : Education Transitions, Track Mobility, and Social Background Eects[END_REF]) amends the previous hypothesis : even when access to the highest educational level increases and becomes almost universal, children from privileged families will essentially enrol into the most prestigious tracks of this educational level. In other words, when there is a reduction in quantitative inequality, qualitative inequality becomes more salient to ensure the intergenerational transmission of advantages.

Rational action theory provides a general framework to explain the persistence of educational inequality [START_REF] Boudon | L'inégalité des chances : la mobilité sociale dans les sociétés industrielles[END_REF][START_REF] Breen | Explaining Educational Dierentials. Towards a Formal Rational Action Theory[END_REF][START_REF] Goldthorpe | On Sociology Second Edition Volume Two : Illustration and Retrospect[END_REF]). This theory posits that individuals develop dierent educational strategies according to their social background. While it has been widely documented that the unequal distribution of resources among families of dierent social backgrounds translates into unequal academic performance at school (primary eect), working-class children tend to choose less demanding educational tracks than upper-class children even when both have the same level of academic performance (secondary eect). Thus, educational choices, as well as unequal academic performances, contribute to the persistence of educational inequality [START_REF] Jackson | Why Does Inequality of Educational Opportunity Vary across Countries ? Primary and Secondary Eects in Comparative Context[END_REF]. Along similar lines, despite poor academic performance, upper-class children are more likely to pass to the next educational level than working-class children with the same level of academic performance [START_REF] Bernardi | Compensatory Advantage as a Mechanism of Educational Inequality : A Regression Discontinuity Based on Month of Birth[END_REF]. This phenomenon, known as the social origin compensatory eect, clearly illustrates that the main concern of individuals when making educational decisions is the avoidance of downward mobility. [START_REF] Breen | Explaining Educational Dierentials. Towards a Formal Rational Action Theory[END_REF] see also : Goldthorpe 2007 :167) indeed argue that Preprint version individuals do not primarily seek to achieve upward social mobility, but rather to acquire a social position at least as favourable as their parents'. This phenomenon, which they coined relative risk aversion, constitutes according to them the main explanation of the persistence of educational inequality and social reproduction. To some extent, these theoretical explanations echo with the Bourdieusian tradition, which showed that to maintain a dominant position within the social structure, the upper class graduates build their educational choices as "reconversion strategies" of their inherited capitals [START_REF] Bourdieu | Les stratégies de reconversion[END_REF].

How education is rewarded on the labour market can also inuence social mobility. With educational expansion, a growing share of higher education graduates enters the labour market. Yet if the supply of higher education graduates exceeds the demand on the labour market, an "ination" of educational credentials is likely to occur [START_REF] Passeron | L'ination des diplômes[END_REF]. Empirical research indeed supports these claims, insofar as returns to education have decreased over time in several European countries [START_REF] Breen | Class, Mobility and Merit The Experience of Two British Birth Cohorts[END_REF][START_REF] Ganzeboom | Recent Trends in Intergenerational Occupational Class Reproduction in the Netherlands 1970-99[END_REF][START_REF] Goldthorpe | Trends in Intergenerational Class Mobility in Britain in the Late Twentieth Century[END_REF][START_REF] Jackson | Educational Fields of Study and the Intergenerational Mobility Process in Comparative Perspective[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF]).

As a consequence, some scholars sustain that educational attainment has become a less reliable signal in the recruitment process, whereas individual characteristics directly related to family background have become more crucial [START_REF] Breen | Class, Mobility and Merit The Experience of Two British Birth Cohorts[END_REF]. For instance, non-meritocratic characteristics such as appearance, self-presentation, savoir-faire, manners and accent seem to have gained importance when it comes to reaching certain top occupations [START_REF] Jackson | Education, Employers and Class Mobility[END_REF]. Further research also qualied Hout"s (1988) statement, which claims that allocation on the labour market is systematically more meritocratic among higher education graduates. [START_REF] Torche | Is a College Degree Still the Great Equalizer ? Intergenerational Mobility across Levels of Schooling in the United States[END_REF][START_REF] Torche | Education and the Intergenerational Transmission of Advantage in the US[END_REF] documented the existence of a nonlinear decreasing pattern in the association between social origin and social destination across levels of education in the United States. She observed a U-shape pattern, wherein the inuence of social background on labour market outcome linearly weakened up to the level of bachelor degree holders and increased among advanced degree holders. A recent study on the UK found some hints towards similar pattern among postgraduate degree holders (Wakeling and Laurison, 2017).

Thus, empirical evidence as to the equalization and meritocratic power of education is quite contrasted.

From this standpoint, we investigate this issue in the French context.

Between universalism and selection : the French educational system Despite its important expansion since the middle of the 20th century, the French educational system has remained highly stratied 4 (see Figure 1). After four years at the collège, the comprehensive and unied rst part of secondary school in France, pupils either The persisting co-existence in France of "small, specialized and highly competitive schools" with "the universities [that] are large and ever growing, and (...) not selective" (Suleiman 1977 : 192) can sound surprising in an era of higher education "democratisation" [START_REF] Beaud | 30 % de boursiers en grande école[END_REF]. However, this idiosyncrasy must be understood through the central role that the grandes écoles play in the training of the elite in France. Historically, the grandes écoles developed Preprint version

Secondary education Tertiary education

after the French Revolution with the goal to train a "meritocratic" elite selected on competence criteria that would be loyal to the state and not based on aristocratic endowmentsat that time there existed a strong political mistrust towards universities, which were closely linked to religious authorities [START_REF] Bourdieu | La noblesse d'Etat : Grandes écoles et esprit de corps[END_REF].

Sociological studies have suggested that the grandes écoles could be considered as an "elite production machine" [START_REF] Darmon | Classes préparatoires. La Fabrication d'une jeunesse dominante[END_REF][START_REF] Eymeri | La fabrique des énarques[END_REF], with the underlying idea that these institutions would have the "power" to erase individual dierences [START_REF] Bataille | [END_REF].

This machine has indeed worked quite well, as most of the French economic, political and academic elite was trained in a grande école [START_REF] Bourdieu | La noblesse d'Etat : Grandes écoles et esprit de corps[END_REF]. Still today, and despite the internationalization of the elite recruitment, having graduated from a grande école constitutes a major asset to attain highly prestigious positions in France [START_REF] Denord | Le champ du pouvoir en France[END_REF]. For all these reasons, the grandes écoles enjoy a high degree of symbolic capital in France [START_REF] Bodin | Les mécomptes du supérieur -Autres Écoles, autres Établissements et autres Formations[END_REF], although over the past couple of decades there has been intense debate in France as to how to increase the social diversity in the student body of the grandes écoles (Van Zanten 2010), as it is widely believed that these institutions constitute an "elite reproduction machine".

