Jérémy Castéra
email: jeremycastera@gmail.com

Pierre Clément
email: pierre.clement@univ-lyon1.fr

Teachers' Conceptions about the Genetic Determinism of Human Behaviour: A Survey in 23 Countries (Preprint, before corrections) Main topic: Genetic determinism/Genetics education

Keywords: Teachers' conceptions, international comparison, genetic determinism, innatism, sexism, racism

This work analyses the answers to a questionnaire from 8,285 in-service and pre-service teachers from 23 countries, elaborated by the Biohead-Citizen research project, to investigate teachers' conceptions related to the genetic determinism of human behaviour. A principal components analysis is used to assess the main trends in all the interviewed teachers' conceptions.

This illustrates that innatism is present in two distinct ways: in relation to individuals (e.g. genetic determinism to justify intellectual likeness between individuals such as twins) or in relation to groups of humans (e.g. genetic determinism to justify the superiority of some human ethnic groups). A between-factor analysis discriminates between countries, showing very significant differences. There is more innatism among teachers' conceptions in African countries and Lebanon than in European countries, Brazil and Australia. Among the other controlled parameters, only two are significantly independent of the country: the level of training and the level of knowledge of biology. A co-inertia analysis shows a strong correlation between non-citizen attitudes towards and innatist conceptions of genetic determinism regarding human groups. We discuss these findings and their implications for education.

Introduction

THE BIOHEAD-CITIZEN PROJECT

This study is rooted in the BIOHEAD-Citizen research project (Biology, Health and Environmental Education for Better Citizenship, 2004-2008, European Community CIT2-CT 2004-5006015). This project involved partners from eighteen countries chosen for their diversity: inside Europe (north to south, east to west) and outside Europe (North Africa, Senegal and Lebanon). Five other countries were then added, under the responsibility of P. Clément, to enlarge the sampling f o r a larger t r a n s n a t i o n a l comparative study: one in Europe (Denmark), two in Africa (Burkina Faso and Cameroon, to provide samples of non-Muslim African teachers) and two in other continents (Brazil and Australia). The participants associated with t h i s p r o j e c t h a d competencies in both biology, health or environment and in human and social sciences, mainly in science education. The aim of this project was to analyse how aspects of citizenship can be promoted through biology, health and environmental education, taking into account the renewal of scientific knowledge as well as the social and affective dimensions linked to these topics. This project was structured by two main axes: a critical analysis of curricula and school textbooks and an analysis of in-service and pre-service teachers' conceptions (including their systems of values as well as their scientific knowledge) in order to answer the following questions:

• Are there reductive simplifications in teaching issues related to our selected topics, like '1 gene → 1 character'; '1 microbe → 1 disease'? Do such teaching issues present or might they present notions of regulation, cycles, complexity? Are there implicit values in the curricula, syllabuses and school textbooks?

• What are the teachers' systems of values, including social dimensions, regarding nature, body and health, sexuality, biologic determinism, evolution? Do their values interact with their scientific knowledge? Are there differences among countries? Can such differences be associated with controlled parameters (gender, disciplines, religion, socioeconomic context, recent history of the country, etc.)?

The theoretical background is the KVP model [START_REF] Clément | Didactic Transposition and the KVP Model: Conceptions as Interactions Between Scientific Knowledge, Values and Social Practices[END_REF][START_REF] Clément | Conceptions, représentations sociales et modèle KVP' (Conceptions, Social Representations and KVP Model)[END_REF], figure 1 below), in which conceptions are analysed as possible interactions between scientific knowledge (K), systems of values (V) and social practices (P), and the goal is to carry out:

• A comparative analysis of syllabuses and school textbooks among the countries. For each selected topic, one grid of analysis was constructed to be used by all the participating countries at all the school levels (primary and secondary schools, i.e. from 6-to 18-year-old students). Several papers were published and we mention here only some of them on each of the six topics of the project: environment (e.g. [START_REF] Caravita | Construction and Validation of Textbook Analysis Grids for Ecology and Environmental Education[END_REF], health (e.g. [START_REF] Carvalho | Comparing Health Education Approaches in Textbooks of 16 Countries[END_REF], sex education (e.g. [START_REF] Bernard | Sexual Transmitted Diseases and C o n t r o l o f R e p r o d u c t i o n i n B i o l o g y T e x t b o o k s . A Comparative Analysis in 16 Countries[END_REF], evolution (e.g. [START_REF] Quessada | Human Evolution in Science Textbooks: A Survey in Eighteen Countries[END_REF], the human brain (e.g. [START_REF] Clément | Do the Images of Neuronal Pathways in the Human Central Nervous System Show Feed-Back? A Comparative Study in Fifteen Countries[END_REF]) and human genetics [START_REF] Castéra | Genetic Determinism in School Textbooks: A Comparative Study Conducted among 16 Countries[END_REF]).

• A comparative analysis of the teachers' and future teachers' conceptions of the six topics. The questionnaire was mainly constructed by including questions from previously well-tested questionnaires on the selected topics followed by validation using a pilot test.

Several papers were also published here, and we mention only some of them related to the environment [START_REF] Munoz | Teachers' Conceptions of Nature and Environment in 16 Countries[END_REF]), evolution [START_REF] Clément | Creationist Beliefs in Europe[END_REF]) and human genetics [START_REF] Castéra | Interaction entre Connaissances Scientifiques et Valeurs dans les Conceptions d'Enseignants Français sur le Déterminisme Génétique de Comportements Humains' (Interaction between Scientific Knowledge and Values in the Conception of French Teachers on the Genetic Determinism of Human Behavior)[END_REF].

The present paper deals with the teachers' conceptions of human genetic determinism in more countries than the 18 included in the BIOHEAD-Citizen project. These conceptions are linked to social challenges, such as differences, but also equality of rights among all human beings, regardless of their gender or their ethnic group. Biology education must involve awareness to teach actualized scientific knowledge. Moreover, the goal of education is not restricted to the transmission of knowledge, but also includes skills and values [START_REF] Delors | Learning the Treasure Within[END_REF]) such as the promotion of citizen human rights, e.g. the equality of all human beings. It is thus essential to analyse whether teachers are conceptualizing clearly the distinction between knowledge and values, and whether some possible interaction between knowledge and values can be identified and analysed in relation to different sociocultural contexts. This interaction can be an obstacle to the renewal of the taught scientific knowledge as well as sometimes facilitating it. That is the educational perspective of our work.

GENETIC DETERMINISM AS A BELIEF

The 'nature versus nurture' debate is an old, traditional but outdated discussion. All biologists consider today that any phenotype emerges from the interaction between the genome (nature) and its environment (nurture). Working on this interaction is a new trend of biology, called 'epigenetics' [START_REF] Wu | Genes, Genetics, and Epigenetics: A Correspondence[END_REF]. Consequently, the traditional debate of genes 'or' environment, or '% of genes and % of environment' (which is possible only for an additive model 'genes + environment'), is outdated because there is an interaction between genes and environment. [START_REF] Jacquard | Eloge de la Différence[END_REF] used a metaphor, comparing the interaction between 'innate' a n d 'acquired' i n h u m a n f e a t u r e s w i th the interaction between cement and bricks in a wall: both are necessary and they interact. [START_REF] Meaney | Nature, Nurture and the Disunity of Knowledge[END_REF] used another metaphor, explaining that asking which factor contributes more to the development of personality, nature or nurture, is akin to asking what contributes more to the area of a rectangle, the length or the width. The question of the relative importance of nature and nurture is irrelevant, because they are both necessary. The most interesting example to show the very high presence of genetic essentialism in our societies is the Human Genome Project (HGP). Presented, at the beginning, as the solution to the genetics roots of human features, including diseases such as cancers, Alzheimer's, diabetes, etc., researchers initially claimed that they were expecting to find 100,000 to 150,000 human genes, while we know today that our genome contains fewer than 23,000 genes. Researchers have recently admitted the very mixed results coming from the HGP: Hundreds of genetic variants have been linked to common diseases through genome-wide association studies, yet each confers only minimal disease risk.

