[by Cyrille Godonou, statistician]

While reading the book Evaluation, a threat? co-written by the trio Céline Darnon, Céline Buchs and Fabrizio Butera, we discover the following passage:

« It goes without saying that choosing to pursue one course rather than another depends, in particular, on the confidence one can have in succeeding in it, and therefore on the assessment one makes of one's own level of competence (self-assessment). This link between expectation of success and choice of orientation has been clearly demonstrated in the scientific literature. Similarly, the feeling of success that students, both girls and boys, develop with regard to mathematics is very largely influenced by the gender stereotype in this field. It turns out in particular that the gender stereotype in mathematics leads parents and teachers to assess the skills of the two sexes differently. Hence the idea of ​​a bias rooted in gender stereotypes.

(Darnon, Buchs, & Butera, 2015).

Several studies show that parents perceive girls as less gifted in mathematics, less interested in this discipline, and therefore more compelled to work to succeed. Perhaps more importantly, these perceptions persist even when girls obtain identical or even higher grades than boys! Jussim and Eccles questioned a hundred mathematics teachers about the competence and efforts made in this discipline by each of the pupils in their 6th grade class (11-12 years old).

Despite any differences (in this study) between girls and boys in terms of grades and time spent on mathematics homework, teachers rated boys as more competent and less industrious than girls in mathematics. It is conceivable that teachers might be mistaken about the amount of time students spend on their homework. It is a priori more difficult to understand why they overestimate the competence of boys, even though they know their grades precisely.

Hence the idea of ​​a bias rooted in gender stereotypes." (Darnon, Buchs, & Butera, 2015).

At first glance, it seems shocking that teachers who grade their students and therefore know the grades they give, judge differently students who have nevertheless obtained the same grades in class: an examination at first glance can only lead to the conclusion of gender stereotypes to the detriment of girls perceived, a priori, wrongly as being less efficient. In the article Girls and boys facing science. Lessons from a survey in high schools in the Paris region, Breda et al. (2018) make a similar argument, using as a benchmark the grades obtained in the national brevet diploma (DNB) to estimate the real level of mathematics of girls and boys in secondary education in order to compare them with their career choices (Breda, Grenet, Monnet, & Van Effenterre, 2018). The results of girls and boys from the Paris region enrolled in the second or final year of science, in the mathematics test of the national brevet des collèges diploma, appear extremely close (Figure 1). And yet " Girls are significantly less likely to report having a good level in mathematics than boys (between 11 and 14 points difference) » (Breda, Grenet, Monnet, & Van Effenterre, 2018).

There is a similarity in the results of girls and boys at the international level.

In some countries, girls score higher than boys in mathematics.

But, to return to the aforementioned work (Darnon, Buchs, & Butera, 2015), is this conclusion leading to the idea that parents and teachers would be strongly biased (and the girls themselves), without empirical foundation, as to the performance gaps in mathematics with equal grades, robust?

As we will see, a careful examination of the literature seems to indicate that there are some important nuances to be made. On the one hand, at the individual level, it is quite possible to observe gender differences in performance in competitive situations in favor of boys, while in exams, girls obtain equivalent or even higher results (Ors, Palomino, & Peyrache, 2013). On the other hand, at the level of groupings by gender, even with equivalent averages, the variance of boys is possibly greater, hence their possible over-representation among the best and worst performers (Halpern, et al., 2007). These two highly counterintuitive mechanisms explain the illusion resulting from an approach consisting of simply considering that two students who have the same grades in class would obtain the same results in competitions or that two sociodemographic groups obtaining similar averages would be expected to achieve the same performances in selective tests. 

Moreover, some quota promoters^{[1]"We can suggest that a small working group at the ENS, bringing together the efforts of individual reflections already initiated, look into the causes of the low number of girls accepted into science. Partial and, we hope, transitional solutions could be proposed. Without anticipating the results of this working group, we can well imagine that it will not be able to avoid thinking about the nature and coefficients of the competitive examinations. Thus the C/S competition only takes into account the mathematics and physics grades to eliminate candidates for the written exam. It is precisely designed to select geniuses, Fields medalists - and besides, it works well that way! This option particularly disadvantages girls, who tend to be good at everything, as we can see from the results of those who are admitted to the oral exam. If we are willing to acknowledge that "the temple of science" is not made up solely of climbing plants, women, with their particular talents, those of communication for example, can make a very important contribution. And besides, nothing prevents them from having a Fields medal themselves one day: this year it was a girl who came first in the Mathematics competition. It will probably also be necessary to rethink the composition of the juries of examiners in the competition and to stick to a strict rule of parity between men and women. We know indeed the positive role of encouragement and support that certain female teachers play in preparatory classes. Finally, it is clear that we will have to re-discuss without prejudice the hypothesis of quotas for girls, disguised or displayed, permanent or progressively decreasing according to evolution. This hypothesis shocks us today, but we must guard against taboos. After all, some major French business schools do indeed practice quotas without saying so through oral exams. And in a context that is certainly very different, the hard feminism of American scientists is recording successes. Discussions with the principals of major high schools and teachers of preparatory classes should be continued. We should no longer leave too few girls in these classes where life is often very hard for those who are isolated. We should also pay special attention to high schools like Fénelon, which concentrate girls in preparatory classes, and develop teaching of the highest quality there. Raising awareness among secondary school science teachers of the specific difficulties of girls would doubtless also be useful. Many other ideas could be suggested" (Leduc, 1995).}and parity do not hesitate to suggest modifying the coefficients of the competitions intended for careers as mathematicians or physicists (higher normal schools): " So the C/S competition only takes into account the math and physics scores to eliminate candidates for the written exam. It is precisely designed to select geniuses, Fields medalists — and it works well that way! This option particularly disadvantages girls, who tend to be good at everything, as can be seen from the results of those who are admitted to the oral exam. If we are willing to recognize that "the temple of science" is not made up solely of climbing plants, women, with their particular talents, those of communication for example, can make a very important contribution. » (Leduc, 1995). These remarks contrast with those of Darnon et al. (2015).

Identical grades in class or on exams do not necessarily mean that performance will be identical in competition or on standardized tests.

First, having similar grades does not necessarily imply obtaining equivalent results in a competitive context or even on standardized tests of an unusual nature.

In the United States, the male advantage in the SAT (Scholastic Assessment Test) in mathematics has persisted for around fifty years (Perry MJ, 2016).

Among the top 1% of math performers on the SAT test in the United States, there were almost twice as many boys as girls each year between 2011 and 2015.

In France, in middle school, a gender asymmetry appears depending on whether we consider strictly academic assessments in continuous monitoring or tests relating to evaluative content with which the students are not familiar: " Cognitive tests are generally more favourable to boys than assessments based on school learning in mathematics but also in French. This effect can be partly explained by the content of the assessments. The greater involvement of girls in learning allows them to do better in the DNB exams. However, girls are less advantaged in the final DNB exam in mathematics which places them in a less familiar situation than that of homework done in class with their teacher during continuous assessment. On the contrary, their mastery of school learning does not prepare them as much for cognitive tests whose exercises and questions are less common. » (Chabanon & Jouvenceau, 2022). This observation is not new^{[2]"Underlying this discussion on assessment is the question of what we intend to learn at school, and what we therefore seek to assess during exams (Murphy, 1991; Stobart et al., 1992). When we observe, for example, that girls do better in continuous assessments than in exams (Murphy, 1991), we should ask ourselves whether what each form of assessment specifically apprehends (regularity of work, presentation skills, on the one hand, more punctual work in a limited time frame on the other) is or is not important in relation to the objectives sought (without a priori devaluing the performance of a group, by assuming in this case that the exam is more objective). A second question is of course (as we mentioned above) whether this difference between the sexes is not due to specific attitudes (themselves produced by the interplay of daily socializations); This second line of inquiry would include the fact that extending the time of tests improves the performance of girls and not that of boys (Zazzo, 1993), or the apprehension of girls in competitive situations (Roberts, 1991), especially when they are public (as shown by a certain number of experiments reported by Monteil, 1993). This discussion also concerns tests. Some researchers (Hyde and Linn, 1988) believe that one of the reasons for the reduction in gender gaps in aptitude tests (see Part 1) comes from the effort that was made to make the items more "neutral", after psychologists showed how the content of the tests was likely to generate differences between the sexes (Dwyer, 1979).}(Duru-Bellat, 1995).