Previous research on France and limitations

Research on intergenerational social mobility in

France has documented a general increase in observed social mobility as well as in social uidity over time [START_REF] Peugny | Éducation et mobilité sociale : la situation paradoxale des générations nées dans les années 1960[END_REF][START_REF] Vallet | Quarante annÉes de mobilite sociale en france : l'évolution de la uidité sociale a la lumiere de modeles récents[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF]Vallet , 2017)).

Both equalization and compositional eects have contributed to this evolution [START_REF] Bouchet-Valat | Inequality of Educational Returns in France. Changes in the Eect of Education and Social Background on Occupational Careers[END_REF][START_REF] Breen | Nonpersistent Inequality in Educational Attainment : Evidence from Eight European Countries[END_REF][START_REF] Breen | Long-Term Trends in Educational Inequality in Europe : Class Inequalities and Gender Dierences[END_REF][START_REF] Thélot | La réduction des inégalités sociales devant l'école depuis le début du siècle[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF]Vallet , 2017 ; ;Vallet and Selz 2007). In a recent study, Vallet (2017) We furthermore restrict our analysis to individuals between 30 and 64 years old 9 who were not studying at the time of the survey and who were born in France.

As we have already highlighted, social change is more likely to occur through cohort replacement ; therefore, we pool the data together and divide the pool into 11 birth cohorts : 1918-1929 ; 1930-1939 ; 1940-1944 ; 1945-1949 ; 1950-1954 ; 1955-1959 ; 1960-1964 ; 1965-1969 ; 1970-1974 ; 1975-1979 ; 1980-1984. We provide detail on the construction of the cohorts in Table A1 in

Log-linear models

In addition to descriptive statistics, we apply loglinear models to assess whether the changes observed in

French society are driven solely by structural changes.

Through the odds ratio statistic, log-linear models 10 allow capturing the association between two or more variables, net of their structural distribution. Applied to the analysis of intergenerational social mobility, "[this method] tells us something about the advantages and disadvantages associated with being born into one class rather than another" (Breen 2004 :20).

In this article, our main concern is to adjust two types of models to the data, namely the constant association model, which assumes for instance that the association between social origin and educational attainment has remained stable over time, and the uniform dierence model (Unidi, see : Erikson and Goldthorpe 1992 ; Xie 1992), which posits that this same association varies log-multiplicatively according to a third variable, such as birth cohort. This model shows whether educational inequality changed across cohorts. Moreover, to thoroughly assess the signicance of a given Unidi trend, we furthermore tted some

Unidi models where we imposed equality constraints on some Unidi parameters. Because of the large sample size of the data, we assess model t with the BIC statistic rather than with conventional statistical testing. However, it must be underlined that "using BIC generally leads to a preference for simple models that reect the broad contours, rather than the details, of the social uidity regime" (Breen, 2004 :27).

Analysis

We rst outline how access to higher education changed across cohorts, then we assess through log-linear models whether observed changes remain signicant net of structural changes.

Descriptive changes in the expansion of higher education across cohorts

Over less than a century, access to higher education in France has greatly opened. While only 7% of men and 4% of women born between 1918 and 1929 reached higher education, for cohorts born between 1980 and 1984 these shares have increased to 40% and 51%, respectively (see Figure 2). These shares underline the existence of a reversed gender gap in access to Access to the grandes écoles has also risen from 3% to 7% for men, and from 0.2% to almost 5% for women across cohorts. Thus, at this level no reversed gender gap is uncovered.

To analyse the evolution of inequality based on social background, we calculated in Table 1 the odds ratios However, in relative terms inequality in access to higher education did decrease across cohorts overall in France.

Relative trends in the intergenerational transmission of advantages across cohorts

To estimate whether the intergenerational transmission of advantages changes across cohorts net of structural changes, we look at the statistical association between social origin, educational attainment and social class destination and their variation by cohort.

We rst test whether there has been any change in the association between social background and educational attainment to assess whether we observe a decrease in educational inequality in France. We use dierent combinations of the educational variable to see whether educational inequality has evolved at a dierent pace across cohorts. First, we model this association using the full detail of our educational variable ; second, we look at this association between all graduates of higher education versus all others ; third, between graduates of at least mid-tertiary education versus all others ;

fourth, for those who graduated from upper tertiary education versus all others ; and fth, for those who graduated from a grande école versus all others. Loglinear models are reported in Table A2 in the Appendix. We reported in Figure 3 the corresponding Unidi parameters for each combination of the educational variable.

For each set of models tted, the BIC statistic

indicates that the Unidi model should be preferred over the constant association model. This implies that there has been some change across cohorts in the association between social background and educational attainment. Unidi parameters indicate that this association has decreased quite linearly across cohorts for men and women. This trend has been more pronounced for women than for men.

Unidi parameters show that inequality of educational

Preprint version Note : odds ratios with a * indicate that they were calculated with a sample size of less than 10 individuals in one group opportunity globally decreased even within the highest educational levels (upper tertiary and grandes écoles).

We can identify three phases in the opening process of the two highest educational levels of the French educational system : rst an opening up to cohorts born in the 1940s, followed by a relative stability for subsequent cohorts ; then nally, another opening trend for cohorts born from the 1960s and from the 1970s respectively at the upper tertiary level and among the grandes écoles.

We then analyse the three-way interaction between social origin (O), educational attainment (E) and social class destination (D) to assess whether the association between social origin and social class destination (henceforth OD association) weakens within higher educational levels (see models tted in Table A3).

As can be seen from Figure 4 [START_REF] Torche | Is a College Degree Still the Great Equalizer ? Intergenerational Mobility across Levels of Schooling in the United States[END_REF][START_REF] Torche | Education and the Intergenerational Transmission of Advantage in the US[END_REF]. We subsequently tested whether we could improve the model by imposing equality constraints on some Unidi parameters, in order to assess the degree of the robustness of the observed U-shape trend (see models M3a-d in Table A3). On the basis of the BIC statistic, models M3a and M3b, respectively for men and women, should be preferred. This indicates that the U-shape trend is not particularly sharp for men, while for women it is, although the Unidi parameter for the grandes écoles is not markedly dierent from the one for upper tertiary education. While reasons for these gender dierences remain unclear, it seems on the one hand that mid-tertiary education constitutes among women a particularly great equalizer. This could pertain to the fact that this female-dominated educational level (see Figure 2 A3) and to cohort (right panelmodel M4 from Table A3).

Last but not least, insofar as recent research reported that the OD association decreases with age (Vallet 2017), we ran a last set of models on the three-way

Discussion and Conclusion

More than fty years after the publication of Les Héritiers by Bourdieu and Passeron (1964) and since the second expansion of the educational system initiated in the mid-1980s, access to education has been considerably democratized in France. We demonstrate that social background inequality in terms of access to higher education has clearly diminished. Through the analysis of eleven birth cohorts born between 1918 and 1984, we document that the disadvantage associated with being from the working class rather than from the upper class in graduating from higher education dropped across cohorts. This is a clear indication that higher education has opened up to individuals originating from the lowest social backgrounds. This decrease in educational inequality is also conrmed through the analysis of the data with log-linear models.

