Importance and possibility of integrating gender competence as a key qualification in mathematics teacher education

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1 Importance and possibility of integrating gender competence as a key qualification in mathematics teacher education Anina Mischau 1 and Katja Eilerts 2 1 Freie Universität Berlin/Humboldt-Universität zu Berlin, Germany; amischau@mi.fu-berlin.de 2 Humboldt-Universität zu Berlin, Germany; eilertsk@hu-berlin.de To overcome gender-specific bias within school subjects and to create equal opportunities for pupils beyond gender-stereotyped knowledge and interest domains we need (more) gendercompetent teachers. That means we need teachers who are aware of the impact they have on creating and reproducing gender stereotypes and gendered school subjects and who are able to implement gender-sensitive lessons at school. This paper presents a pilot project for a two-semester program to integrate gender competence as an occupation-related key qualification and as an important element of teachers professional development into the Master's program of the mathematics teacher education at Freie Universität Berlin and at Humboldt-Universität zu Berlin (Germany). An increase in gender-competent (prospective) mathematics teachers will be a successful strategy to realize the long-term goal of gender equality in mathematics. Keywords: mathematics, teacher education, gender competence. Introduction and background In accordance with previous surveys, PISA 2012 reconfirms: Statistically significant gender differences, in favour of boys, regarding mathematical performance, intrinsic motivation to learn mathematics, mathematics anxiety, self-efficacy, and mathematical self-concept occur in many countries all over the world. While in some countries a reduction of those gender-based differences has been observed over the last decade (Hyde, Lindberg, Linn, Ellis & Williams, 2008), they remained almost unchanged in Germany and tend to be even bigger than in other countries (OECD, 2012, 2014). Therefore, mathematics is still widely regarded as a typical boys subject or male domain in Germany, where gender differences in mathematics already become apparent at the end of primary school, aggravate in the course of secondary school education, and later on become manifest in a gender-based choice of fields of study. For more than 25 years research results have been showing that (gender) stereotypical attributions play an important and problematic role in the processes of teaching and learning mathematics in school, as they reproduce the gendered image of mathematics and various forms of gender bias within mathematics. In order to break the vicious circle thus created, researchers within genderoriented didactics and educational science have emphasized that besides the implementation of gender-sensitive didactics at school it is also necessary to make mathematics teachers aware of their impact on creating and reproducing gender stereotypes and gendered school subjects. Together with other elements, teachers gender stereotypes about the learning of mathematics, mathematical skills and achievements, as well as their potential lack of gender competence concerning teaching frameworks and classroom interactions, can be identified as fundamental reasons for gender bias in the development of young people s interests and competences with regard to school subjects in

2 general and gender inequality in mathematics in particular (e.g. Coradi Vellacott, Denzler, Grossenbacher & Vanhooydonck, 2003; Forgasz, Becker, Lee & Steinthorsdottir, 2010; McCormack, 2013). Therefore (prospective) teachers need to acquire gender competence with regard to didactics and subject-specific contents. However, gender competence (and this is also true for other competences such as cultural competence) is hardly ever included in the respective curricula of mathematics teacher training in Germany (Langfeldt & Mischau, 2011) even though standards for teacher education in Germany, formulated from the Standing Conference of the Ministers of Education and Cultural Affairs of the States in the Federal Republic of Germany, explicitly point out that graduates should be acquainted with the possible impact of gender on educational processes and that graduates should have well-founded knowledge on those characteristics of students (e.g. disabilities, language, social background, cultural diversity, gender etc.), that can facilitate or constrain learning achievement and on how to develop respectively differentiated learning environments (KMK, 2014, 2015). Especially in Berlin, the Federal State from which the authors come, the importance of gender competence as a key qualification for (mathematics) teachers has risen due to a new curriculum for primary and secondary school that will come in force in Beside the different subject-related parts, this core curriculum now includes a part that defines areas of general skills development for pupils that at the same time formulate binding aspects for the educational mission of all particular subjects and their teachers. Among other skills areas, this places now for the first time (in Germany) gender equality on a curricular base. This changed educational policy poses now new conceptual and practical challenges not only for mathematics education at school but also for the respective academic teacher education. Funded by the gender equality program of both universities and the Federal State of Berlin, Freie Universität Berlin and Humboldt-Universität zu Berlin (Germany) are initiating a pilot project to integrate gender competence within the Master s study program for primary and secondary school teachers of mathematics. So for us the first step was to take up the challenge of developing a research-based interdisciplinary program format for this pilot project which combines different empirical findings and theoretical approaches of gender studies in mathematics, educational science, and social sciences with mainstream knowledge from didactics of mathematics, and which meets certain requirements of the didactics modules within the study regulations for mathematics teachers. To start with, it should be pointed out that the developed two-semester program relies upon a constructivist view of mathematics (e.g. McCormack, 2013) on the one hand and on a constructivist perspective on gender on the other hand, i.e. gender differences (and this is also true for gender differences in mathematics) are seen as effects of social practice and the related exclusions, and social hierarchies are seen as products of gendering processes (e.g. Wilz, 2008). Adopting a constructivist perspective of gender also requires recognizing that gender inequality intersects with other social factors or categories such as race, age, ethnicity, class/social stratum and sexual orientation. Because of its interdisciplinary approach, both courses of the program are taught through collaborative teaching by the authors, whose specialisations correlate with mathematics, didactics of mathematics, and gender studies. In the following we would like to introduce our