The lower access of women to elite institutions in the United States would thus be due to the differential in performance in entrance tests (SAT tests similar to a competition) and not to discrimination as such (Bielby, Posselt, Jaquette, & Bastedo, 2014), the authors suggesting modifying the tests since women succeed well upstream (in high school) and downstream (once in universities), the tests would therefore be poorly calibrated according to them. It should be mentioned that similar results have been highlighted for students at the leading French business school HEC where there too girls succeed better than boys in the baccalaureate and in the first year of school while it is the opposite in the entrance exam (Ors, Palomino, & Peyrache, 2013).

In Spain too, mathematics competitions involving 40 students between the ages of 000 and 10 show that the proportion of girls is decreasing, being 16% in the first stage of the qualifiers but only 44% in the second, more competitive stage (more than 34 students), knowing that among the 2 best, girls only represent 800% (Iriberri & Rey-Biel, 146) while the participating girls obtain a slightly higher average level (the gap is not statistically significant) than that of the boys who compete, during the classic non-competitive tests in class: a real "glass ceiling" not attributable to discrimination is therefore observed by the authors.

Two effects explain this phenomenon of attrition: on the one hand, the increasing over-representation of boys as one moves up the scale of best performances and on the other hand, at an equivalent level (controlled by the grades in the classroom tests), poorer responses from girls as the difficulty increases (compared with boys).

This performance differential for identical grades is sufficiently counter-intuitive to give rise to erroneous interpretations. However, it has been clearly highlighted by the literature, as illustrated by the data from the Olympiads and the General Competition in mathematics (see below).

Even with equal means, a different variance could explain the overrepresentation of one sex in the elite in mathematics

Second, a different variance

Secondly, it is important to understand that the same average between two groups can be combined with a different variance. A fictitious caricature example can illustrate this. Consider two groups A and B, group A being half composed of students with a grade of 20/20 and the other half of students with a grade of 0/20. Group B is only composed of students all with a grade of 10/20. The average of the two groups is identical, i.e. 10/20, but the variance is zero for group B while it is relatively large for group A. If an elitist selection takes place, only members of group A will be selected, despite an identical average for both groups A and B.

The more drastic a selection is, the more it is appropriate to take into account the elite of the two groups as a reference for comparison and not the whole of the two groups. Indeed, the individuals selected are atypical, either by their skills, or by their motivation, or by both.

However, there is indeed a phenomenon of reduction in the proportion of girls as one rises in the hierarchy of performance in mathematics, as illustrated in figures 1 and 2 of the work carried out in Spain (Iriberri & Rey-Biel, Competitive Pressure Widens the Gender Gap in Performance: Evidence from a Two-Stage Competition in Mathematics, 2017). In the United States, in the top 1 per 10 of the SAT tests in mathematics, there would be eleven times more boys than girls (Hoff Sommers, 000). In a very detailed review of the gender differential in science, we find "the male-to-female ratio of 2009:2 for adolescents scoring 1 or higher in mathematics on the SAT test, 500:4 for those scoring 1 or higher, and 600:13 for those scoring at least 1" (Halpern, et al., 700).

The male overrepresentation in the highest scores is verified in France in the population of middle school students in mathematics and in psychometric tests, despite a slightly higher intelligence quotient (IQ) (Flynn, 2012) for girls (Guez, Explaining the IQ-Achievement Gap in France: an Epidemiological Analysis using the DEPP Cohort Study, 2017). However, the observation that with equivalent non-verbal IQ, girls obtain lower results in mathematics is paradoxical: in fact, non-verbal IQ is precisely very correlated with results in mathematics (Guez, Panaïotis, Peyre, & Ramus, 2018). In the United States also, we note that the ratio by sex in mathematics for the white population consists of 1,45 boys per girl for the 95^rd percentile and 2,06 for the 99^rd, these figures being respectively 1,09 and 0,91 for the very minority Asian population (Hyde, Lindberg, Linn, Ellis, & Williams, 2008). The authors thus note that an academic discipline requiring cognitive competence with a floor at 99^rd percentile would in principle have a gender ratio of around 2, i.e. 67% men and 33% women, whereas in reality engineering doctorates only include 15% women. The differential in performance in mathematics in the tail of the distribution is therefore not enough to explain the under-representation of women according to the authors, but partly answers the question sometimes asked: "But how can we measure this skill when it never reaches the comparison stage?" (Petrowski, 2018).

The general competition in mathematics and physical sciences has been organized since the 19th^e century allowing us to have a certain perspective on the girls awarded prizes over the course of two centuries^[3]

"Presentation of the general competition: A history of the general competition can be found on the website of the Ministry of National Education, and here we limit ourselves to a few indications. Created in 1744 to reward classical Greco-Latin studies, the general competition diversified in the 1811th century by welcoming mathematics in 1833, physics in 1904, but still only concerned boys from Parisian high schools. Abolished from 1921 to 1924, it opened in XNUMX to students from the provinces and to girls.", the sufficient size of the sample of participants allowing conclusions to be drawn, thanks to the available gender-based statistical data^{[4]"Teachers who present candidates regret, when they do not have any prizewinners, not having any information on the performance of their students. This regret is undoubtedly well-founded. Until now, the jury, for mathematics, has been content to publish the text and sometimes the solutions to the tests, without writing a report. This is certainly a shortcoming that should be remedied. It would undoubtedly be very useful for teachers to have details on the expectations of the jury. In addition, the report could contain some statistics: number of girls and boys registered or awarded prizes; distribution by academy of those registered and awarded prizes. For all these reasons, the jury of the general competition plans to publish the report for the next 2015 session. In addition, the general inspection will take stock of the activities of preparation for the general competition in the establishments of the various academies and will analyze the geographical diversity of the rankings."} for recent years^{[5]"In 2014, there were 2209 registered for the general competition for trades, 14 registered for the general competition for high schools, including 931 in mathematics, the most represented discipline and showing significant growth: 3442 registered in mathematics in 1333, 2003 in 2216, 2008 in 2946. For comparison, the other strongly represented disciplines are physics-chemistry (2012 registered in 1843), English (2014), French composition (1314) and life and earth sciences (1108)."}.

The general mathematics competition seen by teacher Johan Yebbou (Association
of Public Education Mathematics Teachers)^{[6]See source}:

« 2005-2014 Awards Some observations can be drawn from examining the awards of the last ten years.

• A strong gender imbalance: girls generally obtain 10% of prizes, accessits, and mentions. This rate also remains valid if we limit ourselves to prizes in the strict sense, since three young girls have obtained one since 2005: Suzanne Lanéry, 3rd prize in
2005; Irène Waldspurger, 2nd prize in 2006; Diane Gallois-Wong, 1st prize in 2011. It seems that we have to go back to 1934 to find another young girl, Jacqueline Ferrand, 1st prize in the general mathematics competition. »

The jury report for the 2018 Physics-Chemistry general competition, Physics-Chemistry S series states:

« There are therefore approximately 31% of girls among those registered for a representation of approximately 47% in the population of students in the final year S1 classes. » (Obert & Szymczak, 2018).