It furthermore holds for the highest educational levels, such as upper tertiary education (5 years or more of study after baccalauréat) and the highly selective and elitist grandes écoles. This is an important nding given that it was previously reported that the democratization of the access to the grandes écoles had come to a halt [START_REF] Albouy | Les inégalités sociales d'accès aux grandes écoles[END_REF]. With more

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recent data, we show that this democratization trend restarted from cohorts born in the 1970s.

This opening trend of the grandes écoles must however be understood in the light of the restructuration of the educational market since the 1980s in France. Indeed, over the past decades the denition of the grandes écoles has become to some extent more blurred, even within the ocial statistic (Bodin and Orange 2016), insofar as there has been a growth in the share of small higher education institutions, especially in the eld of business and engineering, which have been recognized as grandes écoles because they select their student on the basis of a contest and/or previous grades. These institutions, which are less prestigious than the classical grandes écoles, may oer more opportunities to students from lower social background compared to the classical grandes écoles.

The observed democratisation trend may thus be smaller when distinguishing more nely between the dierent types of grandes écoles as well as between dierent elds of study.

We also nd that, unlike previous assertions [START_REF] Hout | More Universalism, Less Structural Mobility : The American Occupational Structure in the 1980s[END_REF], the inuence of social background on social destination does not linearly declines with educational level. As previously demonstrated by [START_REF] Torche | Is a College Degree Still the Great Equalizer ? Intergenerational Mobility across Levels of Schooling in the United States[END_REF][START_REF] Torche | Education and the Intergenerational Transmission of Advantage in the US[END_REF] in the US, we observe a U-shape pattern in the association between social origin and social destination across levels of education. While this Ushape pattern is not particularly sharp for men, these ndings underlines at least that within the highest educational levels labour market allocation is not as meritocratic as could be expected. Furthermore, insofar as this U-shape trend is more pronounced among women, it seems that highly educated women 2. This is the end of a high school degree in France.

3. Social uidity is the relative measure of intergenerational social mobility.

4. We only outline here the main features of the French educational system. For a more thorough introduction about the French educational system and its reforms across the 20th century, see [START_REF] Kieer | Applying the ISCED-97 to France : Some Issues and Propositions[END_REF].

5. For a more detailed introduction to the grandes écoles, see Van Zanten and Maxwell (2015).

6. A new survey was conducted in 2015, but the data was released after this analysis was performed.

7. This is the "3b" CASMIN category (see for instance [START_REF] Bouchet-Valat | Inequality of Educational Returns in France. Changes in the Eect of Education and Social Background on Occupational Careers[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF], which aggregates university degrees of 3 to 4 years, university degrees of 5 or more years, and grandes écoles degrees.

8. We would like to thank the "Quetelet network" for providing us these data.

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  go to lycée général or to vocational education and training. The lycée général prepares pupils to take the baccalauréat général, which grants access to tertiary education, whereas vocational education and training is designed to prepare them to enter the labour market. Yet those who pass a vocational or professional baccalauréat also have the opportunity to continue to tertiary education. Tertiary education in France is divided into three tracks : (1) the technical and vocational track, (2) the academic non-selective track and (3) the academic selective track. The technical and vocational track oers two to three years of applied trainings. For working-class students, these trainings are usually perceived as a path to reach intermediate occupations. The existence of two parallel tertiary education academic tracks constitutes a French specicity which clearly formalises the dierence between elitist and non-elitist institutions, respectively the grandes écoles 5 and universities. While admittance to the university in France is formally granted to anyone who holds any type of baccalauréat, access to the grandes écoles is highly selective. It is traditionally based on a national competitive examination considered a "meritocratic contest", the concours (Bourdieu 1989). Although theoretically, everyone can take the concours, in practice candidates need to follow a two-year intensive preparatory training called classes préparatoires aux grandes écoles (CPGE) to have a chance of gaining admission to a grande école. Access to this preparatory training is itself highly selective. Yet this preparatory training does not constitute a guarantee to access to a grande école, insofar as less than 5% of each generation graduates from a grande école. Those who fail to get into a grande école after this training usually pursue their education at the university (Beaud and Convert 2010).

Figure 1 :

 1 Figure 1: Overview of the French education system

  furthermore underlined that educational equalization was the main driver of increased social uidity for the1945-1954 cohort, Preprint version while educational expansion was the main factor for subsequent cohorts. He also uncovered that social uidity increases with age, suggesting that career mobility plays an important role on intergenerational social mobility in France.Further research however qualies to some extent these general conclusions. First, the democratization of the educational system has been unevenly distributed based on educational tracks.[START_REF] Ichou | Do All Roads Lead to Inequality ? Trends in French Upper Secondary School Analysed with Four Longitudinal Surveys[END_REF] have shown, for instance, that while inequality in rates of passing the baccalauréat in relation to social background decreased across cohorts, inequality was actually maintained when distinguishing between the dierent types of baccalauréat. Along similar lines, some studies have shown that, after a small opening trend, social selectivity in the access to the grandes écoles has increased in recent years[START_REF] Albouy | Accès à l'enseignement supérieur en France : une démocratisation réelle mais de faible ampleur[END_REF][START_REF] Albouy | Les inégalités sociales d'accès aux grandes écoles[END_REF][START_REF] Duru-Bellat | Patterns of Social Inequalities in Access to Higher Education in France and Germany[END_REF]. Second, returns to education have weakened[START_REF] Bouchet-Valat | Inequality of Educational Returns in France. Changes in the Eect of Education and Social Background on Occupational Careers[END_REF][START_REF] Vallet | Change in Intergenerational Class Mobility in France from the 1970s to the 1990s and Its Explanation : An Analysis Following the CASMIN Approach[END_REF], and downward social mobility has increased over time[START_REF] Peugny | Éducation et mobilité sociale : la situation paradoxale des générations nées dans les années 1960[END_REF][START_REF] Peugny | Le destin au berceau. Inégalités et reproduction sociale[END_REF]. Third, the direct eect of social origin on social destination also increased over time[START_REF] Bouchet-Valat | Inequality of Educational Returns in France. Changes in the Eect of Education and Social Background on Occupational Careers[END_REF].[START_REF] Ichou | Academic Achievement, Tracking Decisions, and Their Relative Contribution to Educational Inequalities[END_REF] furthermore reported an increase in the relative importance of primary eect between individuals born in 1951 and those born in 1984, insofar as the heterogeneity in terms of social background prole of those who reach the next educational transition has increased with educational expansion. Thus, empirical evidence suggests that the opening of French society through increasing social uidity may have come to a halt. However, most studies on intergenerational social mobility in France were conducted using a period approach and data from the Formation et Qualication Professionnelle (FQP) survey, which was last conducted in 2003 6 . As a consequence, those studies may not fully capture recent evolutions in the intergenerational transmission of advantages. Indeed, not only is change more likely to occur through cohort replacement than through period change(Breen and Jonsson 2007 :1805), but also the data do not allow assessing opportunities of cohorts who entered the labour market since the new millennium. Last but not least, those studies have also often failed to nely isolate some educational boundaries, especially at the level of higher tertiary education7 . This research aims to address these limitations and thus extend knowledge as to the development of intergenerational social mobility in France. For this purpose we analyse the evolution of the relationships among social background, educational attainment and social class destination with a unique study design. Methodology Data, population and sample size We use the French Labour Force Surveys (henceforth FRLFS) 8 for the period 1982-2014 to undertake our analysis. The FRLFS collects information on respondents" social background, measured through father"s occupation, since 1982. It was originally conducted annually and since 2003 has been carried out every quarter by the INSEE, the French national statistical oce. This survey displays a high degree of continuity in the measurement of indicators over time, as its design and questionnaire have only been modied twice since 1982, in 1990 and in 2003. The FRLFS has a large sample size and is designed in the form of a rotating panel : every household is interviewed six times (three times before 2003). Thus, we only select individuals during their rst interview to ensure that we do not analyse the same individual twice.