The findings thus far represent only the tip of the iceberg. (National Human Genome Research Institute 2010) This shows that even for what can be considered as simple features (such as diseases), genetic determinism is not sufficient to explain the complexity of human phenotypes.

Only the multiple interactions between genome, environment and organism can give an overview of the biological complexity ('the triple helix' of [START_REF] Lewontin | The Triple Helix: Gene, Organism, Environment[END_REF]. Trying to oppose nature and nurture is a nonsense because both are 100% necessary [START_REF] Jacquard | L'Avenir n'est Pas Ecrit (The Future is Not Written)[END_REF].

Nevertheless, at least before the middle of the twentieth century, nature was opposed to nurture and was often considered as stronger than nurture. This prevalence of nature (innatism) appeared frequently in the common thinking and culminated in colonialism and then with the Nazis' ideology. During this period, the research into genetics was growing and was structured in France in Institutes of 'Genetics and Eugenics' or in America with the American Eugenics Society [START_REF] Aubert-Marson | Les Politiques Eugénistes aux Etats-Unis dans la Première Moitié du XXe siècle' (Eugenic Policies in the United States in the First Half of the Twentieth Century)[END_REF]. These kinds of institutes have certainly disappeared, but the ideology that we could understand the whole human being from its genes was still very present at the end of the twentieth century (e.g. the Human Genome Project, criticized by [START_REF] Song | The Human Genome Project as Soteriological Project[END_REF]. [START_REF] Gericke | Definition of Historical Models of Gene Function and Their Relation to Students' Understanding of Genetics[END_REF], as well as [START_REF] Smith | Updating the Model Definition of the Gene in the Modern Genomic Era with Implications for Instruction[END_REF], analysed the historical progression of the genetic determinism models, showing that these models had difficulties in i n t e g r a t ing t h e influence of the environment. Indeed, several scientists tried to correlate complex behaviours with some particular sequences in genomes, such as in the journal Science in which [START_REF] Hamer | A Linkage between DNA Markers on the X Chromosome and Male Sexual Orientation[END_REF] claimed to have found DNA sequences that influenced the male sexual orientation (the 'gene of homosexuality' was taken up by the media). In 1999, Rice et al. published contradictory data in the same journal, showing no linkage with the particular sequence found before: Hamer et al. overestimated the genetic determinism. In addition, according to [START_REF] Nelkin | The DNA Mystique: The Gene as a Cultural Icon[END_REF], the imprinting of innatism in western societies can be found in 'mass culture': in TV shows, movies, journals, etc. The most common way used by this 'mass culture' to explain genetic determinism was to reduce one phenotype (such as behaviour) to one gene. That could only be explained by the ultra-simplification of a scientific fact, but these authors also suggested a parallel between DNA and soul: Such spiritual imagery sets the tone for popular accounts of DNA, fuelling narratives of genetic essentialism and giving mystical powers to a molecular structure. Indeed, DNA had assumed a cultural meaning similar to that of the Biblical soul. (Nelkin & Lindee 1995, p.40) They suggested that innatism could be more than a misunderstanding or simplification of science but could be anchored in deep beliefs. Other authors, writing on biology or on the epistemology of biology, developed the idea that genes took the place of God in explaining t h e d e t e r m i n i s m o f h u m a n b e h a v i o u r s a n d p e r f o r m a n c e s . T h e y s a w t h e 'genetic programme' as being a kind of predestination created by God: everything that happened was written in advance [START_REF] Kupiec | Ni Dieu, Ni Gène (Neither God, Nor Gene[END_REF][START_REF] Forissier | Teaching "Biological Identity" as Genome/Environmental Interactions[END_REF].

For these authors, the common understanding of genetic determinism is rooted in a social religious culture of predeterminism. At the end of the twentieth century, this awareness encouraged some scientists to denounce the problem of an innatist society (e.g., Atlan 1999 in France, [START_REF] Lewontin | Not in Our Genes: Biology, Ideology and Human Nature[END_REF] or Nelkin & Lindee 1995 in the U.S.).

In France, the media has often discussed this problem, with many controversies about genetic determinism. Maybe one of the most famous was the debate between the philosopher M. Onfray and the future President of the French Republic, N. Sarkozy, who claimed genetic determinism of human behaviours such as smoking, juvenile violence or suicide (Philosophie Magazine 2007).

Finally, well-known researchers in genetics (such as [START_REF] Lewontin | The Triple Helix: Gene, Organism, Environment[END_REF][START_REF] Jacquard | L'Avenir n'est Pas Ecrit (The Future is Not Written)[END_REF] and philosophers (in the line of Jean-Paul Sartre and Simone de Beauvoir for instance) alert us to the fact that genetic determinism explanations can be used as a justification for social fatalism, with political or religious issues.

INNATISM, A MANY-FACETED BELIEF

Several authors have developed critical analyses of innatism (for instance [START_REF] Lewontin | Not in Our Genes: Biology, Ideology and Human Nature[END_REF][START_REF] Nelkin | The DNA Mystique: The Gene as a Cultural Icon[END_REF][START_REF] Atlan | La Fin du 'Tout Génétique' (The End of 'All-Genetics[END_REF][START_REF] Jacquard | L'Avenir n'est Pas Ecrit (The Future is Not Written)[END_REF]. Brun and Maurel (2005, p.14) proposed a synthesis by distinguishing four forms of innatism:

(1) The first one claims that there would be inherited biological differences in mental abilities between individuals within each human group.

(2) The second postulates such differences between racial groups.

(3) The third claims that social structures and behaviours (identifiable by the diversity of cultures and personal attitudes) would reflect the weight of genetic factors. Indeed, sociobiology (as [START_REF] Wilson | On Human Nature[END_REF] postulates a genetic selection of the main cultural and social human features.

(4) The fourth form of innatism considers the belief that mental gender differences would be genetically determined.

Psychologists such as [START_REF] Keller | Genes We Trust: The Biological Component of Psychological Essentialism and its Relationships to Mechanisms of Motivated Social Cognition[END_REF] in Germany or [START_REF] Dambrun | Why Does Social Dominance Orientation Decrease with University Exposure to the Social Sciences? The Impact of Institutional Socialization and the Mediating Role of "Geneticism[END_REF] in France have shown innatism among university students' conceptions, justifying racist or sexist attitudes. More precisely, [START_REF] Keller | Genes We Trust: The Biological Component of Psychological Essentialism and its Relationships to Mechanisms of Motivated Social Cognition[END_REF] showed that when a group of people read a progenetic determinism article (indicating the importance of genes for humans) before completing an intolerant attitudes test, the answers are significantly more intolerant than those of a g r o u p w h o r e a d a n e u t r a l a r t i c l e . F o r K e l l e r , b e l i e f s i n s t r o n g g e n e t i c determinism engender intolerant attitudes. Moreover, in a recent work, [START_REF] Ranger | Essentialism Goes Social: Belief in Social Determinism as a Component of Psychological Essentialism[END_REF] proposed a complementary approach in order to clarify the conceptions about determinism considering not only the belief in genetic determinism (BGD) but also the belief in social determinism (BSD). In this way, they showed a correlation between BSD and intolerant attitudes when prejudices h a v e b e e n a c t i v a t e d experimentally. The reductionism linked to BSD is probably rooted in some works of sociology or social psychology, while the reductionism linked to BGD generally claims to be justified by research in biology. Working on didactics of biology, our work is, firstly, mainly focused on BGD.

WHAT ARE CONCEPTIONS?

Conceptions are central to this research. Giordan and de Vecchi (1987, p.79) defined conceptions as 'a coordinated set of ideas and coherent explanatory images, that learners use for reasoning in context of problem-solving'. [START_REF] Clément | Didactic Transposition and the KVP Model: Conceptions as Interactions Between Scientific Knowledge, Values and Social Practices[END_REF][START_REF] Clément | Conceptions, représentations sociales et modèle KVP' (Conceptions, Social Representations and KVP Model)[END_REF] proposed analysing conceptions as the possible interaction between three poles (figure 1):

• Scientific knowledge (K): knowledge published and identified as scientific by the scientific community at a precise moment: today, but sometimes several years earlier.