In 2018, there were 712 girls for 1589 boys in the general physics-chemistry competition among those registered, i.e. 31% girls.^{[7]“The 2301 candidates registered for the general physics-chemistry competition for the 2018 session are distributed as follows according to their gender and territorial origin.” (Obert & Szymczak, 2018).}.

The report of the jury for the 2017 general competition for the Physics-Chemistry test in the S series states: “ There are therefore more than 32% of girls among those registered (for a representation of 47% in the population of students in the final year of high school). » (Obert & Szymczak, 2018).

Here is what we can read in the jury report of the general competition Mathematics Series S—Session 2017: “ The jury received 4311 copies. Only 18 copies can be awarded, according to the rules of the competition. The prize list includes 3 girls. However, the jury considered that 93 other copies were of very high quality or even of remarkable quality. (there are 10% girls in this list). » (Torossian, 2017).

« Regarding participation by academy and country, here is a more precise table. The percentage of girls has stabilized for several years at 30%. The jury encourages teachers of Terminale S classes to encourage young girls in these classes to take the competition with confidence. (Torossian, 2017).

Let us note that girls constitute 47% of students in the final year of science but more than 30% of students participating in the general competition and ultimately more than 10% of the copies. of very high quality or even remarkable quality "This "glass ceiling" among adolescents is hardly likely to be explained by family responsibilities linked to motherhood.

Here are the results of the Mathematics Olympiad in the fourth grade for the Grenoble academy between 2014 and 2017: girls are in the minority among the prizewinners (26%) and those ranked for each year (38%).

In 2014, they constituted a quarter of the prizewinners and a third of the ranked (Figure 6). In 2015, the share of girls among the prizewinners fell to 15% but that among the ranked increased, reaching 41% (Figure 7). In 2016, 27% of the prizewinners were girls and 35% of the ranked were girls. Between 2014 and 2016, the share of girls among all the ranked and prizewinners was around 30%. An increase in the share of girls occurred in 2017 with 36% of the prizewinners being girls and 44% of the ranked (Figure 9).

In total, over this period, a quarter of the prize-winning students were girls and a third of all those who were awarded prizes or ranked, these are shares that can be compared with the share of women in engineering schools and in research in mathematics and physical sciences (17% and 18% in 2006)^{[8]"At the end of 2006 it had 26 people, 078% of whom were women, including 43 researchers, 11% of whom were women.
The proportion of women is very unequal depending on the disciplines:
17% of researchers in mathematics,
18% in physics,
19% in engineering sciences,
31% in chemistry,
39% in life sciences,
44% in human and social sciences.
For all disciplines, they were 38% of research officers, 22% among research directors. » (Haton, 2014). By comparison, at university, 40% of lecturers, 18% of professors. » (Haton, 2014).}.

Figure 8 Rankings by gender in mathematics in the fourth-grade Olympiad competition in 2016 in the Grenoble academy
Figure 9 Rankings by gender in mathematics in the fourth-grade Olympiad competition in 2017 in the Grenoble academy
Figure 10 Rankings by gender in mathematics in the fourth-year Olympiad competition from 2014 to 2017 in the Grenoble academy

http://www.ac-grenoble.fr/disciplines/maths/articles.php?lng=fr&pg=218

The glass ceiling in science would thus appear as early as secondary education (or even earlier according to some studies), without any apparent discrimination at its genesis. While female students in science at the École Normale Supérieure and the École Polytechnique obtained more very good grades in the baccalaureate than their male counterparts, in the general competition boys have the advantage.

100% of the scientific graduates of the École Normale Supérieure who obtained a distinction in the general competition are boys, or 10,5% of male École Normale Supérieure students. The gap is smaller among the École Polytechnique students, with 5,3% of male École Polytechnique students obtaining a distinction in the general competition compared to 3,9% of female École Polytechnique students. Among the École Polytechnique students obtaining a distinction in the general competition for all sexes, 94% are boys and 6% are girls.

Little or no significant change at the international level

At the international level, between 1936 and 2018, out of around sixty winners of the Fields Medal (the highest distinction in mathematics, equivalent to the Nobel Prize), one woman was awarded the prize in 2014: the Iranian Maryam Mirzakhani.

Studies show that women are now favored in recruitment in mathematical disciplines (Williams & Ceci, 2015): they are twice as likely to be recruited with an equivalent profile according to a testing study where identical CVs were sent to recruiters in American universities. Some authors claim that gender discrimination has ceased to be a major cause of the underrepresentation of women in mathematical fields.^{[9]“Importantly, of those who obtain doctorates in math-intensive fields, men and women entering the professoriate have equivalent access to tenure-track academic jobs in science, and they persist and are remunerated at comparable rates-with some caveats that we discuss. The transition from graduate programs to assistant professorships shows more pipeline leakage in the fields in which women are already very prevalent (psychology, life science, social science) than in the math-intensive fields in which they are underrepresented but in which the number of females holding assistant professorships is at least commensurate with (if not greater than) that of males. That is, invitations to interview for tenure-track positions in math-intensive fields-as well as actual employment offers-reveal that female PhD applicants fare at least as well as their male counterparts in math-intensive fields. Along these same lines, our analyzes reveal that manuscript reviewing and grant funding are gender neutral: Male and female authors and principal investigators are equally likely to have their manuscripts accepted by journal editors and their grants funded, with only very occasional exceptions. There are no compelling sex differences in hours worked or average citations per publication, but there is an overall male advantage in productivity. We attempt to reconcile these results amid the disparate claims made regarding their causes, examining sex differences in citations, hours worked, and interests. We conclude by suggesting that although in the past, gender discrimination was an important cause of women's underrepresentation in scientific academic careers, this claim has continued to be invoked after it has ceased being a valid cause of women's underrepresentation in math-intensive fields. consequently, current barriers to women's full participation in mathematically intensive academic science fields are rooted in pre-college factors and the subsequent likelihood of majoring in these fields, and future research should focus on these barriers rather than misdirecting attention toward historical barriers that no longer account for women's underrepresentation in academic science. » (Ceci, Kahn, Ginther, & Williams, 2014).}

(Ceci, Kahn, Ginther, & Williams, 2014). It can be said that it would therefore take time for the effects to be felt. In this regard, we can refer to the history of the 1901th century to examine, in light of the spectacular changes in the status of women, how the share of women among Nobel Prize winners in physical sciences and chemistry has evolved. During the "unequal" period when the first wave of the feminist movement had not yet won its demands (the right to vote) in most Western countries, i.e. from 1918 to 5, XNUMX% of Nobel Prize winners in physical sciences and chemistry were women.

From 1919 to 1968, in a context of democratization and Sovietization, women massively obtained the right to vote, i.e. the political equality of the first feminist wave, the feminization rate of the Nobel Prize being then 2%.

From 1969 to 1999, the second wave of feminism achieved its goals, with professional equality and reproductive rights being enshrined. More generally, this period corresponds to formal equality in socio-economic matters. Above all, this period is characterized by the massive entry of women into higher education and the world of work. However, no woman has been awarded the Nobel Prize in material sciences, nor in physical sciences nor in chemistry.

The third feminist wave from 2000 to 2021 focuses on the social construction of gender, the fight against discrimination despite formal rights and, in short, an objective of equality of results which replaces the previous objective of equality before the law. So-called positive discrimination measures are multiplying. The digital revolution democratizes access to information, increasingly allowing people to break down the barriers of yesteryear. The Nobel Prize in material sciences is then 4%.