  the Appendix. In the end, we reach a sample size of 754,611 individuals and use the weighting variable designed for rst interview respondents, which we adjusted to the sample size for the model estimation.IndicatorsSocial class destination and social origin are measured through the EGP class schema[START_REF] Erikson | The Constant Flux : A Study of Class Mobility in Industrial Societies[END_REF]. We used the coding procedure outlined byBouchet-Valat (2015 :52021) based on the French occupation codes. We grouped classes into seven categories : higher service class (I), lower service class (II), higher white collar (IIIa), petite bourgeoisie (IVab), farmers (IVc), skilled workers (V+VI), and lower white collar and semi-/unskilled workers (IIIb+VIIab). We also used a collapsed version of this class schema into three categories to distinguish the upper class (I+II), the intermediate class (IIIa, IVabc,), and the working class (V+VI, IIIb+VIIab).Preprint versionEducational attainment is coded into seven categories, which nely distinguish dierences in higher education : less than baccalauréat, baccalauréat, lower tertiary vocational (2 years of study after baccalauréat), lower tertiary general (2 years of study after baccalauréat), mid-tertiary (3 to 4 years of study after baccalauréat), upper tertiary (5 years or more of study after baccalauréat), and grandes écoles.

  higher education, a trend widely documented for many Western countries (DiPrete and Buchmann 2013). All educational levels have seen their share increasing, with the exception of the lower tertiary general level, which has never represented more than 3% and has fallen below 1% in the 1980-84 cohort. Almost half of the educational expansion of higher education has been driven by lower tertiary vocational degrees. More advanced higher education levels have also contributed to this trend, notably through mid-tertiary university degrees. The share of upper tertiary degree holders has also increased, particularly for people born since 1975.

  of reaching each higher education level for the upperclass compared to the working-class and intermediateclass backgrounds. We observe that across cohorts the gap between social backgrounds decreased within each higher education level. While in the 1918-29 cohort, someone from the upper class was 17 times for men and 21 times for women more likely to graduate from higher education than someone from the working class, in the 1980-84 cohort this upper-class advantage had dropped to less than 6 times more likely for both men and women. In particular, at the level of lower tertiary vocational education, social background inequality almost disappeared : upper-class men only have a 1.3 times larger chance than working-class men to graduate from this educational level. However, within other educational levels, there still remains important social background inequality. People from upper-class backgrounds are in the 1980-84 cohort about twice as likely to graduate from mid-tertiary education, upper tertiary education or a grande école than people from intermediate class backgrounds. This gap is bigger between the upper class and the working class : a person from the upper class is 5 times more likely to graduate from upper tertiary education or a grande école than a person from the working class. Thus, while there has been an overall improvement Preprint version

Figure 2 :

 2 Figure 2: Trends in educational expansion across cohorts for men and women

  (left panel), while the intergenerational transmission of advantages weakens linearly until mid-tertiary education, it then reinforces for holders of an upper tertiary degree and of a Preprint version

Figure 3 :

 3 Figure 3: Unidi parameters for the association between social background and educational attainment across cohorts

  ) tends to lead to female dominated occupations from the service sector (school teacher, nurse, civil servant, etc.) in which social background assets are less important. On the other hand, these ndings tend to indicate the existence of a glass ceiling based on social background among women, insofar as highly educated women from an intermediate or working class background seem to face greater obstacles in reaching top-level positions, compared to highly educated women from the upper class.In a further set of models, we tested whether the Ushape trend increased or decreased across cohorts. For model simplication, the cohort variable was collapsed into three categories. The right panel of Figure4displays Unidi parameters for the interaction between education and cohort (model M4). We observe some important variations in the OD association according to level of education across cohorts, although according to the BIC statistic we should reject this model in favour of the simpler model without Unidi variation across cohorts (model M3). Therefore, to assess for each educational level the degree of robustness of variations across cohorts, we imposed equality constraints on Unidi parameters for cohorts (models M5-11abcd). We observe a marked increase in the OD association across cohorts among some educational levels, especially for the baccalauréat (M6d for men and M6a for women), lower tertiary vocational education for women (M7a), and mid-tertiary education for men (M9b). However, we nd no strong evidence that the U-shape trend increased across cohorts, although in the oldest cohort of men the U-shape pattern was particularly large.Preprint version

Figure 4 :

 4 Figure 4: Unidi parameters for variation in the association between social origin and class destination according to educational attainment (left panelmodel M3 from TableA3) and to cohort (right panelmodel M4 from Table

  from an intermediate or working class background face greater obstacles in reaching top-level positions. In other words, our study suggests that among highly educated women in France there exists a glass ceiling based on class background. Altogether, these ndings should invite both scholars and policymakers who address the issue of the intergenerational transmission of advantages to pay more careful attention to how non-educational assets are used to maintain social class advantages, especially on the labour market (Jackson et al. 2005). While educational equalization constitutes one way to achieve equality of opportunity, what happens during the occupational trajectory largely remains a black box. The recent study from Rivera (2016) on elite recruitment clearly sets an example in this respect. Because, despite a clear equalisation trend in access to the highest educational levels in France, educational merit remains better rewarded on the labour market among the better o. Notes 1. This quote is from the translated version of their book in English by Richard Nice (on page 2), which was published in 1979 by the University of Chicago Press.

9 .

 9 30 years old on the one hand to reduce career mobility bias and 64 to reduce mortality bias based on social class. 10. Due to space limitations, we cannot present this modelling technique in detail. Those interested in this method can however read Breen (2004) as well as Falcon (2013 :12131).11. The age variable was grouped into three categories :30-39 ; 40-49 ; 50-64.