• V a l u e s ( V ) : 'what we use for our decision making'. V a l u e s j u s t i f y o p i n i o n s , ideologies or beliefs, but also science (e.g. the rejection of any fraud is a value). Innatism, as the belief in the great importance of genetic inheritance, is an interaction between some scientific knowledge about genetic determinism and a value such as fatalism, and as the reduction of a sociocultural feature to a mere biological basis.

• Social practices (P): this pole represents all individual or collective social practices, whether professional, religious, political or in other domains. For instance, fatalism is a value sustaining conservative political positions (political practice).

Figure 1: Conceptions (C) can be analysed as interactions among the three poles knowledge (K), values (V) and practices (P) [START_REF] Clément | Didactic Transposition and the KVP Model: Conceptions as Interactions Between Scientific Knowledge, Values and Social Practices[END_REF].

For instance, the conception of a person who has already learned that genes do not determine a macrophenotype directly, but are in interaction with their environment, will differ from the conception of a person who does not know that: the influence of K on conceptions about genetic determinism can be strong. Alternatively, a person who is a fatalist, thinking that everything has already been written in advance, will easily agree with genetic determinism: the values can also influence strongly conceptions about genetic determinism. The practices of a researcher in genetics are also different if they wish to test a genetic or an epigenetic influence. Social practices (such as the goals of the school and of any education) will differ if they are or are not rooted in a strong belief in genetic determinism regarding students' performances.

SITUATED CONCEPTIONS, CONCEPTIONS AND SOCIAL

REPRESENTATIONS

According to [START_REF] Clément | Représentations, Conceptions, Connaissances' (Representations, Conceptions, Knowledge)[END_REF], the researcher can only analyse the 'situated conceptions' of a person, i.e. the conceptions mobilized by a person when placed in a precise situation.

Researchers consider for instance a response to a question (written or oral), or a behaviour or achievement, in relation to its specific context. The situated conceptions depend on the way in which the researchers collect the information. To gain an idea of a conception of a person relating to a precise topic, it is necessary to place that person in different situations. This enables the mobilization of several facets of his/her conceptions: several situated conceptions. It is from t h e c o m b i n a t i o n o f t h e s e v a r i o u s s i t u a t e d conceptions that the researcher can infer hypotheses about the conception of a person related to a specific topic (Figure 2). For instance, in the present work, we will use several situations to try to analyse conceptions of genetic determinism: some dealing with identical twins, some with human clones, some with predeterminism of a feature from the parents' genes, etc.

Social representations [START_REF] Moscovici | The Phenomenon of Social Representations[END_REF][START_REF] Jodelet | Représentation Sociale: Phénomènes, Concept et Théorie[END_REF], called collective representations by [START_REF] Durkheim | Représentations Individuelles et Représentations Collectives[END_REF], can be considered as conceptions shared by the individuals belonging to a social group [START_REF] Clément | Conceptions, représentations sociales et modèle KVP' (Conceptions, Social Representations and KVP Model)[END_REF]. One of the goals of this study is to explore the main collective conceptions (social representations) regarding genetic determinism in several countries. The comparison is based on an intercultural approach to identification that is defined by [START_REF] Hofstede | National Cultures and Corporate Cultures[END_REF] as 'the collective programming of the mind which distinguishes the members of one group or category of people from another (p.5). In the same way, Spencer-Oatey (2000, p.4) explained intercultural research more precisely with the following definition of the cultural dimensions: a fuzzy set of attitudes, beliefs, behavioural norms, and basic assumptions and values that are shared by a group of people, and that influence each member's behaviour and his/her interpretation of 'meaning' of other people's behaviour.

The intercultural comparison developed in the project BIOHEAD-Citizen is based on these assumptions in order to understand the diversity of social representations, which also means the diversity of interactions between science and society. We explore here teachers' conceptions about the genetic determinism of humans' behaviours i n 2 3 countries.

Hypotheses and Research Questions

This study is based on the following research questions:

• What are the different conceptions about genetic determinism among our total sample of teachers in 23 countries? Until now, no research has been performed from a large intercultural perspective to analyse teachers' conceptions related to genetic determinism.

• Are these different conceptions correlated with one or some of the controlled parameters (country, taught discipline, level of training, religion …)?

• Is the eventual teachers' innatism related to convictions of intolerant attitudes?

From analysing biology textbooks in 16 of the 23 countries studied in the present work, [START_REF] Castéra | Genetic Determinism in School Textbooks: A Comparative Study Conducted among 16 Countries[END_REF] found important differences among the countries. As a consequence, we predict that there are at least some differences among the 23 countries, but we are also expecting differences among other parameters across all these countries, based on the following hypotheses:

• The belief in predestination may be linked to conceptions overestimating the importance of genetic determinism, but it can differ from one religion to another, or can be linked only to the degree of belief in God and practising religion.

• The teachers' level of knowledge in biology should also influence the analysed conceptions: teachers with a diploma in biology could be mor e a wa r e t ha t huma n behaviour and performance are also built by epigenesis and not only by genes. However, the epigenetic processes, as well as cerebral epigenesis, are not yet taught in most of the countries [START_REF] Castéra | Genetic Determinism in School Textbooks: A Comparative Study Conducted among 16 Countries[END_REF]): as a consequence, the eventual difference between biology teachers and other teachers must be evaluated.

• As found by [START_REF] Keller | Genes We Trust: The Biological Component of Psychological Essentialism and its Relationships to Mechanisms of Motivated Social Cognition[END_REF] and [START_REF] Dambrun | Why Does Social Dominance Orientation Decrease with University Exposure to the Social Sciences? The Impact of Institutional Socialization and the Mediating Role of "Geneticism[END_REF], we predict a correlation between 'intolerant attitudes' (such as sexism or racism) and conceptions overevaluating the importance of genetic determinism.

Methods

In order to answer these research questions, a precise methodology was adopted by all the teams involved in the BIOHEAD-Citizen Project and in the following research.

PROCEDURE

We took two full years to design the BIOHEAD-Citizen questionnaire collectively [START_REF] Clément | Biology, Health and Environmental Education for Better Citizenship: Teachers' Conceptions and Textbook Analysis in 19 Countries[END_REF]. Starting with a bibliography for selecting some alreadyvalidated questions, we added others related to our hypotheses, using interviews and then a long pilot test. This pilot test was translated into each national language using several complementary processes: parallel independent translations, from which was built a consensual translation, this then being retro-translated and compared with the initial formulation (the reference questionnaire was in English). In several countries, the questionnaire was filled in twice by the same students, with one month of delay, to analyse the reliability of their answers: when answers were not reliable, they were eliminated. The data from at least 50 pre-service teachers, in most countries, were then analysed, and only the questions differentiating the teachers' answers were utilized in the final questionnaire.

The process for collecting the completed questionnaires was very similar from one country to another. Usually pre-service teachers filled in the questionnaires during a training course and in-service teachers in their school or during training workshops on topics different from those of our investigation. In all cases, the 10-page questionnaire was answered in the presence of the researcher, who guaranteed that the whole process was totally anonymous and immediately gathered the completed questionnaires. In each country, the answers were entered into an Excel file, and all the data were centralized in the Didactic Laboratory of University Lyon 1 (France) for comparative analyses.

QUESTIONNAIRE

This anonymous questionnaire included 144 questions dealing with the 6 topics of the BIOHEAD-Citizen project, and also contained questions on personal information, in particular gender, age, the teacher's subject and several other questions related to religious, political, social and economic opinions. The full questionnaire took approximately 30 to 40 minutes to complete. The exact processes of construction and validation of the instruments are described in [START_REF] Clément | Biology, Health and Environmental Education for Better Citizenship: Teachers' Conceptions and Textbook Analysis in 19 Countries[END_REF].