Thus, regardless of the period considered, the share of women winning a Nobel Prize in material sciences does not exceed 5% and rises to 2% between 1901 and 2021.

In computer science, there has been a strong evolution in recent years. While no woman had been awarded the Alan Turing Award in computer science between 1966 and 1999, 9% of the recipients of this greatest international distinction were women between 2000 and 2021. Since the creation of the award in 1966 until 2021, women constitute 4% of the winners.

Comparative advantages or absolute advantages according to the distribution quantile

Gendered educational orientation may result in part from comparative or absolute advantages, to use the terminology of Adam Smith and David Ricardo. For example, if girls perform better than boys in the arts but also in the hard sciences, although to a lesser extent, then they may be more likely to choose the arts. Their comparative advantage in this case is in the arts despite an absolute advantage in both the sciences and the humanities. Heterogeneity along the distribution in mathematics may give boys an absolute advantage even though they have no advantage at the mean or median level.

At an equivalent educational level, girls are less likely to apply for the so-called "S" scientific stream (first filter in the subset of "good students" in the second year of general education, themselves already the result of a filter among middle school students (see also (Hulin, 2008)). However, girls have better success rates in the scientific baccalaureate ("bac S") and obtain more distinctions than their male counterparts.

At an equivalent educational level, girls apply less to preparatory classes for the grandes écoles scientifiques (CPGE) mathematics-physics (MP) or physics-chemistry (PC), which is a second filter since 14% of students in a cohort of 6th graders in 1995 reach Terminale S without having repeated a year and 14% of S baccalaureate holders in 2008 go into scientific CPGE (0,14*0,14=0,0196 from which we only get 2% of a cohort of 6th graders).^rd integrates a scientific CPGE MP or PC).

In scientific CPGE, girls are less likely to enter the star class corresponding to the elite classes (third filter): more generally, girls drop out more, their share in the second year (the year of the competition) being lower than in the first year, "the competition, which we know is increasingly strong as you progress through the CPGE stream (Darmon, 2013; Masy, 2014b), is detrimental to women" (Dutercq & Masy, 2016). In CPGE MP and PC, girls are less ambitious for the top schools when they are questioned. Girls are also less likely to apply for the top schools' competitions (fourth filter), even when taking into account their weight in the numbers (Blanchard, Pierrel, & Buisson-Fenet, 2017).

Speaking about the place of women in science, Michèle Leduc says about girls in preparatory classes for the grandes écoles: “ The investment required for science studies puts them off, the highly specialized competitive examination, terrifying due to its small number of places, at ENS-Ulm in science does not attract them much, and the research careers that result from it frighten them in advance. » (Leduc, 1995).

Among the candidates of the major Parisian high schools between 2008 and 2013, the success rate of girls from the middle or working classes at the ENS in the MP and PC stream is 0%: none are admitted. Boys from the working classes have a success rate of 2,9%, not so far from that of girls from the upper classes (3,8%). It is the boys from the middle classes (6%) and especially from the upper classes (9,7%) who are most successful in the entrance exam for the Ecole Normale Supérieure.

So despite a drastic selection of girls, who are subject to a filter at each stage of the selection process, their success rate at the ENS in MP and PC is lower.

Reading: Among the girls from higher classes applying to the ENS for the MP and PC competitions between 2008 and 2013, 3,8% were declared admitted.

More spectacularly, CREDOC was able to illustrate that despite acquiring a higher level of education, women could obtain counter-intuitive results when certain questions were asked of them. CREDOC thus conducted a survey on the financial culture of the French (Bigot, Croutte, & Muller, 2011). The proportion of individuals who say they are not comfortable with calculations is 16% among men compared to 28% among women. Despite everything, since it is only a feeling, subjective by nature, one can wonder what it really is. CREDOC thus asked the following question: "Let's imagine that you place 100 euros in an account remunerated at 2% per year. You no longer make any deposits into this account and you do not withdraw any money either. How much will you have in your account a year later, once the interest has been paid?" CREDOC notes that 64% of men found the right answer compared to 39% of women. Surprised by the magnitude of this result, CREDOC sought to neutralize the structural effects but notes: "Nothing works: econometric models confirm that at equal age, comparable profession, similar income level and equivalent diploma, men find the right answer much more often than women."

Moreover, the feeling of financial competence is more common among men than among women. This example perfectly illustrates the fact that being equally or more qualified does not always confer an exploitable advantage to maximize one's financial interests: it is to recognize "the economic and financial illiteracy to which women, more than men, are subject, regardless of the level of education and income." (Rubinstein, 2019). Thus, as Marianne Rubinstein mentions, despite a higher level of education and strong participation in the labor market, even for the younger generations, women are more affected by financial illiteracy, which is confirmed by the OECD for whom financial literacy is potentially decisive in people's lives, in their opportunities, in their success. The TNS Sofres survey conducted in 2012 (it is a question of knowing how much money one has at the end of a year when at the start there was 1000 euros invested at 2% interest without withdrawal or payment into the said account) also results in significant gaps between the sexes although this time an attempt at explanation is based on the argument that women are more often non-qualified: "We can note a gap between men and women of 13% which is relatively significant and can be linked to a demographic structure effect, the proportion of non-qualified women being higher than that of non-qualified men within the population." (Haas, 2012).

Looking at the percentage of adults with sufficient financial knowledge in the sample, by country and by gender, Allianz finds that the gap between men and women is quite significant, particularly in Spain (31,8% for men versus 13,3% for women), Germany (39,0% for men versus 24,7% for women) and Italy (44,7% for men versus 24,0% for women).

Teachers' bias in favor of girls in mathematics, or so-called positive discrimination

According to the OECD, girls in France spend almost two hours more per week on homework than boys (Borgonovi & Achiron, 2015) while other studies show similar results between the sexes in mathematics during the national brevet diploma test (Breda, Grenet, Monnet, & Van Effenterre, 2018). The OECD thus shows that the performance differential, to the advantage of boys, in science and mathematics would be even more marked with equal time spent on homework (see OECD Figure 2.13).
Furthermore, women are advantaged in the oral part of the entrance exam to the ENS in the subjects most dominated by men (mathematics, physics, philosophy), the opposite being true for literary disciplines dominated by women (Ly & Breda, 2014). Young women are therefore not necessarily discriminated against when they try to enter disciplines traditionally dominated by men (Ly & Breda, 2014).
What is true for the ENS entrance exams seems to be true for the École Polytechnique as well, with officials acknowledging that they are making efforts to get more girls admitted (Floc'h, 2014): however, in the entrance exam, boys do better in the written exam which is anonymous.^{[10](Floc'h, 2014): "For girls, on the other hand, speaking is beneficial. In MP, 24% of girls are « eliminated » orally, compared to 32% of boys. In MP info, it is 7% of girls (compared to 27% of boys). "It is known, underlines Eric Keslassy, ​​sociologist at the University of Paris-Diderot,Girls are better at establishing contact with a jury than boys. And since there are fewer of them at Polytechnique, I imagine that examiners pay more attention to what they say. »}

while girls perform better orally (Heidsieck, 2018). This discrimination in favor of women is also said to be at work in secondary education, with girls receiving biased grades, obtaining 6% more than similar boys (when the tests are not anonymous), which would explain their academic progress throughout their schooling in mathematics, without this evaluative bias being able to be attributed to behavior in class (Terrier, 2014).