7 Note:

 7 Cond. Ind. = conditional independence model ; Const. Ass. = constant association model ; Unidi = uniform dierence model. Df = degree of freedom, L2 = deviance, DI = dissimilarity index, BIC = Bayesian information criterion.

Table 1 :

 1 Odds ratios of reaching higher education between people of upper-class and working-class origins and

	between upper-class and intermediate origins
		1918	1930	1940	1945	1950	1955	1960	1965	1970	1975	1980
		-	-	-	-	-	-	-	-	-	-	-
		1929	1939	1944	1949	1954	1959	1964	1969	1974	1979	1984
	Odds ratio : upper class origin versus working class origin
	Higher education (all levels together)
	Men	17.2	13.8	10.1	8.8	8.8	8.4	7.1	6.6	5.5	5.0	5.3
	Women	21.5	15.2	10.5	9.6	9.2	7.9	6.8	5.9	5.9	4.8	5.3
	Lower tertiary vocational
	Men	7.2	5.1	3.4	2.9	2.9	2.9	2.6	2.2	1.6	1.3	1.3
	Women	19.7	10.8	7.6	4.6	4.0	3.2	2.8	2.0	1.6	1.2	1.1
	Lower tertiary general
	Men	6.4	4.7	2.4	2.3	3.3	4.0	3.7	3.2	2.5	2.1	1.6
	Women	5.8	4.6	3.5	3.1	3.1	3.5	3.7	2.8	1.9	0.9	0.5*
	Mid-tertiary
	Men	12.3	9.3	5.3	5.2	5.9	5.0	4.9	3.6	3.0	3.0	2.9
	Women	50.4	22.0	9.8	8.2	7.9	5.9	4.5	3.5	2.9	2.1	2.9
	Upper tertiary
	Men	18.2	14.0	10.2	10.6	11.5	9.5	7.2	6.3	6.1	5.8	5.8
	Women	48.2	30.5	11.2	12.7	12.0	11.7	8.6	8.2	6.1	6.4	5.2
	Grandes écoles
	Men	14.1	11.7	10.5	7.8	7.8	8.4	8.6	7.9	6.4	4.9	4.8
	Women	48.2*	16.2	22.5	12.8	14.4	11.5	10.2	7.8	6.9	5.7	5.5
	Odds ratio : upper class origin versus intermediate class origin
	Higher education (all levels together)
	Men	8.9	8.4	5.6	5.3	5.0	4.5	3.9	3.7	3.2	2.7	2.7
	Women	7.9	7.1	5.7	4.9	4.4	4.1	3.5	3.1	3.2	2.9	2.5
	Lower tertiary vocational
	Men	4.5	4.0	2.4	2.2	2.0	1.8	1.6	1.3	1.1	1.0	0.8
	Women	6.5	5.8	4.2	2.8	2.1	1.9	1.7	1.3	1.1	0.9	0.9
	Lower tertiary general
	Men	3.2	3.3	1.7	2.0	2.4	2.4	3.0	2.5	1.7	1.6	2.8*
	Women	3.6	2.7	2.4	1.9	1.9	2.1	2.1	1.8	1.9	1.0	0.8*
	Mid-tertiary
	Men	6.1	5.0	3.6	3.2	3.4	3.0	2.8	3.0	2.4	1.8	2.6
	Women	8.4	8.2	5.0	4.3	4.0	3.3	2.7	2.1	1.8	1.6	1.5
	Upper tertiary
	Men	9.9	7.4	4.8	5.6	5.3	5.4	3.8	3.3	3.3	3.1	2.3
	Women	8.0	9.1	5.9	5.3	5.1	5.3	3.8	3.9	3.0	3.9	2.5
	Grandes écoles
	Men	7.6	7.3	5.0	3.8	3.9	3.9	4.1	4.0	2.8	2.3	2.5
	Women	18.3	8.1	4.5	5.1	4.1	4.6	4.7	3.2	2.8	2.0	2.0

  OED mobility table across age 11 categories (see TableA4in Appendix). While we nd some signicant eect of age, with a lower OD association among the two oldest age groups, controlling for a Unidi trend on the

	OD association across age, does not alter the Unidi
	trend across educational levels (see M5). Our ndings
	are thus robust, even after controlling for age eect.
	From this standpoint, despite a clear reduction of
	educational inequality, this analysis underlines that the
	intergenerational transmission of advantages does not
	systematically weaken with level of education.

Table A2 :

 A2 Log-linear models for the association between social origin and educational attainment

		Men				Women
	Model	DF	L2	DI	BIC	DF	L2	DI	BIC
	All educational levels
	M1. Cond. Ind.	396	59229.8.	13.2	54155.3	396	59682.5	13.0	54592.2
	M2. Const. Ass.	360	2245.4	2.0	-2367.7	360	2705.5	2.2	-1922.1
	M3. Unidi	350	1953.0	1.9	-2535.0	350	1985.2	1.8	-2513.8
	Higher education
	M1. Cond. Ind.	66	42100.7	10.6	41255.0	66	40338.1	10.1	39489.7
	M2. Const. Ass.	60	1224.4	1.4	455.5	60	1213.4	1.5	442.2
	M3. Unidi	50	389.4	0.7	-251.3	50	475.0	0.8	-167.7
	Mid-tertiary education or more
	M1. Cond. Ind.	66	36206.6	8.1	35360.9	66	29407.8	6.7	28559.4
	M2. Const. Ass.	60	666.0	0.9	-102.9	60	1084.7	1.1	313.5
	M3. Unidi	50	162.1	0.4	-478.6	50	276.5	0.5	-366.2
	Upper tertiary degree
	M1. Cond. Ind.	66	12880.3	2.9	12034.6	66	12585.3	2.7	11736.9
	M2. Const. Ass.	60	336.1	0.4	-432.8	60	510.5	0.5	-260.8
	M3. Unidi	50	96.5	0.2	-544.3	50	194.9	0.3	-447.8
	Grande école degree
	M1. Cond. Ind.	66	14376.6	3.4	13531.0	66	5409.0	1.2	4560.6
	M2. Const. Ass.	60	398.7	0.5	-370.2	60	258.4	0.2	-512.8
	M3. Unidi	50	175.9	0.3	-464.8	50	126.0	0.1	-516.

Table A3 :

 A3 Log linear models for the three-way interaction between social origin, educational attainment and social class destination across birth cohorts

		Men					Women
	Model	DF L2	DI	BIC	DF	L2	DI	BIC
	Table cohort origineducationdestination (COED)

European sociological review (online rst), pp.

Europe, edited by R. Breen. Oxford : Oxford University Press. Vallet, L.-A. (2017). Mobilité sociale entre générations et uidité sociale en France. le rôle de l'éducation.