For this research, we consider 16 questions about genetics, mainly related to the genetic determinism of behaviour and intellectual performance (table 1), to analyse the possible interactions between the teachers' knowledge and their values. The answer to some questions is mainly oriented by the teacher's knowledge, or by interaction between his/her knowledge and his/her values. We also use some questions mainly related to values: the teachers' attitudes towards foreigners or towards poor people, or about the rights of homosexuals and gender equality (table 2). All these questions constitute the analysed variables. Another set of questions is related to teachers' personal information (age, gender, etc.) and social practices: their religion, level of belief in God and of practising religion, level of training (number of years after secondary school), subject taught, etc. These questions are used as instrumental variables (e.g. to define the compared groups).

Table 1: The 16 questions related to biological (mainly genetic) determinism (their ranking throughout the whole questionnaire is stochastic).

A3.

If clones of Einstein could be obtained, they all would be very intelligent. I agree I don't agree

A6.

Due to identical genes, identical twins have identical immune responses to transplants from another person. I agree I don't agree

A9.

Women are less intelligent than men because their brains are smaller than men's brains. I agree I don't agree

A14.

Thanks to their physical features, men perform better in athletics than women. I agree I don't agree

A19.

Due to identical genes, identical twins have identical brains and, therefore, identical behaviour and ways of thinking. I agree I don't agree A21. Biologically, women can be as intelligent as men. I agree I don't agree

A24.

If clones of Mozart could be obtained, they all would be excellent musicians. I agree I don't agree

A25.

It is for biological reasons that women cannot hold positions of high responsibility as men can. I agree I don't agree

A27.

The human genome contains more genes than the genome of any other living being. I agree I don't agree

A31.

When a couple has already had two girls, the chances that their third child will be a boy are higher. I agree I don't agree

A35.

Ethnic groups are genetically different and that is why some are superior to others. I agree I don't agree

A36.

Men might be more able to think logically than women, because men might have different brain bilateral symmetry. I agree I don't agree

A38.

It is for biological reasons that women more often than men take care of housekeeping. I agree I don't agree

A43.

In identical twins, one can be right-handed and the other left-handed. I agree I don't agree

A46.

Biologically, men cannot be as sensitive and emotional as women. I agree I don't agree

A53.

Due to identical genes, identical twins have identical immune responses to micro organisms.

I agree I don't agree

The responses to all the questions about genetics are based on a Likert scale on which each teacher was asked to tick one of four boxes, ranging between 'I agree' and 'I don't agree'. The majority of the questions concern genetic/biological determinism of human behaviour. These questions can be grouped into four different categories:

(1) Genetic determinism of personal or individual features: questions about clones and twins (A3, A6, A19, A24, A43 and A53).

(2) Genetic/biological differences related to gender (A9, A14, A21, A25, A36, A38 and A46).

(3) Genetic differences among ethnic groups (A35).

(4) Two questions about more general knowledge of genetics (A27, A31: pole K in figure 1), although recognizing that question A27 can also be influenced by innatism.

The answers to the questions of the three first groups are based on scientific knowledge interacting with values (poles K and V in figure 1). They are also related to the different facets of innatism summarized by [START_REF] Brun | Introduction à l'Histoire de la Controverse "Inné/Acquis"' (Introduction to the History of the Controversy 'Nature/Nurture[END_REF], but the facet related to sociobiology is missing (questions about sociobiology were in an optional part of the questionnaire, not used in all 23 countries and consequently not used here).

Table 2: Questions measuring attitudes towards groups of individuals.

A2.

In a modern society, men and women should have equal rights. I agree I don't agree

A30.

It is important that there are as many women as men in Parliament.

I agree I don't agree

A26.

There are too many foreigners in my country: the government should limit immigration. I agree I don't agree

A41.

Homosexual couples should have the same rights as heterosexual couples. I agree I don't agree

A15.

A priority of the government must be to guarantee resources for health protection of the poor. I agree I don't agree

A52.

It is acceptable that poor people do not have access to the same health care quality as rich people. I agree I don't agree Zimbardo and Gerrig (1999, p.745) defined an attitude 'as a positive or negative evaluation of people, objects, event, activities, ideas, or just about anything in your environment'. Here, w e a s s e s s the attitudes towards d i f f e r e n t g r o u p s o f p e o p l e : foreigners, homosexuals, the opposite gender or poor people. The Likert scale used here was initially created for the purpose of assessing this kind of attitude [START_REF] Likert | A Technique for the Measurement of Attitudes[END_REF].

SAMPLES

The questionnaire was completed by a balance of in-service teachers (i.e. currently active) and pre-service teachers (i.e. adults in their last year of teacher training), in both primary and secondary schools in the 23 countries. In each country, 6 categories of samples were defined: in-service primary school teachers (inP), in-service secondary school biology teachers (inB), in-service secondary school language teachers (inL), preservice primary school teachers (preP), pre-service secondary school biology teachers (preB) and pre-service secondary school language teachers (preL). In each country, about 50 teachers in each category (only 30 in the smallest countries, such as Malta and Estonia) completed the questionnaire, with a mean of 300 per country (and more in some countries where complementary hypotheses were tested). A total of 8,285 teachers completed the questionnaire; see table 3 for the size of the samples in each country. 3.4 DATA ANALYSES

Validity and Reliability

Firstly, we analysed the results of the pilot test, involving a longer questionnaire than the final one. In four countries (France, Lebanon, Germany and Portugal), we applied the same pilot test questionnaire twice to the same population of pre-service teachers, after at least one month. It was totally anonymous and each student had to memorize his/her nickname used then for analysing the reliability of their answer to each question. In this way, every question on the pilot questionnaire with less than 70% reliability was deleted from the final questionnaire, used in this paper. This was the case for all the open questions and the questions with a ranking. We kept mainly questions based on a Likert scale or on a choice between two or four items. We conducted several types of multivariate analysis, before finally deciding to use the software 'R' and the analyses presented below. We published a few of the data and analyses from the pilot test (e.g. [START_REF] Clément | Differences in Values Associated to Biology, Health and Environmental Questions among France[END_REF]. In these analyses, we also decided to suppress questions when they were not differentiating the teachers' conceptions, and also when they were too redundant. A challenging problem was the translation of the questionnaire into each national language, and we exposed above how it was performed in each country:

independent translations, then a retro-translation of the synthetic initial translation.

Using the final questionnaire, a principal component analysis (PCA) was applied to the questions used in this paper in order to assess the internal validity of the scale (see paragraph 4.1). This PCA confirms the way in which the questionnaire was constructed:

there are different views of innatism (justifying performances between individuals or between groups of individuals).

Statistical Analyses

All the computations were performed using the statistical software R [START_REF] Ihaka | R: A Language for Data Analysis and Graphics[END_REF] with the multivariate analysis package ade4. More precisely, we used four different methods:

• Principal component analysis or PCA [START_REF] Lebart | Statistique Exploratoire Multidimensionnelle (Exploratory Multivariate Statistics[END_REF] to analyse the general structure of the answers.

• Between analyses [START_REF] Dolédec | Rythmes Saisonniers et Composantes Stationnelles en Milieu Aquatique II -Prise en Compte et Elimination d'Effets dans un Tableau Faunistique' (Seasonal Rhythms and Aquatic Stational Components II -Recognition and Elimination of Effects in a Faunistic Table)[END_REF] to discriminate between groups of individuals (different countries, biology teachers and non-biology teachers, different religions, etc.) in order to analyse which conceptions differentiate the most between these groups. A Monte-Carlo permutation test [START_REF] Romesburg | Exploring, Confirming, and Randomization Tests[END_REF] implemented in the ade4 libraries was then used to test the statistical significance of the instrumental variables' analyses (to ascertain whether the difference between groups is significant or not).

• Sometimes, differences between groups can be a single consequence of another difference. For instance, a gender difference can result from the greater number of males in the biology teachers' group than in the language teachers' group. Using the principal component analysis of the orthogonal instrumental variables (PCAVOI), it is possible to suppress the effect of one variable [START_REF] Sabatier | Principal Component Analysis w i t h Instrumental Variables as a Tool for Modelling Composition Data[END_REF]. For instance, we suppressed the 'effect of biology/not biology teachers' to determine whether the gender difference persists or not.