Gregory Rozières notes:

“Positive discrimination in maths, physics-chemistry and philosophy
In a study published in Science on Friday, July 29, Thomas Breda and Mélina Hillion, researchers at the CNRS, arrived at this result, which may seem counterintuitive, by analyzing the results of the various competitive examinations: the CRPE (primary school teachers), the Capes and the agrégation (high schools and middle schools). In total, more than 100.000 people who took these exams between 2006 and 2013 were analyzed.
Each time, several written and then oral tests take place. The researchers therefore compared the candidates' results in the written test, where the jury could not know the person's gender, and in the oral test. For the school teacher competition, which is not linked to a particular subject, no difference was noted.
On the other hand, for the Capes and the agrégation, it is no longer the same thing, the study specifies: "In the fields where women are underrepresented (mathematics, physics, chemistry and philosophy), the oral exams favor women rather than men.
men”. And this is true both for the Capes and for the aggregation (more difficult).
The example is striking for mathematics where women's results in oral exams are 10% higher than their results in written exams, compared to men. In fields where men are underrepresented, researchers have also noticed a similar effect, but much weaker.

"Thomas Breda and Mélina Hillion finally imagine three things to change in public policies to reduce these gaps in representation in view of these results:
• Active policies aimed at reducing stereotypes and discrimination should focus on young students, before they choose their educational path
• Reviews and hiring should not be anonymized to reduce gender inequality
• It would be good, to encourage them, to highlight the fact that women, if they choose fields where men are in the majority, have more chances of success"

(Rozières, 2016).

It is therefore recommended not to use anonymous procedures in order to discriminate in favour of girls.

These so-called positive discriminations also exist in Australia in a more explicit way, with additional points being awarded to girls to enter university science courses at the University of Technology Sydney (Martin, 2019). In the United Kingdom, the University of Oxford has extended the time taken for mathematics exams to reduce the gender gap in performance (Matthews, 2018).

Moreover, so-called positive discrimination seems to have been practiced for a long time since we find references to this practice in academic literature since at least 1995: " Finally, it is clear that we will have to discuss again without prejudice the hypothesis of quotas for girls, disguised or displayed, permanent or progressively decreasing according to the evolution. This hypothesis shocks us today, but we must guard against taboos. After all, some major French business schools do indeed practice quotas without saying so through oral exams. » (Leduc, 1995).

There is every appearance that the differential in appetite and performance is at the origin of the disparities, which has led some to want to set up and perpetuate quotas.

Reluctance to operate in a highly competitive environment is put forward as an explanation for the under-representation of girls in elite fields.^{[11]"Ultimately, I think that we should rather look at the very form that scientific studies take in France, particularly in preparatory classes. These studies are dry and difficult, they are often conducted in the mode of sports competition. The teaching of mathematics and physics lends itself well to this, since the evaluation of performance can be easily quantified, exactly as for that of an athlete. Einstein wrote: "The temple of science is a composite building. Some occupy themselves with science with the joyful feeling of the superiority of their intellectual faculties: science is the sport that suits them." We could not better characterize our teaching of science, which produces climbing plants whose goal is to rise above others by all means. Girls suffer from this elitism which can take on a destructive character for them." (Leduc, 1995).}: " Girls suffer from this elitism which can be destructive for them. » (Leduc, 1995).

A taste for competition is a good predictor of choices of school specialization in mathematics in Switzerland at high school (Buser, Peter, & Wolter, 2017): based on a sample of 1514 secondary school students, 259 of whom chose selective training (baccalaureate) the experience of administering paid tests (piecework remuneration or competitive mode) with the possibility of choosing a mode of remuneration based on competition has made it possible to assess the link with choices of academic orientation. Students who have an appetite for competition are 12 points more likely to choose a specialization such as mathematics or physical sciences. Girls are less inclined to choose these specializations but when we take into account the willingness to compete, the gap is reduced by 17%. The appetite for competition therefore explains part of the self-selection in the sectors (Browne, 2006).

One may wonder whether the fear of discrimination or a deleterious atmosphere may be the cause of dropouts or reluctance to enroll in scientific courses, but the share of women taking MOOC (Massive Open Online Course) courses is also not equal, as can be seen with 2012-2013 data (Jiang, Schenke, Eccles, Xu, & Warschauer, 2016). MOOCs are online courses that have the advantage of being, with some exceptions, free of entry selection, free of charge, accessible remotely and therefore with flexibility to organize but also to avoid potentially harmful interactions in person (harassment, etc.). There is therefore no barrier to entry.

Before the 2018 reform as part of the "Student Orientation and Success" law creating Parcourssup, access to the first year of university outside of IUT is non-selective as long as the student holds a baccalaureate. However, between 2009 and 2017, in the sectors under pressure, the post-bac admission platform^[12]Visit (created in 2002 initially for selective courses) allowed for a random draw when the number of places was insufficient. Scientific courses such as mathematics, physical sciences, chemistry, biology, life and earth sciences were rarely, if ever, under pressure. It can be considered that before 2018, no discrimination was possible for enrolling in scientific courses at University as long as one had a baccalaureate, so it is interesting to examine the share of girls in scientific courses before the 2018 reform and a fortiori before 2002 (the generalization to non-selective courses having taken place between 2005 and 2009 then a generalization at the national level between 2009 and 2017). In Ile-de-France, between 1987 and 2004, the RAVEL platform recorded the wishes of high school students^{[13]See source}.

However, between 1970 and 1990, the proportion of girls in science at university was around a third of the workforce, this proportion being higher than 60% in the human sciences during the same period. It is therefore clear that in the absence of selection at university, there was no parity in science, the proportion of girls being around a third in scientific disciplines (Lelièvre & Lelièvre, 1991).

The role of preferences in orientation

Some studies show that women in the academic elite in science in France (Ecole Normale Supérieure, Polytechniciennes) make deliberate choices.^{[14](Ferrand, Imbert, & Marry, 1996): "The low presence of girls in the most valued scientific fields does not necessarily mean "exclusion" but corresponds to a deliberate choice." "After a presentation and a general discussion of this, we will show that the comparison of the social and academic background of female students at the École Normale Supérieure and École Polytechnique with that of their male classmates does not go in the expected direction. We do not observe the obvious social and academic over-selection of girls that their gender handicap would induce. These results and those from the interviews lead us to propose a more positive reading of gender differences in academic orientation. By opting for scientific courses in which mathematics occupies a less prominent place (biology for example rather than mathematics), we hypothesize that girls would make freer, more diversified choices than boys because they would be less subject than them to the imperative of success by the only recognized path to excellence, that of mathematics. »} to pursue what interests them rather than committing

systematically in a prestigious path (Ferrand, Imbert, & Marry, 1996). Consistent results are obtained in the United States from the study of university disciplines chosen in cohorts of high potentials of both sexes, based on the scores of standardized tests Invalid specified source., these choices resulting in high levels of satisfaction later in professional life in the mid-thirties, with few regrets being expressed (Benbow, Lubinski, Shea, & Eftekhari-Sanjani, 2000). However, Lubinski and Benbow show that high-potential women are overrepresented in the humanities, life sciences and social sciences while men are overrepresented in mathematics, physical sciences, computer science and engineering. Despite this academic “segregation” within a subset of a high-potential cohort, satisfaction levels by gender are comparable (Lubinski D., Benbow, Webb, & Bleske-Rechek, 2006).
The scarcity of women in higher education science courses in France is not the result of female ineptitude but of a disaffection that results in a more consistent orientation towards other courses, or a persistence of obsolete conceptions denying them good abilities in science (Hulin, 2008). According to Hulin (2008), these cultural blockages could be significantly reduced, thanks to a better knowledge of the history of women scientists, which is one of continuous progression but whose female successes are too little known.