Revue de l 'OFCE, 150, 141. Vallet, L.-A. and Selz, M. (2007). Évolution historique de l'inégalité des chances devant l'école : des méthodes et des résultats revisités. Éducation & Formations, 74(1), 6574. Van Zanten, A. (2010)

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European sociological review (online rst), pp.


Marc Perrenoud
email: marc.perrenoud@unil.ch

Pierre Bataille

This article deals with the life and careers of ordinary musicians in France and Switzerland. These musicians are neither rich nor famous but represent the large majority of the occupational group. After presenting the methodology of our French and Swiss surveys, we show the importance of the national context in shaping the bundle of tasks which denes the job of a musician. We then compare the dierent types of careers and the dierent ways of being a musician in the two countries.

Introduction

Recent publications have underlined how national policies shape the various developments of popular music in each specic socio-historical context, even during the era of the triumph of globalization and the so called abolition of national boundaries (Cattermole, Cloonan & Homan). In line with these works, this article shows how national employment policies are a key issue in the analysis of musical labour and in understanding the various ways of being a musician among popular music players in contemporary societies, especially for those located at the grassroots level of the professional hierarchy.

Thus this article is about musical work, musical employment, and musicians' careers. Its empirical focus is a comparison between France and Switzerland, two countires which are very close geographically and culturally, and share a common language within the French-speaking part of Switzerland. It addresses the life and work of ordinary musicians (Perrenoud, Les musicos ; Faulkner and Becker), people who are neither rich nor famous, but make a living as musicians at the lower stages of the professional pyramid. While such musicians are often less visible in the public eye, they are also by far the most numerous.

1 University of Lausanne, LACCUS, Switzerland 2 Université Libre de Bruxelles, METICES, Belgium Our work combines the study of social dispositions and of symbolic interactions in a constructivist and empiricist approach. We address various issues such as the construction of a professional/occupational identity from material and symbolic resources (economic, social and cultural capital) and from the bundle of tasks (Hughes) dening the job of ordinary musicians, the structure of the job market and of the professional/occupational space (social stratication, inequalities of gender, etc.) and the inuence of the national context (law, economics and cultural policies).

This article contributes to understanding how the ordinary musicians live their professional lives, in the context of the classic oppositions between the will of creative autonomy and the need to work as service providers (Becker, Outsiders ; Perrenoud, Jouer le jazz ), between cultural legitimacy (Bourdieu, La distinction ; Coulangeon, Les métamorphoses de la distinction) and commercial success, or between local and cosmopolitan careers (Merton ; Perrenoud, Les musicos). All of these alternatives shape very dierent ways of being a musician. Then we ran a campaign of long structured interviews which included the gathering of standardized data to collect more precise information about the musicians' social origins like their education, the sequences of their careers, the kind of repertoire they played during their careers and the evolution over the time of the composition of their income.

In this article we present only a sample of the interviewees that we met during this more quantitative part and focus on the analysis of some of the results of this second phase of the survey. Musicians are generally under-represented in national workforce surveys because they are often working at the margins of traditional workforces. For this reason, recruit an ad hoc sample is often the best solution for academics seeking data on musical workers. To build our sample, we used the Respondent Driven Sampling method as dened by Douglas D. Heckathorn and Joan Jeri in their work on American jazz musicians (Heckathorn & Jeri). This sampling method is related network sampling methods, where interviewees are recruited trough a peer to peer process. Here it involved recruiting a small but motivated group of people of Preprint version the target population (known as seeds ) and asking them to respond to our questionnaire. The seeds were asked to introduce us to three of their contacts within the musician population. We then asked the same thing to their contacts and so on. This sampling method led to the constitution of a relatively small but diversied group of our target population. We repeated the process of recruitment for 8 waves and, starting with a group of 7 seeds , we were able to meet 123 other musicians who work and live in the French-speaking part of Switzerland and with whom we made recorded interviews (about two hours each) which included standardized data.

Among this data was information about the composition of the interviewees' earning. the musical income composition of the interviewees. This income data will be at the core of our analysis of the Swiss case. For this we used the artist revenue stream typology. This tool has been created and developed We started from the idea that the meaning of being a musician is at least partially shaped by national employment and cultural policies (or the lack of such policies) and we present here the unemployment schemes for live artists in France and Switzerland.

The case of France : a unique system

The unemployment scheme in France for live artists is reputed to be unique. Under the scheme dancers, actors, and musicians have to declare 507 hours of work or 43 gigs within ten months to access a daily unemployment benet during the next eight months.

Unfortunately, in France, like many other places, many gigs are not declared by the employer (such as the bar or restaurant owner, the father of the bride etc.)

and a massive amount of the working activity of ordinary musicians is undeclared work which is not taken into account for accessing the unemployment benet. Of course, the more a musician plays in small places, underground scenes etc., the less his or her work is likely to be declared. On the opposite side, the more a musician plays in well-known venues, the more likely he or she is to have work declarations.

They will thus be able to easily access to the French unemployment system for intermittents du spectacle . for its destruction, this unemployment scheme is still ongoing and is rmly defended by ordinary musicians and other live performers. French musicians often see that system as a subvention, which would not take into account the content of the work (Langeard).

One direct eect of that scheme is that French musicians try to play as often as possible, sometimes at any gig. For at least the rst ten rst years of The case of Switzerland : an unfavourable scheme for musicians

In Switzerland, there is also an unemployment insurance system specically dedicated to intermittent worker such as artists, but also opened to technicians who are working in show business and to other comparable freelance professions such as journalism.

The main dierence with the French system is the Compared to other European countries, the rate of Swiss people who report themselves as being able to play a music instrument as an amateur is very high.

In 2008, around 20% of the Swiss reported playing a music instrument or singing regularly as amateur (OFS, Les pratiques culturelles en Suisse, musique).

The main implication of this fact for those seeking work as a musician is that there is a high demand for music teachers. Being at simultaneously both a parttime teacher and a part-time performer can constitute a highly appealing option.

In order to analyse the composition of the bundle of tasks of ordinary Wiss musicians, we focus here on the sections of our survey concerning the dierent types of income, as outlined earlier in the article. The relative weights of each of these ten categories within the total musical incomes of our interviewees for 2013 are represented in Figure 1.

Here we see that unemployment benets represent a really small part of overall musical income.

This observation conrms that accessing the Swiss intermittent scheme is highly dicult. If we look at the mean weight of each of these categories (represented here by a diamond), the two main sources of earning among Swiss musicians come from teaching and playing music in public. These two kinds of tasks are at the core of musicians' work in Switzerland.

Unlike working patterns amongst French musicians, teaching appears here as a normal kind of task for professional musicians. It should also be noted that royalties represent on average less than 10% of the total musical income , a gure which can be considered to be on the low side.