• Co-inertia analysis is used to compare two sets of questions -for instance, those related to genetics and attitudes -and to determine the possible correlations between them [START_REF] Dray | Co-inertia Analysis and the Linking of the Ecological Data Tables[END_REF].

These kinds of statistical methods are often used in ecology [START_REF] Escoufier | The Duality Diagram: A Means of Better Practical Applications[END_REF][START_REF] Dolédec | Rythmes Saisonniers et Composantes Stationnelles en Milieu Aquatique II -Prise en Compte et Elimination d'Effets dans un Tableau Faunistique' (Seasonal Rhythms and Aquatic Stational Components II -Recognition and Elimination of Effects in a Faunistic Table)[END_REF]) in order to obtain a general overview of the repartition of species, which is contingent on a number of physical parameters. However, these kinds of methods are also frequently used in sociology [START_REF] Busca | Analyse Factorielle Simple en Sociologie (Factorial Analysis in Sociology)[END_REF] and are suitable for analysing our data [START_REF] Munoz | Teachers' Conceptions of Nature and Environment in 16 Countries[END_REF]).

Results and Discussion

THE MAIN TRENDS IN TEACHERS' CONCEPTIONS

Each response from of a teacher expresses his/her situated conception related to the topic of the question, but the coherence of the answers to several questions dealing with the topic 'genetic determinism' expresses his/her conceptions related to that topic more.

Moreover, several coherences can be identified among all the teachers, each one expressing a trend that we call a collective conception (a social representation as defined by [START_REF] Moscovici | The Phenomenon of Social Representations[END_REF]. The goal of the principal component analysis is to identify the general trends of answers among the teachers of our sample, the most discriminative questions and how they are inter-correlated. In other words, we can identify opposite conceptions within our total sample.

The histogram showing the part of the variance explained by each component (figure 3c) illustrates that the first component (horizontal axis C1 in figure 3a) is the most important for differentiating the responses of teachers, explaining more than 20% of the total variance (in the absence of any coherence of answers, each component would be, for 16 questions, about 6%). The second component (C2) explains more than 10% of the variance, and according to the histogram, the other components can be assimilated as background noise. So, the interpretation of the two first components explains the main part of the teachers' conceptions according to their responses.

Each question is represented, in the correlation circle (figure 3a), by a vector ending with the question number (A3, A6, etc.). The more a question contributes to the variance, the longer its corresponding vector. The table (in figure 3b) helps readers to interpret the correlation circle with the exact coordinates of the vector in the correlation circle.

Two groups of questions emerge from the correlation circle:

• The first group represents the conceptions related to genetic determinism of human groups (gender and ethnicity), because it is structured by the answers to questions A35, A25, A38, A9, A46, A36, A31, A27, A14 and A21 (negative correlation). These questions concern the possible innate differences between human groups as gender groups or ethnic groups.

• The second group represents the similarities or differences between individuals (due to genes) without consideration of the 'human groups' (gender or ethnicity), because it is structured by the answers to questions A24, A6, A3, A53, A19 and A43 (negative correlation). These questions concern clones or twins.

According to the PCA, the conceptions of teachers are shown by the two axes of the correlation circle. C1 can be interpreted as the axis of general innatism; both groups of questions are well represented on the C1 axis (6 questions in the first group and 2 questions in the second group have a value between |0.59| and |0.40| on C1; see table b).

The C2 axis can be interpreted as the axis of individual innatism (only 4 questions, all We wish to point out that questions A31 and A27, linked to basic knowledge about genetics (the number of genes in the human genome and the laws of probability), make a small contribution to C1 and almost nothing to C2. So, the answers to these two questions are not correlated with the answers to the questions defining the components C1 and C2.

The most important oppositions between teachers' conceptions are defined by the questions including values with a clear interaction between their knowledge and their values (the poles K and V in figure 1). For instance, the most sexist values are justified by the outdated knowledge that it would be biological justification for the higher status of men (A25) or of housekeeping by women (A38) while the less sexist conceptions do not agree with these justifications. The biological justification is seen as the size or the lateralization of the brain in questions A9 and A36. This opposition also relates to the genetic justification of the superiority of some ethnic groups (A35) and is also related to the identity of twins: the biological justification here is the outdated idea of common identity of the brains (question A19) or of the immune systems (question A53) of identical twins, due to their identical genes.

Nevertheless, these last two questions about twins, as well as the two questions related to clones (of Einstein: A3 and of Mozart: A24), define component 2 (the vertical axis in figure 3), which is independent of component 1. This means that, for some teachers, the innatism linked to the conviction of individual genetic determinism among twins or clones can be juxtaposed with an absence of innatism linked to egalitarian values concerning the gender or ethnic groups. While [START_REF] Devine | Stereotypes and Prejudice: Their Automatic and Controlled Components[END_REF] mentioned a conflict between stereotypes and recent beliefs, we prefer to interpret this apparent contradiction as a juxtaposition of situated conceptions (figure 2) that are not yet in conflict. We agree with the model of [START_REF] Lepore | Category and Stereotype Activation: Is Prejudice Inevitable?[END_REF] when they explain that it is not an inhibition of the part of a conception.

ARE THESE CONCEPTIONS SOCIAL REPRESENTATIONS?

When a conception characterizes a group of actors, it can be called a social representation [START_REF] Moscovici | The Phenomenon of Social Representations[END_REF][START_REF] Clément | Conceptions, représentations sociales et modèle KVP' (Conceptions, Social Representations and KVP Model)[END_REF]. We thus now try to determine whether the identified conceptions can be specific to social contexts or groups by testing whether they correlate with one or some of the controlled parameters characterizing each teacher. We then analyse whether these eventual correlations are independent of each other or not.

Strong Differences among Countries

A between-class analysis of the country groups (figure 4) shows that the conceptions of teachers are very different from one country to another. The histogram showing the percentage of variance of each component (figure 4a)

shows that the first component (D1) is the most important (D1). This component (D1)

subsumes almost all the information (68% of the variance). The other components can be considered as background noise and need not be taken into account. The correlation circle of the 16 variables on the plane defined by the two first components (figure 4b, and table 4e giving the exact coordinates of each question in the circle of correlations) shows that D1 is mainly defined by questions about differences between human groups (A35, A38

and A25) but also by questions related to twins (A19, A53). There is opposition between general innatism (groups and individuals) and non-innatism among countries. On the left in D1 (figure 4d) are the countries with a more innatist conception of human behaviours or performances and on the right are countries with less innatist conceptions. The most important innatism is observed in Africa and Lebanon. The caption for figure 4 indicates the ranking of countries according to their conceptions about genetic determinism (strong innatism to less innatism).

The randomization test (Monte Carlo, figure 4c) shows that the observed distribution (the trait on the right) is entirely outside the histogram built from 1000 essays by chance (on the left). The differences among the 23 countries are strongly significant (p < 0.001).

This test assigns a new nationality to each individual randomly and the variance is calculated between these newly formed groups. The operation is repeated 1000 times and all the calculated variances are shown by the bar plot (on the left). The trait on the right of the bar plot is the variance of our sample. The difference between the variance of our sample and the variance resulting from random dispersions shows that the difference observed between countries is not random.

Question A35 (ethnic groups are genetically different and that is why some are superior to other) is the most discriminating question for countries (χ 2 = 2346, df = 66, p < 2.2e-16). Figure 5 shows the percentage of teachers who, in each country, agree or disagree with the affirmation that can be considered as expressing racist positions: ethnic groups are genetically different and that is why some are s u p e r i o r t o o t h e r s . T h e percentages fluctuate between 97% of teachers totally or rather disagreeing in France and only 38% in Lebanon. Even in some European countries, such as Denmark, Lithuania and Poland, between 17% and 34% of teachers agree or rather agree with 'Ethnic groups are genetically different and that is why some are superior to others'.