Stereotype threat does not appear to play the predominant role attributed to it.

Stereotype threat is when an individual who is a member of a socially stigmatized group (by a negative stereotype) feels anxiety when the stereotype is activated, so that the individual tends to confirm the stereotype, through reduced performance due to the stereotype being made salient. Insistence on identity or simply recalling it before a test can also activate the stereotype.

The publication of The bell curve in 1994 (Hernstein & Murray, 1994) sparked immense controversy because the authors suggested that ethnic differences in performance on intelligence tests (IQ) could be partly explained by genetic factors. The following year, psychologists demonstrated the existence of stereotype threat when a group is stigmatized before taking a cognitive test (Steele & Aronson, 1995), suggesting that inferring innate potential from performance tests was a hasty conclusion, the demonstration being false by this overly simplistic reasoning: performance itself depends on the context (Diaye, 2001). Since then, social scientists have not been able to ignore this complex interaction between stigma and performance. In fact, self-fulfilling prophecies have been highlighted in sociology since 1948 (Merton, 1948).

However, the extent to which stereotype threat explains performance gaps between disadvantaged and non-disadvantaged groups remains unclear. For example, some criticism has been raised to highlight certain pitfalls (Ganley, Mingle, Ryan, Ryan, & Vasilyeva, 2013) such as publication bias (Flore & Witcherts, 2015) and hasty generalizations from laboratory experiments to the real world, particularly regarding the magnitude of stereotype threat (Stoet & Geary, Can stereotype threat explain the gender gap in mathematics performance and achievement?, 2012). Some researchers (Sackett, Hardison, & Cullen, 2004) have raised methodological issues with the Steele and Aronson study, pointing out that they statistically adjusted students' test scores by taking into account their prior SAT scores. Furthermore, by analyzing 20 attempts to replicate the stereotype threat of women in mathematics (Stoet & Geary, Can stereotype threat explain the gender gap in mathematics performance and achievement?, 2012) researchers demonstrated that only 55% of the studies managed to replicate the pioneering work in the field but almost all of these apparently successful replications (8/11) had also adjusted the scores (once again by relying on SAT test scores).

These results challenge the importance of the role of stereotypes, as the differences observed in the assessment of stereotype threat could arise from differences in previous SAT test scores, which may call into question its relevance in explaining the observed disparities.^{[15]“Even when assuming that all failures to replicate have been reported, we can only conclude that evidence for the stereotype threat explanation of the gender difference in mathematics performance is weak at best, as less than half of the studies from which clear and unconfounded conclusions can be drawn did not show such an effect. » (Stoet & Geary, Can stereotype threat explain the gender gap in mathematics performance and achievement?, 2012).}. It should be kept in mind that the variable examined is the difference in mathematics scores, assuming that the groups do not differ in their previous mathematics skills. In the event that they differ, this gap could be explained by this disparity, which would make stereotype threat obsolete. Some researchers have thus questioned the canonical interpretation of Steele and Aronson's results by specifying that approximately 90% of the interpretations available to them omit the adjustment by SAT scores, arguing that the entire gap between the two groups can be explained by stereotype threat when at best it can only explain the gap between students of the same level. Thus, misinterpretations are commonplace suggesting that, even when there is adjustment by SAT scores, the entire gap between the groups could be explained by stereotype threat (Sackett, Hardison, & Cullen, 2004).

On gender issues, a Dutch study weakens the scope of stereotype threat in the real world, by relying on a large sample size unlike most studies to test the validity of stereotype threat: by collecting data on 2067 students (including 946 girls), aged 13 or 14 and using a Bayesian analysis, the researchers show with greater robustness that stereotype threat has no significant impact on girls' performance in mathematics (Flore, Mulder, & Wicherts, 2019). The stereotype is activated by mentioning to the treatment group that a previous study on the mathematics test reveals performance gaps between boys and girls. The control group is read a text specifying that there is no difference in performance between boys and girls. The sample is larger than that used in other studies, for example 28 men and 28 women, then 30 women and 24 men and 36 women and 31 men (Spencer, Steele, & Quinn, 1999).

In short, despite its well-established existence in the laboratory, as long as the groups compared are of similar level, the relevance of stereotype threat seems largely overestimated in the real world. Indeed, unlike in laboratory experiments, in reality, stereotype threat is not activated before the examination tests. The invigilators of the (mathematics) test do not remind the girls of gender stereotypes just at the beginning of the test, so that stereotype threat does not necessarily appear in reality.

Publication bias is also deplored (Flore & Witcherts, 2015), due to the tendency to publish only studies finding a significant result regarding stereotype threat or worse, the use of p-hacking (a statistical technique which consists of only publishing sample compositions and observation periods favorable to the hypothesis tested).

The paradox of gender equality in science in the Nordic countries

There is a "gender equality paradox" (Stoet & Geary, The Gender-Equality Paradox in Science, Technology, Engineering, and Mathematics Education, 2018). Women are less involved in scientific fields in the most egalitarian countries than in those that have much less developed equality policies. The share of women among science students (STEM) exceeds 35% in Indonesia, Turkey, the United Arab Emirates, Tunisia, Vietnam, Albania and even 40% in Algeria (Geary & Stoet, 2018). Conversely, it is less than 30% in Denmark and even 25% in Sweden, Finland and Norway. However, the Scandinavian countries are the most advanced in terms of gender equality, particularly in comparison with countries in the Middle East or North Africa. There is therefore a paradox in observing more gendered career choices (fewer women in science) in countries more sensitive to gender equality. Some academics such as psychologist Jordan Peterson have seen this as an invalidation of socio-constructivism.

According to Stoet and Geary, simply examining performance averages is not enough to elucidate the paradox: it is necessary to examine comparative advantages (Ricardo, 1817) and not absolute advantages in scientific and literary subjects, a phenomenon of gender specialization being at work even when girls have better results in science than boys, as is the case in Finland. Thus, in the United States, the share of girls is greater within the group of students with high levels in both mathematics and verbal tests than in the group with high levels in mathematics but moderate levels in the verbal domain (Wang, Eccles, & Kenny, 2013). However, profiles with high levels in mathematics but moderate performance in the verbal domain are more likely to choose scientific fields. In short, those who have a high level in both domains are more likely to choose the literary field.

Some researchers have sought to resolve the paradox, but their answer is nonetheless somewhat paradoxical.^[16]

" Conclusion

The theory and results above reinforce the idea that gender segregation across fields of study or occupations will not decrease by itself as societies become more developed and egalitarian (24, 45). Appropriate policies are needed to induce such a change, or at least to limit the extent to which gender segregation generates inequality on the labor market. Similar conclusions are likely to be reached regarding gender differences in personality traits, values, or behaviors such as willingness to compete or risk aversion: These differences, which can also contribute to economic inequalities between women and men, are likely to remain even when countries become more developed. This is not because they are innate, but because they are the product of new forms of social differentiation between women and men that have replaced the male primacy ideology. » »

 : " These differences, which can also contribute to economic inequalities between men and women, are likely to persist even as countries develop. This is not because they are innate but because they are the product of new forms of social differentiation between men and women, which have replaced the ideology of male preeminence. » (Breda, Jouini, Napp, & Thebault, 2020). In essence, in the developed countries that are most advanced in promoting gender equality and the advancement of women, new social differentiations would take place such that we arrive at a counterintuitive result: there are proportionally fewer women in science than in less developed countries. The more gender egalitarian and developed a country is, the more gender stereotypes there are that dissuade girls from doing math. Gender essentialism (a differentialist ideology but not necessarily an egalitarian one in practice) would have taken over from male supremacy (legal inequalities or discrimination in social practices to the detriment of women). No longer able to achieve their gender performance (in the sense of Judith Butler) through explicit gender discrimination, individuals would construct their gender identity through these beliefs in the innate difference of the sexes, in spheres of personal choice. This work is based on the examination of 64 countries!

