A map of the places where mathematics, education and gender cross
To what extent is the nature of science linked to the idea of masculinity? This question was launched by feminist physicist and epistemologist Evelyn Fox Keller in the 1980s, in the book Reflections on gender and science. To answer the question, he analyzed some historical ways of characterizing scientific knowledge. Through the work of Francis Bacon, for example, he demonstrated that gender roles and stereotypes have had an important influence on the ways of characterizing the science of the time. In fact, Bacon considered the mind to be male and the feminine nature; he affirmed that scientific knowledge is the domain of nature and equated the relationship between mind and nature with a heterosexual marriage. The analysis of René Descartes' thought, on the contrary, served to see that the ways of characterizing science also have an impact on gender systems. Descartes said that man is made up of two disjunctive parts: mind and body. The dichotomy of the mental body led to the development of much more extreme stereotypes of masculinity and femininity, as masculinity was associated with the mind and femininity with the body and, above all, with the uterus. This meant a sexual division of labor, which relegated women to the reproductive sphere.
Many other feminist epistemologists have also highlighted the non-neutral, androcentric and sexist nature of scientific research. Attempts to emerge gender dynamics within mathematics have been much lower. Although there may be several reasons, the high degree of abstraction of mathematics is probably one of the most outstanding, since this abstract character has given a privileged position both to the field of knowledge and to the mathematical truth. In order to help fill this gap, I have researched the thesis in the forms that gender takes in mathematical education, based on the experiences, discourses and actions of mathematicians, math teachers and math students.
Compasses and methodological coordinates
The thesis is a case study. I've analyzed mathematics, education and the conditions in which gender intersects in everyday life, taking the classroom as the primary scenario. Although the objective is to analyze in detail the particularity, uniqueness and complexity of the case, I have also made more general statements on the theme, following the instrumental nature of the research. In these cases, it is common for the study of the single case to raise doubts about the possibilities offered by the analysis to make statements about a more general phenomenon, due to the lack of statistical resources used in quantitative designs. However, there are other ways to reinforce the validity of research that better adapt to qualitative designs.
One of them is triangulation, a form of cross-analysis that allows contrasting and analyzing the themes from different angles, as well as reinforcing the evidence behind the most important statements. In the thesis I have used two types of triangulation: data triangulation and methodological triangulation. As far as triangulation of data is concerned, I have addressed different sources of information, as both students and mathematics teachers have participated in the research. Regarding methodological triangulation, I have used different techniques and tools to produce information: in-depth interviews, open, closed and mixed questionnaires, among others. In addition, I've done over 200 hours of observation in three math classrooms. I have also sought the validation of the participants to verify that they agree with the meanings they have given to their words. Finally, I have used theory to deepen the ideas produced in the analytical process, conceptualize stories and give strength to my interpretations.
So, I've developed a cartography that reports some places where mathematics, education and gender intersect, an interpretation entangled in the present, partial and unfinished. To make these places known I have outlined four tours (Figure 1) that I will summarize in the following lines.
First tour: mathematics at the top of the pyramid
In the last century, mathematics has become one of the main means of defending the interests of nations. Since the Second World War, the increase in the number of scientists, technologists, engineers and mathematicians has been associated with the strengthening of the economy and national security. Behind this commitment to being at the forefront of scientific discoveries and technological innovations is the modern conception of progress, which links economic and political progress with scientific and technological development. This optimistic attitude towards science and technology has led to scientific and technological superiority becoming the national priority of many countries.
This centrality of mathematics in society also influences mathematical education, and in my thesis I have identified some elements that account for that privileged position of mathematics in the pyramid of areas of knowledge, among which is the recognition of the importance of mathematics in relation to other subjects.
Why is this happening? Because math scores are considered an indicator of future success and are used to select and tag students. In fact, one of the functions attributed to mathematics is Mental Meter. In addition, mathematics is also appropriate for academic talent, as the educational community tries to make high-performing students choose a route related to mathematics. Students who do not show high academic performance are informed that they are not good enough to conduct these studies.
Consequently, mathematics plays a role of segregation. Likewise, the assimilation and repellency tactics of mathematics encourage academic decision-making in terms of dexterity and enjoyment in the background. In addition, the talent for mathematics is essentialized and dichotomized: the talent for mathematics is not something that can be acquired, but something that you have or do not have since birth.