Figure 5: Histogram of countries according to the affirmation A35: 'Ethnic groups are genetically different and that is why some are superior to others'.

Question A25 ('It is for biological reasons that women cannot hold responsible positions as high as men'; figure 6) indicates supposed genetic or biological determinism of social performances for women and men. The responses to this question show that the differences among countries are significant (χ 2 = 1648.192, df = 66, p < 2.2e-16) with more or less the same differences among countries as for the precedent question on ethnic groups.

The same significant differences among countries are observed for the two questions dealing with gender differences of brains: A9 ('Women are less intelligent than men are because their brains are smaller') and A36 ('Men might be more able to think logically than women, because men might have a different brain bilateral symmetry').

Figure 6: Histogram of the responses by countries to A25: 'It is for biological reasons that women cannot hold responsible positions as high as men'.

The justification of biological reasons for intellectual superiority in men has been claimed since the end of the nineteenth century, beginning with Broca's work based on craniology, then in the 1970s by Witelson based on socio-biology and later by different studies in neurobiology. [START_REF] Gould | The Mismeasure of Man[END_REF] demonstrated that the claim by Broca was not scientifically rooted (reanalysing Broca's data) and was in fact ideological. [START_REF] Clément | Using Complex Images in the Popularization of Science: Scientific or Ideological Agenda?[END_REF] and [START_REF] Vidal | Cerveau, Sexe et Pouvoir (Brain, Sex and Power)[END_REF] undertook the same kind of critical analysis of the publications of neurobiologists. It is accepted today that the size or lateralization of the human brain is not correlated with being more or less intelligent.

Nevertheless, this outdated idea is still accepted by a large number of teachers in some countries (figure 6), again showing a clear correlation between their knowledge and their values, probably linked to their social practices at home (the three poles K, V and P in figure 1).

Are There Differences Linked to Religions?

Our hypothesis was the existence of a correlation between innatism in teachers' conceptions and their practised religion. To test this we undertook different analyses.

In undertaking a between-religion analysis to compare the teachers' conceptions from one religion to another, as already undertaken for countries (figure 4), we effectively found significant differences. Nevertheless, these differences can be taken to be a single consequence of the country effect, because the religions differ greatly from one country to another. For instance, almost all the Muslims in our sample are from African countries.

As a consequence, a difference between Christian and Muslim teachers' conceptions is probably a single component comprising differences already described between African and other countries.

To solve this problem, we used a compl ement ar y t ype of mul t i var i at e anal ys i s , PCAVOI, which allows the suppression of the effect of one variable [START_REF] Sabatier | Principal Component Analysis w i t h Instrumental Variables as a Tool for Modelling Composition Data[END_REF]. This mathematical process is used to suppress an effect before undertaking a between-variable analysis, e.g. suppressing the effect of the countries. Thus, it is possible to test whether the significance of a variable (e.g. the religions) is independent of the suppressed variable or not.

As a consequence, we suppressed the variance between countries in order to determine whether the residual variance between the religions is still significant. The randomization test (Monte Carlo, figure 7) shows that the observed distribution is inside the histogram built from 1000 stochastic essays: the observed distribution is not different from a random distribution. The practised religion does not correlate with particular conceptions about genetic determinism, i n d e p e n d e n t o f t h e e f f e c t o f t h e country. On the contrary, when suppressing the variance coming from religions, we still found significant differences among the countries. The conclusion is that the effect of religion is not independent of the country effect, which cannot be reduced to the religion effect.

Each teacher indicated his/her religion (including the possibility to tick 'agnostic', 'atheist' or 'I don't wish to answer') and also his/her degree of belief in God and of practising religion, using a scale of five boxes ranging between 'I believe in God' and 'I don't believe'; 'I practice religion' and 'I don't practice'. For the responses to these two last parameters, we undertook the same analyses as those just described above for the religions. We obtained the same kind of result: a significant difference, which disappears when suppressing the country effect. However, the country effect is still significant when suppressing the effect of the degree of belief in God or the effect of practising religion.

As a consequence, we cannot say that there is no correlation between belief in genetic determinism and belief in God or practising religion, but that this correlation is mainly part of the sociocultural context of each country.

As an illustration, we compared the conceptions of teachers belonging to the same religion but living in different countries, for instance the responses to question A35 by only Catholic teachers living in France, Italy, Lebanon or Cameroon (figure 8): the differences are very significant (χ 2 = 362.102, df = 9, p < 2.2e-16). We also observed significant differences for the responses to other questions such as A25, A36, A38 and A19.

A Difference Linked to Knowledge of Biology

To ascertain whether the level of knowledge can influence conceptions about genetic determinism, a comparison between teachers (pre-and in-service) of biology and teachers of the country language (pre-and in-service) is assessed (after suppressing the country effect with PCAVOI): the outcomes show that the Monte Carlo test is significant (p < 0.001) and that questions A31 and A27 explain these significant differences. That is not surprising, because they are the two questions that are the most related to biological knowledge. When the questions include some opinions about genetic determinism, they do not differentiate between biology teachers and non-biology teachers: the level in biology does not influence the beliefs in innatism.

Influence of the Level of Training

Teachers were categorized depending on the number of years they h a d s t u d i e d at university (regardless of whether they studied biology, language or another subject), to form three groups: N1 = 1 year at university, N2 = 2 or 3 years and N3 = 4 years or more.

The difference between the three groups is very significant. Even after a PCAVOI suppressing the country effect, a between-study analysis according to these three groups, completed by the Monte Carlo test, showed a significant difference between the three levels of training. The lowest one showed a higher level of innatism: the number of genes being more important for humans compared with other species (A27), some human ethnic groups being superior to others due to their genes (A35) or for biological reasons women taking care of housekeeping more often than men (A38). So, the lower the level of training, the more teachers believe in innatism, independent of the country. This effect is very important, giving encouragement to calls for an increase in the level of teacher training, but not only in biology.

Co-inertia Analysis: Correlation between Innatism and Non-Tolerant Attitudes

The idea of co-inertia is the comparison of the structure of a dot cloud (our sample of teachers) with two sets of variables (genetics and attitudes), using two different PCAs. In other words, it is possible to display the similarities (or dissimilarities) of teachers' responses to two different topics: in this case, genetic determinism and more or less tolerant attitudes.

The existence of a strong significant co-structure for the two sets of variables is confirmed using a Monte Carlo permutation test (figure 9b). The first component explains 85% of the variance of both PCAs (figure 9a). The analysis of figures 9c and 9d shows the meaning of this co-structure. The most weighted questions (figure 9c) are A25, A38, A35, A46 and A9, while in figure 9d, the most weighted questions are A41 ('Homosexual couples should have the same rights as heterosexual couples'), A2 ('In a modern society, men and women should have equal rights') and A30 ('It is important that there are as many women as men in Parliament').

The vectors related to these questions tend to point out the tendency that when teachers formulate innatist conceptions for human groups, they also formulate intolerant attitudes related to the rights of women or of homosexuals, and vice versa. Questions on individual innatism are less important (see figure 9c showing the small vectors for questions A24, A6, A3, A53, A19 and A43), so an actual correlation between individual innatism (related to human twins or clones) and intolerant attitudes is not demonstrated.