In In the local career, one plays a repertoire of covers, standards etc., reproducing tunes which already exist and which the audience wants to be able to easily recognize. People play in venues for entertainment (such as bars and clubs) or even for an anonymous hirer (for thigns such as private parties and corporate events). Sometimes such musicians get some attention and are appreciated by their audience, but often they just do the job for any employer who needs a musical background for an event at which nobody listens and nobody will applaud. In this type of career, ordinary musicians usually play in bands of men, and the local entertainment scene is merely a social space of male hegemony (Perrenoud, Les musicos et la `masculinité' ) even if there are some women (mostly singers, but also, thankfully, increasingly more instrumentalists).

Consequently the ordinary local male musician allies frequently with a spouse from outside the art world, often of working class origin with a low but steady income, thus reproducing a classical pattern for the independent craft workers (Bertaux & Bertaux-Wiame ; Perrenoud, Les musicos). Ordinary musicians as local craftsmen make money from gigs and get unemployment benets as intermittents du spectacle .

They rely on the specic human capital of the instrumentalist and a range of social capital including relations with the other musicians in the area and with potential employers such as bar owners etc. Such musicians do not rely on legitimate cultural capital because they usually do not have much (in most of the cases encountered during the ethnography musicians had a high school diploma at best). Moreover they don't really need it for the job they do, as independent service workers. In this rst type of career music is a craft, playing is a type of service work and the musician an independent craftsman or employee, or even a proletarian (when, for example, one plays jingles for Rotary Club speakers). He or she is playing something totally shaped by an extrinsic utility, which is a social convention separating art from craft (Becker, Art worlds). In this case, the (Buscatto) and an important structural gender diversity in the dance and drama companies.

Within such careers musicians make money from

shows, but also from public grants, sometimes royalties if their music beomes popular, possibly some master classes and always the possibility of unemployment benet, which remains a key source of income for many.

In this kind of career, musicians often meet people with a high cultural, social and economic capital. Here music is an art and the musician is an artist.

In reality these two types of careers are not strictly demarcated as pure categories and can be considered as being two ideal-types. However, but it appears that in both cases, professionalism is built on stage, in front of an audience. Some of the local craftsmen teach but that activity is often seen as a problem for career development, as the teaching hours cannot be declared as gigs and therefore are not taken into account for accessing unemployment benets. So

French musicians are mainly attached to the stage and gigs, with teaching activities coming mostly in the latter part of their careers, seemingly more for the local craftsmen who will try to nd a steady job in a music school when they are tired of chasing gigs and have accepted the fact that they will never have a more successful career.

The tripartition of the musician population in

Switzerland

To analyse the internal structure of the Swiss musicians' group, we ran a Principal Component Analysis (PCA) using the revenue stream data.

Inspired by Geometrical Data Analysis (GDA) (Le Roux & Rouanet), such an analytic strategy is extremely useful in identifying a partition within a population through the analysis of the more frequent associations between dierent tendencies. Figure 2 represents the two rst dimensions of this PCA, which are clearly the more important dimensions by analyzing the decrease of the variance of the axes 4 . Nevertheless, the weight of royalties is signicantly high at this northeast pole. Thus, it can be said that amongst the artists people who produce and sell their own music are the more numerous.

Once this space is drawn, one can see how individuals are located within it according to several characteristics. This helps to provide a deeper understanding of how these three ideal-types vary in term of social recruitment and professional practices.

In Fig. 3

Royalties

Salary

Shows

Records

Sessions

Merch.

Teaching

Techn. Unemp.

Oth.

- On this point, the next step for us may be to encourage more international comparisons, in order to see if the bipolarisation emerging from our two cases is evidenced everywhere, to see whether music teaching is integrated or not into the bundle of musical tasks and to see how people cope with daytime jobs (grant number : 51NF40-160590). We wish to thank the SNF for that nancial support.

3.

Approximately 6,150 USD.

4.

The third dimension and the following ones represent less than 10 % of the variance when the rst and the second dimensions represent respectively 17,9 % and 15,9 %.

5.

In all our gures, each ellipse represent the zone where 90 % of the individuals with the characteristic analysed.

  Following a short presentation (part one) of the two surveys that this article relies on, the second part compares the national unemployment schemes in France and in Switzerland. While those two countries are neighbors, the forms of musical labor and musicians careers are quite dierent in each case. French musicians can gain access to a unique unemployment benet system. Conversely, Swiss musicians are generally excluded from unemployment benets mainly because of the extreme fragmentation Preprint version 2 Popular Music and Society 40(5), pp.592-604 of their employment periods as explained in part two. Importantly this exclusion leads them to diversify their activities by undertaking jobs such as teaching music or having daytime employments outside of music. The national unemployment schemes particularities strongly shape the ways of being a musician for French and Swiss musicians : since doing nothing but playing music is the main criteria for being a professional in the French case, partaking in multiple parallels activities does not disqualify Swiss musicians from being considered as professional. The third part shows that despite these dierences the main types of musical careers prevailing in France and in Switzerland are still aligned on the question of the opposition between music as an art -music for itself on one hand and on the other music as a craft, a service labor. Nevertheless, we suggest that the national Swiss context produces a third type -the teacher, whose situation is somewhere between the artist and the craftsman. Part One. Introducing two surveys : methods and substance This article is based on two surveys led in France and Switzerland with two methodological designs (mostly qualitative for the French survey, mixing qualitative and quantitative approaches in the Swiss case). We thus will lead a twofold comparison of the dierent ways of being an ordinary musician in two dierent countries, by analyzing variations among several national contexts, but also by confronting results gathered with dierent methodological tools (qualitative and quantitative). The rst survey is the long eldwork that Perrenoud did during his Masters and PhD researches in social anthropology between 1997 and 2005, when he was a musician based in the South-West of France (Perrenoud, Les musicos). He made a living playing the double bass and the electric bass, performing more than six hundred gigs, from anonymous labor in Rotary Club banquets (playing jingles when each speaker comes to the microphone, playing not too loud a musical carpet during the banquet) to international festivals in Amsterdam or Barcelona. That eldwork was also an occupation, featuring a job in regular bands (one played noisy postrock, another Gipsy swing, another sophisticated contemporary jazz etc.) or in ephemeral gatherings of players around a repertoire of standards and jazz classics or for totally improvised music, or even for replacements in many kinds of groups and styles, such as in popular balls in the countryside between the Pyrenees and the Mediterranean sea. This survey mostly utilized participant observations during gigs, rehearsals, recording sessions, tours, and everyday life among musicians. In addition Perrenoud also undertook around thirty semi-structured interviews. The survey was entirely qualitative. However but despite the lack of a representative sampling, it provides very useful information on the dierent bundle of tasks musicians undertake -i.e. the dierent ways of doing the job and/or living the art and on the dierent patterns of and segments within musicians' careers and life courses. Furthermore, it provided a rst basis for the second survey, which was undertaken in Switzerland. The Swiss data is more recent. We and our team 1 collected it for the Musicians' LIVES research project at the University of Lausanne between 2012 and 2015. Directed by Marc Perrenoud, Musicians' LIVES was a subproject of the National Center for Competence in Research program LIVES overcoming vulnerability, life course perspective 2 . Our main objective was to provide data in order to analyze the life conditions of ordinary musicians living and working in Frenchspeaking Switzerland. To catch the multidimensional aspect of musicians' careers, we chose a mixed methods approach. During the three years, there were two phases of the survey. We rst led an ethnographic study in which we shed light on what might be the most relevant issues and variables dierentiating the careers.