It would seem that we have here a kind of irrefutability in the sense of Karl Popper: if we had noted that in the more feminist Nordic countries, women were more involved in scientific fields, then we could have said that gender stereotypes are less prevalent there thanks to equality policies, but if on the contrary we note that women are less involved in scientific fields, then we deduce that gender stereotypes are more powerful there, having taken another form. In any case, whatever the results, the conclusion seems irremediable: only gender stereotypes would be able to explain the disparities and we could therefore not be content to limit ourselves to noting differences in appetite.

The relative benevolence of the teaching world is also irrefutably interpreted in Popper's sense as being detrimental to girls: " Thus, although overall girls receive more positive assessments and fewer negative assessments, both the occurrence of these judgments and the attribution made by teachers would invite them to explain their failures by stable and uncontrollable factors (lack of aptitude for example), and not by factors such as motivation or effort (this "learned helplessness" that we discussed in Part V). We would thus understand that boys have more self-confidence even though they receive more criticism and fewer compliments... » (Duru-Bellat, 1995).

What is referred to as job segregation may well be the result of women being relatively more reluctant to pursue technical careers, with Austrian data indicating that the greater the share of girls in the earlier classes at the time of orientation, the more they choose technical or scientific fields (Schneeweis & Zweimüller, 2009). Even in India, girls are less likely to go into science, even when controlling for the level of science with 20% less chance of going into it (Sahoo & Klasen, 2018). This gap is not so far from what we observe in France: " 44% of boys in the second year of GT move on to a first year of S the following year, this is only the case for 35% of girls » (Breda, Grenet, Monnet, & Van Effenterre, 2018).

Gender stereotypes and their link to reality: the case of teachers

In reality, one can ask the question of the causal link between stereotypes and observed reality because in fact work carried out in Italy by the economist Michela Carlana on the impact of gender bias of teachers on their students "The gender stereotypes of teachers contain an element of truth"^{[17]“Teacher gender stereotypes are driven by a kernel of truth”} specifying that "For example, girls are 1,6 times more numerous than boys in the top 10% of the reading distribution, but 1,5 times less numerous in the top 10% in mathematics"^{[18]“For example, girls are 1.6 times more likely than boys to be represented among the top 10% of the reading distribution, but 1.5 times less likely to be represented among students in the top 10% of the math ability distribution”} (Carlana, 2019): even if alleged biases measured by an implicit association test to which teachers submitted themselves are highlighted in relation to the attitude of girls in middle school, it is interesting to note in secondary school that despite an overwhelming majority of women among teachers ("Most teachers are women (81% in mathematics and 90% in literature)."^{[19]“Most teachers are women (81% for math and 90% for literature). »}), the gender differential in performance and especially in orientation in mathematics persists, even though other researchers claim that "having women leaders reduces implicit bias against women" (Glover, Pallais, & Pariente, 2016). ^{[20]4 Certainly, there is no contradiction strictly speaking since Carlana notes that "the gender of teachers is correlated with the Gender-Science IAT score and that the effect of implicit stereotypes on student outcomes is slightly stronger for male teachers, compared to female" (Carlana, 2019), but the gap seems small. In addition, the standardized IAT scores are interpreted as being unbiased when they are in the interval [-0,15; 0,15]: "where “no stereotypes” is the interval of IAT raw score between −0.15 and +0.15". However, the scores of mathematics teachers appear globally unbiased since they are included in this interval "the score of math teachers is on average substantially lower (mean 0.09, std. dev. 0.37, as shown in Table I), while literature teachers are very close to this mean (mean 0.38, std. dev. 0.39)". Indeed, there is no significantly differentiated impact of the teacher's gender on students once "all things being equal" although contradictory results are found in the literature, but also the effect of the male bias is slightly greater than the female bias: "Ceteris paribus, female students assigned to female teachers have slightly (albeit insignificantly) higher math performance in grade 8 compared with their classmates.40 The absence of a differential impact on boys and girls of teacher gender is consistent with the result of Bharadwaj et al. (2016). ». According to Carlana, however, the association biases (measured in milliseconds by means of the speed of word association with a concept pair on the left of the screen, for example feminine/science and another pair on the right of the screen, masculine/literature, this speed being compared with the reversed pairs in a second step, in other words feminine/literature on the left and masculine/science on the right of the screen, the reaction time differential then being the "proof" of the bias of the subject subjected to the test) would be significant: "16% of teachers associate math with girls, 23% present little to no clear association, 19% show male math association and 42% show moderate to severe male-math association".}

The gender performance gap generated by a biased teacher is of the order of 3% of a standard deviation, or the equivalent of a tenth of a point on a 0 to 20 grading scale (Carlana, 2019). The raw math score gap between boys and girls being of the order of 20% of a standard deviation, this is already a small effect size. The first explanatory variable in the model is gender (17% of a standard deviation of the math score gap), which it does not comment on (explaining 85% of the gender gap versus 15% for teacher bias). There are a plethora of explanatory variables, but they appear insignificant.

Gender stereotypes and their link to reality: the case of parents

To explain that despite the fact that a country is developed and tends to be more egalitarian or more feminist, there is a more gendered orientation in mathematics, one of the ideas of the article by Breda et al. (2020) is to measure stereotypes in the following way: examine the gender difference at equivalent level by sex in aptitude tests^[21]

“Our country-level measure of internalized Gender-Math Stereotypes (GMS) is based on the PISA 2012 survey, which includes in the students' questionnaire items about subjective norms and perceived control in math.

Our main index relates on national differences between girls and boys in the degree to which they agree with the following assertions:

– “Doing well in math is completely up to me” (perceived control, item st43q02, hereafter called B1)

– “My parents believe that math is important for my career” (subjective norms, item st35q05, hereafter called B2)

Possible answers to these two statements are 1: Strongly agree, 2: Agree, 3: Disagree and 4: Strongly disagree.

This implies that smaller values ​​of B1 and B2 correspond to more perceived control and worse subjective norms.

We consider these items as good proxies for the internalization of gender math-related stereotypes, as they do not express intrinsic motivation or preferences for math, but rather what students perceive as their ability to succeed and norms from significant others. » (Breda, Jouini, Napp, & Thebault, 2020).

[/Ref] (Breda, Jouini, Napp, & Thebault, 2020).

In short, with question B1 ("Succeeding in maths depends entirely on me") we see that girls consider more often than boys that their results in mathematics, at an equivalent level in the PISA tests, do not depend on them. With question B2 ("My parents believe that maths is important for my career"), we see that the parents of girls consider less often than the parents of boys, at an equivalent level in the PISA tests, that mathematics is important for their career.

The fact that such gaps exist despite an equivalent level in maths according to the tests is interpreted by researchers as being the result of gender stereotypes. Why would girls perceive themselves as less competent in maths at an equivalent academic level? For these researchers, it is necessarily sexist gender stereotypes that are captured by these indicators.

Question B1 probably reflects more questions of self-confidence, or even of real level. Indeed, even at an equivalent level in the tests, there is the effort made to reach said level: if one has to work much more to have a given result it is not the same as if one has facilities. Regarding self-confidence, this could be a personality trait. But, it is true that one can wonder where this differential in self-confidence at an equivalent level would come from, if not from gender stereotypes.