Nevertheless, as [START_REF] Keller | Genes We Trust: The Biological Component of Psychological Essentialism and its Relationships to Mechanisms of Motivated Social Cognition[END_REF] As a complementary approach, multiple regression analysis was applied in order to evaluate the influences of the independent variables 'genetic determinism' (IV1) and 'country' (IV2) on the dependent variable: intolerant attitudes (DV). According to the value of the multiple correlations (R), only IV1 (genetic determinism) contributes significantly (R = 0.348; p < 0.001) to explaining DV (intolerant attitudes). Nevertheless, IV2 (countries) and the interaction between IV1 and IV2 are not significant (respectively p = 0.158 and p = 0.052). This kind of analysis confirms that the variable 'genetic determinism' explains the most important part of the intolerant variation, as shown in our figure 9, but without differentiating the two groups of genetic determinism emerging from our analyses. This multiple regression analysis is not able to put into evidence the differences among countries related to intolerant attitudes, because the item groups such as 'intolerant attitudes' (table 2) are heterogeneous. When conducting a between analysis differentiating the 23 countries from only the 6 variables 'intolerant attitudes' (figure 10), the difference among countries is very significant and mainly due to axis 1 for the questions A41 (homosexuals' rights), A2 and A30 (gender equality). The more tolerant countries are to the left of this axis, and the less tolerant ones to the right, with a ranking very similar to the ranking observed in figure 4 for the variable 'genetic determinism'. Finally, when carrying out another between analysis discriminating countries by using the 22 questions (genetic determinism + intolerant attitudes), the results confirm the very significant differences among countries and the correlation showed by the co-inertia analysis (figure 9): some intolerant attitudes (related to the rights of females and homosexuals, pole V = values in figure 1) are strongly correlated with some conceptions of genetic determinism, those justifying by biological arguments the differences among genders or ethnic groups, corresponding to an interaction between scientific knowledge (K) and values (V).

Conclusion

Our research firstly investigated the different conceptions about genetic determinism from our total sample of teachers in 23 countries. The results showed that conceptions about genetic determinism cannot be reduced to a simple dichotomy between more innatism and less innatism. When teachers are located more on the innatism pole, we can distinguish two categories of innatism:

• The first one justifies for biological reasons the differences or similarities between human groups (gender or ethnic).

• Another trend justifies for biological reasons the differences and similarities between individuals (of the same group, such as twins or clones).

Our third research question was: is innatism related to intolerant attitudes? The outcomes showed correlations between intolerant attitudes and innatism. However, only the innatism related to human groups is correlated with some intolerant attitudes (see coinertia analysis, figure 9; and figure 10). This means that on one hand some teachers believe in innatism but with only a strong influence of genes to differentiate individuals and they refuse to justify gender or ethnic differences by genetics. On the other hand, other teachers at the same time accept innatism explaining individual but also collective differences, e.g. related to gender and ethnic groups, and show intolerant attitudes related to rights linked to gender or homosexuality.

The second research question tried to identify t h e p a r a m e t e r s c o r r e l a t e d w i t h innatism. The analysed data show that innatism related to groups (ethnic or gender) is the main difference among countries (figure 4) as well as some intolerant attitudes (figure 10). The 23 countries differ from their specific scociocultural context, including religion as well as the level of believing in God or of practising religion. In the majority of European countries, as well as in Australia and Brazil, teachers' innatism linked to some intolerant attitudes is less important while in other European countries (such as in Poland or Lithuania), the number of teachers strongly believing in genetic determinism of sociocultural human features is higher. In the African countries of our sample, as well as in Lebanon, more than half of the teachers believe in innatism (individual and collective innatism). These differences in social representations between countries are probably linked to several parameters, including economical, political, geographical and historical dimensions, and are also linked to the way in which the 'mass media' deal with the topic of genetic determinism. In each country, more studies could be developed in order to analyse this last parameter. For instance, in France, the low level of innatism among teachers is probably linked to the history of France, including the strong media coverage of scientists and philosophers formulating ideas about the dangers of this ideology in society.

The level of teachers' training also influences their conceptions, mainly related to genetic determinism about groups, with innatism decreasing when the level of teacher training increases. This result is particularly important, showing from this first international survey (until now, no international survey of this size has been undertaken concerning this topic) that a more citizenship-focused education can be linked, in any country, to an increase in the level of qualification of teachers, for primary as well as for secondary school teachers, and for language or biology teachers.

Improving the way in which biology is taught is also very important. Several researchers [START_REF] Roth | Educating for Citizenship: Reappraising the Role of Science Education[END_REF][START_REF] Leach | Science and Citizens: Globalization and the Challenge of Engagement[END_REF], Grace 2010, etc.) have already noticed that science education is an important topic for (democratic) citizenship. [START_REF] Marks | Public Understanding of Genetics: The Deficit Model[END_REF] argued that a lack of genetic literacy leads to an inability to participate fully in social life and potentially a lack of support for new genetic technologies. The role of education is to give keys to citizens for their decision-making. However, according to our research, we think that genetics education can also lead to better tolerance, whi c h i s al s o a pi l l a r of citizenship. Thus, it is suggested that 'genetic determinism' should be included and discussed in biology teachers' training, with coverage of epistemological approaches including social and ethical dimensions, and with the analysis of the possible interaction between knowledge, values and social practices (KVP: figure 1). Explaining how science can be used to justify ideology can help teachers and students become aware of their own conceptions. As shown by our results, biology teachers do not differ from other teachers, meaning that knowledge of bi ol ogy doe s not influence their opinion about ge ne t i c determinism and innatism. During teaching, students' values and social practices are more difficult to change than their scientific knowledge. Nevertheless, [START_REF] Kochkar | Les Déterminismes Biologiques. Analyse des Conceptions et des Changements Conceptuels Consécutifs à un Enseignement sur l'Epigenèse Cérébrale chez des Enseignants et des Apprenants Tunisiens (Biological Determinism[END_REF] showed that if recent knowledge such as epigenetic processes is included in students' training, innatism can decrease in the population tested. A multi-dimensional approach to considerations of the determinism of human features, including their behaviour and intellectual performances, should help teachers to become less focused on outdated stereotypes of innatism. Training biology teachers could link their biological knowledge to historical, epistemological, psychological and social dimensions. [START_REF] Dambrun | Race", Sex and Social Class Differences in Cognitive Ability: Towards a Contextual rather than Genetic Explanation[END_REF] already concluded that an understanding of the differences between human groups is possible 'towards contextual components'. That is an area for urgent improvement of the citizenship dimension at school.

Figure 2 :

 2 Figure2: Links between conception and situated conception (SC1 to SC5 here), according to[START_REF] Clément | Représentations, Conceptions, Connaissances' (Representations, Conceptions, Knowledge)[END_REF] and[START_REF] Clément | Conceptions, représentations sociales et modèle KVP' (Conceptions, Social Representations and KVP Model)[END_REF] (SC = situated conceptions).

  from the second group, are between |0.54| and |0.40|). In this total sample (coming from 23 countries), most teachers are opposed based on their beliefs to g e n e r a l g e n e t i c determinism of differences (individual, ethnic or gender: component C1), and for some teachers, there is no correlation between their beliefs in individual or collective genetic determinism (component C2).

Figure 3 :

 3 Figure 3: Principal component analysis (PCA) of the responses from 8,285 in-service and pre-service teachers and the 16 variables on genetics. (a) The correlation circle shows that the differences between the teachers' conceptions come from two independent axes: C1 and C2. (b) The table of coordinates of the variables for the first components C1 and C2. (c) The histogram of the proportion of variance for each component: the first two are the most informative (C1 = 20% and C2 = 10% of the total variance).

Figure 4 :

 4 Figure 4: Between-class analysis differentiating between the 23 countries. From left (innatist conceptions) to right (less innatist conceptions) of the horizontal axis D1: DZ = Algeria, TN = Tunisia, LB = Lebanon, CM = Cameroon, MA = Morocco, SN = Senegal, BF = Burkina Faso, LT = Lithuania, PL = Poland, RO = Romania, HU = Hungary, CY = Cyprus, EE = Estonia, DK = Denmark, DE = Germany, PT = Portugal, MT = Malta, FI = Finland, GB = Great Britain, BR = Brazil, AU = Australia, IT = Italy, FR = France. See the text for explanations of (a), (b), (c), (d) and (e).

Figure 7 :

 7 Figure 7: The Monte Carlo permutation test, indicating the non-significant results among groups of religions (in our sample: Catholics, Protestants, Orthodoxies, Shiites, Sunnites, Druzes, Agnostics/Atheits, other religions).

Figure 8 :

 8 Figure 8: Responses of Catholic teachers in France, Italy, Cameroon and Lebanon to the question A35 'Ethnic groups are genetically different and that is why some are superior to others' (number of French Catholic teachers = 279, Italian Catholics = 440, Cameroonian Catholics = 173, Lebanese Catholics = 152).