Second route: distorted portraits
The thesis does not characterize mathematical talent in this dichotomous and essentialist way. On the contrary, it considers it an ideological construction and poses some elements related to such construction. One of these elements is that of gender stereotypes that historically and socially construct the characteristics and attitudes differentiated, historical and socially assigned to men and women, naturalizing and biologizing hegemonic gender identities, and promoting discriminatory relations between genders.
There are a number of gender stereotypes related to the teaching of mathematics. For example, boys are often thought to be better for math on their own and, on the other hand, there is a tendency to overvalue boys' abilities and to underestimate girls' abilities. In addition, the mathematical success of girls is associated with effort and obedience, while that of boys is related to intelligence or interest. Failure is attributed in the case of girls to the lack of ability to understand mathematics, in the case of boys to the poor relationship with the teacher or to the lack of help.
In my thesis I have identified several phenomena derived from these distorted portraits. In the case of mathematical students, the performance of mathematical talent usually gives rise to a gender truthfulness in the case of boys and a gender falsehood in the case of girls. In fact, the presentation of oneself as a mathematical talent coincides with the hegemonic masculinity, but it clashes with the hegemonic femininity because it supposes a rupture of gender norms. As for the incidence of gender stereotypes in mathematics faculty, greater recognition of formal authority for men than for women also entails greater recognition of epistemic authority for men. The incorporation of a male teacher into the classroom, due to its own configuration, will allow students to pay more attention than to a woman, so it may be recognized that she has more mathematical capacity than a mathematics teacher.
Third tour: the property of the sound space
Participation in mathematical education, from a gender perspective, is also a problematic element. According to the studies, students usually receive more individual support, start more conversations with teachers of mathematics and master the conversations that emerge in the large group. In addition, they have greater visibility, as teachers learn and remember more easily the names of the children and facilitate the identification of the mathematical talent of the children. There is also a tendency towards a widespread distribution of teamwork: girls perform more often reproductive and non-spectacular tasks, and boys participate more in activities that show a proactive attitude.
In order to increase the participation of girls, the teacher must control the participation quotas so that the students occupy the sound space in the most balanced way possible. In addition, the focus of relationships in small groups can help increase the feeling of participation of students who do not participate in a large group. Moreover, it is essential that the faculty focus on everything that is happening in small groups and intervene in the exclusionary dynamics. Finally, it is important to agree rules that are taken into account for mutual care when working in small groups, so that all students feel respected and heard.
Fourth route: from criminalization of lack to valuation of vulnerability
In math, failure can have a greater impact on girls than boys. And that is, girls learn from a young age so that they value and value them, they must be educated and humble and respect the norms, while expressing perfection and beauty. Kids are accepted into chaos, which prepares them to be in imperfection. Consequently, failure often causes more fear in girls than in boys.
The punishment of error incites that fear, because it harms mathematical trust. Competitiveness also has a negative impact, and in mathematics students' reports, it is frequently related to mathematical anxiety. This is significant from the gender point of view, since when the environment is competitive, mathematical anxiety is manifested more in girls than in boys.
In order to deal with these inertias, a different management of failure is needed. To offer students positive experiences related to failure, working metacognition or integrating error into the mathematical activity, among other aspects. In fact, accommodating failure and putting vulnerability at the centre can help combat the fear of error, the damaging aspects of perfectionism and blockages.
Epilogue: a cartography that highlights the interdisciplinarity in gold
This research has been done by a mathematician, but not only by mathematics, but the didactics of mathematics and feminist learning have also been sources of fundamental knowledge. Therefore, on the cover of the thesis, in addition to the textures that symbolize the four upper trajectories, there is a golden plot that aims to visualize this interdisciplinarity (Figure 1). The golden weft symbolizes the kintsugi technique, a form of repairing ceramic objects that, instead of concealing the cracks with the golden dust, the cracks are part of the history of objects and, therefore, instead of hiding them, should be shown and valued.
Sometimes, the kintsugi technique is to gather fragments from different places to form something new. And that is precisely the thesis: an attempt to unify the fragments that make up my academic and professional trajectory. A cartography that highlights with gold the interdisciplinarity of work.
Bibliography
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