  by a team within the Future of Music Coalition (FMC), an association of musical activists, union members and academics who led a large survey among North American musicians in 2011 (DiCola). To better understand the composition of musicians' income, the members of the FMC team used eight categories of musical income : royalties ; salaries (if they are permanent musicians in an orchestra) ; earnings from shows, public performances in a non-permanent position (which is by far the most common situation) ; income from records sales ; studio sessions ; sales of merchandising and from teaching (music). The other category regroups all those kinds of earning which dont match with any of the categories. In our work on Swiss musicians, we added two more categories of earning : those coming from unemployment insurance specically dedicated to intermittent artist workers and those coming from technical activities linked with music (like being the sound engineer in addition to an instrumentalist, something of which we had found several cases during the ethnography). Those two surveys provided us with some very interesting results concerning what it means to be a musician in the two countries.

  But for over two decades, most French musicians have worked with non-prot associations which provide a service (live music) to the hirers such as the bar owner or the father of the bride, who becomes a client who just pays a fee to the association. The association then becomes the employer of the musicians and deals internally with informal agreements on the distribution of the money between the members of the band in accordance with considerations such as who has already plenty of gigs declared, and who is short and needs a work declaration to complete the necessary 43 in ten months etc. Despite the attacks of the biggest French employers' association, the The Mouvement des entreprises de France (MEDEF), who keep calling

  way in which access to the unemployment benets is computed by the relevant administration. Swiss people working in an intermittent profession have to prove that they have worked at least ten months during two consecutive years to access the unemployment insurance benet. Here, the time unit used by administration to determine the potential unemployment benets of intermittent workers is the entire week. This system does not t well with the employment patterns of musicians, who are generally engaged for a few hours of performance and not an entire week. Such a system is more appropriate to the working patterns of the other performing artist, especially dancers and actors who are more usually hired for several days in a row including both rehearsal sessions and shows.Moreover, Swiss musicians also face diculties which arise due to the characteristics of their home country.First, Switzerland is a small country in geographical and demographic terms, meaning that it is often dicult to nd enough gigs inside the country.Secondly, Swiss life standards are comparatively high (the median monthly wage is over 6 000 Swiss francs 3 OFS, Enquête suisse sur le niveau et la structure des salaires). If they are to maintain their living standards, Swiss musicians cannot aord to play too often in France or Germany for the same money as French or German musicians. Thus, Swiss musicians have to nd other ways of earning enough money to live.

  terms of the recurrent debates on the digitalization of music distribution, its (mis) exploitation by big web platforms such as Deezer and I-Tunes, and its eect on musicians' incomes, such a nding is very interesting. In spite of the place taken within the public debate by the problem of artist remuneration trough the sale of the musical production on the web, this nding remind us that for the larger body of musicians royalties in reality a minor source of income. Thus despite important debates concerning the state of the recording industry, only a small minority of musicians have ever sold signicant amounts of records and the lives and careers of the majority of musicians are mainly shaped by the type of live gigs that they careers in France The ethnography which Perrenoud did in France showed that after a relatively unstable period during the beginning of musicians' careers -which can last up to ten years, according to Philippe Preprint version

Figure 1 :

 1 Figure 1: The Swiss musicians revenue stream (2013)

  Income types with major contribution to the axis i.e. with a contribution that exceeds 10% are represented in bold and are underlined. Readings of PCA graphs, like Fig.2, are based on two principles : (i) the longer are the arrows, the more the related categories strongly align to one of the axis ; and (ii) the more arrows have a similar direction, the more the related categories are frequently associated among the sample. Two main oppositions emerge from the PCA. The rst dimension (Dim1) opposes those musicians who mainly earn money through teaching to those who earn money through royalties and records sales. The second dimension (Dim2) opposes musicians who mainly earn musical income by playing live to others with more diverse income streams. Within the space of incomes drawn by these two major oppositions, three main poles can be distinguished, corresponding to three main musicians ideal-type proles : The live musicians ; the teachers and the artists . The two rst types are clearly related to one specic main source of income : on one hand show fees for the live musicians and on the other teaching fees for the teachers . The revenue streams of the third type (the "artists") are a little more of a composite, involving a mixture of income from royalties, records and merchandising sales, studio sessions and even unemployment benets from the specic regime of Swiss intermittent workers.

Figure 2 :

 2 Figure 2: The space of Swiss musicians incomes (PCA)

  Figure 3: Cloud of individuals and musicians educational achievement

  7 . With regard to bipolarisation, we already have many indications that it is more or less the same everywhere, but there are many variations which have to be analyzed. We are now trying to develop such research, since one of us is supervising the PhD research of a Chilean student in to ordinary musicians in Santiago, while the other is about to start two years post-doctoral research in Brussels where he will try to work on the Belgian case. We have also undertaken some live observation and informal interviews in Dongguan (South of China), Beijing, Chicago, New York and New Orleans. In addition some online research is also going in the same direction. We recently found two US websites, both claiming to tell about the real story about musician's work and to get beyond the myths. The rst one gives tips on such things as how to use social medias, how to brand yourself, to avoid playing covers and only play your own compositions, in line with the artist-entrepreneur model. 8 The other one says to the average non-musician reader I have a job like you , Preprint version

Figure 4 :

 4 Figure 4: Cloud of individuals and gig type (2013)

  for us now including nding out the extent to which bipolarisation can be discerned in various types of careers across national boundaries.For example, would we nd more musicians with a daytime job in the UK than in Switzerland ?Would the ordinary musical animation jobs be the same for craft-musicians in Spain or in Belgium ? What are the employment and unemployment schemes for artists -and specically musicians -in each European country ? These questions, and many more, will inform out future work, all the time following the idea that sociology of music and art in general can denitely not be isolated from sociology of work (Cloonan, Musicians as workers ; Becker, Quelques implications de l'équation art=travail ). for Competence in Research LIVES Overcoming vulnerability : life course perspective is funded by the Swiss National Fund

  /musicians.about.com/od/LifeasaMusician/tp/5-Other-Ways-To-Make-Money-With-Your-Musiconeworkingmusician.com/what-it-reallymeans-to-be-a-working-musician.

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