  [START_REF] Dambrun | Why Does Social Dominance Orientation Decrease with University Exposure to the Social Sciences? The Impact of Institutional Socialization and the Mediating Role of "Geneticism[END_REF] pointed out, we found a significant correlation between intolerant attitudes (for Dambrun et al.: 'antiegalitarianism') and innatism-related human groups (differences among gender or among ethnic groups).

Figure 9 :

 9 Figure 9: Co-inertia analysis: (a) histogram of eigenvalues; (b) Monte Carlo test; (c) correlation circle of genetics variables; (d) correlation circle of attitude variables.

Figure 10 :

 10 Figure 10: Between-class analysis differentiating between the 23 countries. From the left (more tolerant) to the right (less tolerant) of the horizontal axis (a: histogram of variance; b: correlation circle; c: Monte Carlo test; d: reparation of countries).

Table 3 :

 3 Teachers' samples in each country

	Countries	Number of teachers
	Algeria	223
	Australia	201
	Brazil	402
	Burkina Faso	296
	Cameroon	373
	Cyprus	322
	Denmark	259
	Estonia	182
	Finland	306
	France	732
	Germany	365
	Great Britain	154
	Hungary	334
	Italy	559
	Lebanon	722
	Lithuania	316
	Malta	198
	Morocco	330
	Poland	311
	Portugal	350
	Romania	273
	Senegal	324
	Tunisia	753

Acknowledgements A large part of this work has been supported by the Biohead-Citizen European Research Project (Specific Targeted Research n° CIT2-CT2004-506015, FP6, Priority 7: 'Biology, Health and Environmental Education for Better Citizenship'). We particularly thank all the teams that gathered the data used in the present work, under the responsibility o f t h e f o l l o w i n g t e a m l e a d e r s : A l g e r i a : F a r i d a K h a m m a r , B i o l o g y , U S T H B ; Australia: Frances Quinn, University New England, NSW; Brazil: Graziela Lopez, University Sao Paulo & Paloma Silva, UNESP, Bauru; Burkina Faso: Ivette Béré -Yoda, ENS Ouagadougou; Cameroon: Lawrence Ntam Nchia, ENS Yaoundé; Cyprus: Nicos Valanides, University of Cyprus; Denmark: Pierre Clément & Jan Solberg, IND, University of Copenhagen; Estonia: Kai Pata & Tago Sarapuu, University of Tartu; Finland: Anna-Liisa Rauma-Kosonen, University of Joensuu; France: Pierre Clément, Univ. Lyon 1 & Daniel Favre, Univ. Montpellier 2; Germany: Franz Bogner, University of Bayreuth; Great Britain: Stephen Tomkins, UCAM-EDUC, London; Hungary: Attila Varga, National Institute for Public Education; Italy: Silvia Caravita & Adriana Valente, CNR, Roma; Lebanon: Iman Khalil, Faculty Pedagogy, Université Libanaise; Lithuania: Jurga Turcinaviciene, University of Vilnius; Malta: Paul Pace, University of Malta; Morocco: Sabah Selmaoui, ENS Marrakech; Poland: Elwira Samonek-Miciuk, University of Lublin; Portugal: Graça Carvalho, IEC, University of Minho; Romania: Adrienne Kozan-Naumescu, Babes-Bolyai University Cluj; Senegal: Mame Seyni Thiaw, FASTEF, UCAD; Tunisia: Mondher Abrougui, ISEFC, University of Tunis.

We want also to thank Professor Jack Holbrook for his precious help in the final proofreading.


The hyperbolic control system considered Our hyperbolic control system is (1)

y t + A(y)y x = 0, (t, x) ∈ [0, T ] × [0, L],
where, at time t ∈ [0, T ], the state is

x ∈ [0, L] → y(t, x) ∈ R n . Let y * ∈ R n be fixed. Assume that A(y * ) has n distinct real distinct eigenvalues: Λ 1 (y * ) < . . . < Λ m (y * ) < 0 < . . . < Λ n (y * ) for some m ∈ {0, • • • , n}.
After a linear change of variables, we mays assume that

A(y * ) = diag (Λ 1 (y * ), . . . , Λ n (y * )). For y ∈ R n , let y -∈ R m and y + ∈ R n-m be such that y = y - y + .
The control is y + (t, 0) and y -(t, L).

x L 0

H(t,x) V(t,x) u 0 u L Z 0
The Saint-Venant equations

The index j is for the j-th reach. Conservation of mass:

(1)

H jt + (H j V j ) x = 0.
Conservation of momentum:

(2)

V jt + gH j + V 2 j 2 x = 0.
Flow rate:

Q j = H j V j .
Barré

y t + y x = 0, y(t, 0) = u(t), x ∈ [0, L], t > 0.
x L t (0, 0)

y t + y x = 0, y(t, 0) = u(t), x ∈ [0, L], t > 0. x L t (0, 0) x L t (0, 0) T Case 1: T < L y 0 (x) u(t) not controllable y t + y x = 0, y(t, 0) = u(t), x ∈ [0, L], t > 0. x L t (0, 0) T Case 2: T > L controllable y 0 (x) u(t) x t T Sketch of proof (continued) x t T T 1 y 0 + - Sketch of proof (continued) x t T y 0 + - T 1 y 1 - + T -T 1 Sketch of proof (continued) x t T y 0 + - T 1 y 1 - + T -T 1 Sketch of proof (continued) x t T y 0 + - T 1 y 1 - + T -T 1
Sketch of proof (continued)

y t + y x = 0, y(t, 0) = u(t), x ∈ [0, L], t > 0.

Riemann coordinates

Let l be the number of reachs. Let n = 2l,

Then the Saint-Venant equations can be written as

The flow is subcritical flow The control problem

Let T > 0. Given y 0 : [0, 1] → R n and y 1 : [0, 1] → R n . Does there exist a solution of the control system such that y(0, x) = y 0 (x) and y(T, x) = y 1 (x)? Local controllability: y 0 and y 1 are close to y * .

Controllability theorem

Theorem (Tatsien Li and Bopeng Rao ( 2003))

The local controllability for the C 1 -norm holds if and only if T > T c with

Complements

• For the control on one side only, see T. Li and B. Rao (2002).

• Global steady states controllability for the Saint-Venant equations:

M. Gugat ( 2003), M. Gugat and G. Leugering (2003Leugering ( , 2009)). Friction and slopes are allowed in the last paper. • Generalization: A(t, x, y): Z. Wang (2007).

Complements: BV solutions • F. Ancona and A. Marson (1998): y t + f (y) x = 0, x ∈ (0, +∞), y(0, x) = 0: reachable set.

• Th. Horsin (1998): y t + (y 2 /2) x = 0, x ∈ (0, L), y(0, x) = y 0 (x): approximate controllability under general conditions on the desired target. • V. Perrollaz (2012): y t + (f (y)) x = u(t), x ∈ (0, L), y(0, x) = y 0 (x): global controllability in small time.

• Adimurthi, S. Ghoshal and G. Gowda (2014): y t + (f (y)) x = 0, x ∈ (0, L), y(0, x) = y 0 (x): reachable set.

• A. Bressan and G. Coclite (2002): In the BV class of entropy solutions, already with n = 2, there are cases where one cannot steer the control system from y 0 to y * even if y 0 is close to y * (if one remains close to y * in the BV-norm).

• O. Glass: One-dimensional Euler isentropic (2007) and non-isentropic system (2014), both in Eulerian and Lagrangian coordinates: Study of the controllability. Corollary: one can steer the control to y * if y 0 is close (in the BV-norm) to y * (while remaining close to y * in the BV-norm).

Sketch of proof of Li-Rao's theorem

We assume that

Let T 1 > 0 be such that

2T 1 < T.

(3) Let us recall that, for y ∈ R n , y -∈ R m and y + ∈ R n-m are such that y = y - y + .

T 1 > max{L/|Λ i (0)|; i ∈ {1, . . . , n}}/2.