Question B2, whether or not parents think that mathematics is important for their child's career, raises questions. This may also reflect the child's preferences, who, given an equivalent result with another, may not want to make mathematics their career, which may in turn influence the parents' assessment. This does not necessarily imply that the parents discourage the child. Parents can take into account the child's aspiration, which may be stereotyped^[21]

"Generally speaking, young people say they want to implement qualities, or seek, in the professions they are aiming for, types of activities that are very much in line with gender stereotypes. In 2nd grade (Wach et al., 1992), girls want above all to "help, care for and take care of others" (this type of motivation comes first for girls and second for boys), or "inform and communicate", while boys emphasize the fact of "studying, researching, inventing", "organizing, supervising, directing", or even "making, achieving, producing". In addition, young girls doubt their skills in "masculine" professions, which they tend to consider more difficult than traditionally feminine professions (Eccles, 1).

More generally, professions are evaluated differently according to gender (Wachs et al., 1992): alongside professions considered prestigious by all (architect or doctor), girls judge more favorably the professions of journalist, lawyer, teacher or social worker, while boys rank engineer, TV repairman or truck driver better." (Duru-Bellat, 1995).

. It turns out that " Girls primarily want to "help, care for and take care of others" (this type of motivation comes first for girls and second for boys), or "inform and communicate", while boys emphasize "study, research, invent", "organize, supervise, direct", or "make, realize, produce". In addition, young girls doubt their skills in "masculine" professions, which they tend to consider more difficult than traditionally feminine professions. » (Duru-Bellat, 1995).

Students' preferences for a particular subject are also correlated with their perception of the difficulty of the subject.

But basically, the approach of this article (Breda, Jouini, Napp, & Thebault, 2020) is based on the postulate that any difference in appetite is perceived as an anomaly to be corrected, with necessarily a culprit who can be the parent, the teacher, society, the press etc. at the origin of the stereotype.

In 1992 and 2003, parents expected their daughters to have a generally higher level of education than their sons (Gouyon & Guérin, 2007). However, they were more likely to want their sons to enter the science stream of the baccalaureate than their daughters. That said, 31,6% of parents wanted a science baccalaureate for their son compared to 28,3% for their daughter, a gap of 3,3 points (parents of children enrolled in middle school or general second year at the start of the 2003 school year).

The role of social norms in the choice of scientific fields

After the fall of the Berlin Wall in 1989, a large influx of immigrants from the former Soviet Union into Israel made it possible to compare the educational and professional trajectories of native girls with those who immigrated at a very young age, since they were very often born between 1987 and 1989 (99% of the sample) or arrived before the age of six (Friedman-Sokuler & Senik, From Pink-Collar to Lab Coat. Cultural Persistence and Diffusion of Socialist Gender Norms, 2020). It turns out that girls from Soviet immigration are more likely to engage in science (STEM) than their native counterparts or those from other migratory flows.

In secondary education, among girls with an immigrant background from the former Soviet Union, 18% choose an advanced mathematics course compared to 14% of Israeli natives and 12% of girls with an immigrant background from other geographic areas. For STEM, these figures are respectively 33% for Soviet immigrant girls, 26% for natives and 24% for immigrant girls born elsewhere. Conversely, girls with a Soviet immigrant background choose social sciences less (28%) than their native peers (34%) and than other girls (27%).

In higher education, similar trends are found. STEM choices are made by 13% of immigrant girls from the former Soviet Union, 10% of Israeli natives, and 8% of immigrant girls from other geographic areas.

However, the scores of Soviet immigrant girls in mathematics tests are lower than those of native and other immigrant girls.

This natural experiment in Israel thus suggests that girls may more often choose scientific and mathematical options when they have been immersed in egalitarian values ​​that value science (in this case promoted in the Soviet Union). Let us recall that these are girls who immigrated before the age of six and even in almost all cases before the age of three.

Another study allows for a gender comparison in the choices of scientific courses in secondary education in Israel (Friedman-Sokuler & Justman, 2018). In high school, 14% of girls in Hebrew-language schools choose the advanced mathematics course compared to 16% of boys, while we have seen previously that 18% of girls in Israel born in the Soviet Union made this choice. Interestingly, in Arabic-language schools 12% of girls take the advanced mathematics course option compared to 8% of boys.

In physical sciences, computer science, biology or chemistry, in Hebrew-speaking schools, 31% of boys and 26% of girls choose these STEM courses, while we have seen previously that 33% of girls in Israel born in the Soviet Union made this choice. Interestingly, in Arabic-speaking schools in Israel, 50% of girls take the option of physical sciences, computer science, biology or chemistry, compared to 30% of boys.

Conclusion

The concordance of gender stereotypes with reality has been the subject of research. In particular, the academic Lee Jussim underlines in his literature reviews and his works that people evaluate gender trends rather well, with correlations often being higher than 0,5. It has even been shown that people questioned on gender trends in cognitive tasks not only correctly evaluated their meaning but also tended to underestimate the differences (Halpern DF, 2011). Moreover, stating that "men are better at math" is considered to be a stereotype, shared by nearly 30% of boys in the Paris region in the second general and technological class (Breda, Grenet, Monnet, & Van Effenterre, 2018) and a little less in the final year of science, while girls adhere to it significantly less (18,3% and 16,2%).

The better overall academic success of girls tends to mask more subtle phenomena which reverse this trend in sub-fields: tail of distribution, different variance according to gender, competitive examination situation, unusual exercises, specialization in mathematics, etc. The disparities in numbers in higher education sectors as well as in research and engineering professions essentially reflect the choices of orientation and the results in competitive examinations and competitions. The key point is that it seems that the gender distribution in the so-called hard sciences reflects, at least in part, the effect of comparative advantages (for skills close to the average in secondary education) or absolute advantages (at the tail of the distribution of the best performances): in the sense of the economist David Ricardo, boys seem to have a comparative advantage in mathematics at the average level, which means that despite scores close to those of girls, this is relatively their strong point, but an absolute advantage at the top of the distribution, that is to say that there are more boys than girls in the high scores and in any case in situations of elitist competitions as has been shown (Olympics, general competitions, entrance exams to major scientific schools such as the École Polytechnique, the École Normale Supérieure, etc.).

Equivalent grades in secondary education do not allow us to infer the same future in specialized higher education courses due to the different nature of the tests. Nor are the results by gender on average very close. The male overrepresentation in high scores (Halpern DF, 2011) or in competitive exam situations or when faced with new tests (Chabanon & Jouvenceau, 2022) should be linked to the judgments of parents and teachers, which can give the false impression of being nothing more than unfounded stereotypes. The reality is more nuanced. If parents and teachers are likely to introduce gender bias with an impact on academic orientation, they are also, and perhaps above all, well placed to assess students' inclinations and skills.

Thus, Lee Jussim deplores that some researchers have tried to hide or minimize the link that has been established between gender stereotypes and reality (Jussim, 2018). Similarly, David Geary maintains: "Stereotypes only describe the typical behaviors of boys and girls" (Strauch-Bonart & Sastre, 2021).

Certainly, Pauline Givord highlights stereotypes to explain the choices of study courses as well as the career preferences of adolescent girls, but this is an assertion rather than a detailed demonstration (Givord, 2020). Using the example of Israel, Claudia Senik shows that gender norms have an impact on the choice of scientific courses, with girls from the former Soviet Union clearly standing out from natives and other immigrants (Friedman-Sokuler & Senik, From Pink-Collar to Lab Coat. Cultural Persistence and Diffusion of Socialist Gender Norms, 2020). Nevertheless, the mathematics scores of young immigrant girls from the former Soviet Union in Israel appear lower than those of other girls, whether they are natives or immigrants from other countries.

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