3 program which has been running for several semesters already, while also emphasising assumptions of the project. Constructs of the program During the first semester students receive an introduction and overview of fundamental aspects of gender competence as an occupation-related key qualification for mathematics teachers. The approach of this course is based on an earlier course developed within the framework of the former research project GenderMathematics: Gender competence as an innovative element of the professionalisation of teacher training in mathematics (Blunck, Mischau & Mehlmann, 2014; Langfeldt & Mischau, 2011). For the program presented here, this construct has been slightly modified and further developed by the authors. According to our underlying assumption, which was developed as a definition in the project mentioned above, gender competence comprises four dimensions: professional competence, methodological and didactical competence, interactional competence, and self-competence. Professional competence (also called dimension of gender knowledge ) entails basic and specialized knowledge in the field of gender studies, foremost about socio-cultural constructions of gender and their impact on societal structures, institutions and individuals, as well as about the development of gendered disciplinary cultures. Methodological and didactical competence (also called dimension of the teaching framework ) means competence with regard to a gender-sensitive arrangement of teaching and learning processes. Interactional competence means competence in creating a gender-sensitive teaching culture (also called dimension of classroom interactions ). Self-competence consists of the ability to reflect on one s own gendered biography, gender-based views and assumptions, social norms, stereotypes, and the ability to reflect gender-based attributions, expectations and evaluations (also called dimension of self-reflectivity ) (Blunck et al., 2014; Langfeldt & Mischau, 2011). Gender competence in this sense aims toward sensitizing the students for the significance and role of gender in the processes of teaching and learning mathematics at school. Moreover, it includes the knowledge of mechanisms and consequences of gender-stereotypical attributions for the reproduction of gender differences in mathematics as well as theoretical discourses and approaches which should enable (prospective) teachers to open opportunities for pupils to learn mathematics beyond gender-based restrictions. Finally, gender competence includes the ability to critically reflect on one s own gender-based views and attitudes as well as institutional frameworks like curricula or teaching material and the ability to reflect on one s own professional ways of acting, interacting and communicating with respect to possibly unintentional gender-stereotyping effects (Blunck et al., 2014; Langfeldt & Mischau, 2011). The basic course focuses on the distribution of knowledge and competencies in all four already mentioned dimensions of gender competence. The course covers topics like a reflective analysis of selected results from international studies such as PISA or TIMSS, a critical examination of various explanatory approaches to gender differences in mathematics, the identification and problematization of selected aspects concerning the planning and designing of mathematics lessons but also concerning the attitudes and interactive behaviors of teachers, which may contribute to and influence the (re)production of gender differences with respect to the pupils mathematical self-

4 concept and mathematical performance (for an deeper insight see Blunck et al., 2014). The course also covers an introduction to different theoretical approaches and discussions about, for example, the social construction of gender, the chilly classroom climate, the hidden curriculum and concepts of reflexive coeducation or of doing/undoing gender in school. Finally, the course includes discussions about a feminist epistemology of mathematics (Burton, 2008), the relationship between the social construction of gender and the social construction of mathematics (e.g. McCormack, 2013) and about historical and contemporary gendered representations of mathematicians and mathematics which support inter alia the association of mathematics with masculinity (e.g. Mendick, Moreau & Hollingworth, 2008) and finally (re)produce to date the image of mathematics as a male domain. The advanced course in the second semester focuses mainly on methodological and didactical competence. That means the main objective of the course is to provide students practical ideas and examples for developing learning environments and mathematics lessons in a gender-sensitive way. Key references for this are our developed criteria or guidelines, which are based on merging, and further development of, various approaches and ideas from different discourses around gender- (and diversity-) sensitive mathematics lessons (see e.g. Curdes, 2007; Jungwirth, 2003). The criteria or guidelines concern the didactical principles, the forms/methods of teaching and learning, the design, development and application of task formats, the learning materials and the image of mathematics. For an enhanced understanding some of the criteria will be introduced in the following. First of all, it can be stated that also gender-sensitive mathematics lessons or learning environments are committed to the didactic principle of individualization and differentiation (see e.g. Curdes, 2007; Mischau & Bohnet, 2014). Therefore, the planning target takes into account varied (individual) accesses/approaches and varied methods of differentiation (e.g. differentiation by task, methods, learning materials, outcome, work, and social forms or classroom formats), so that all pupils in a class have the best possible chance of learning regardless of their gender or of other social categories such as class/social stratum, ethnicity, sexual orientation. According to Mischau and Bohnet (2014) on the premise diversity of methods instead of monoculture gender-sensitive mathematics lessons are characterized by using a well-balanced mixture of methods, with a preference for cooperative learning methods which open up for example possibilities for autonomous, experience-oriented, action-oriented, research-oriented and discovery learning, for cross-disciplinary, interlinked learning and for experiences of learning mathematics as a social, creative, and communicative process. Gender-sensitive mathematics lessons are also characterized by a balanced mixture regarding the task formats, with a preference for open tasks, which help strengthen inquiry-based and problem-based learning, permit the development and application of varied solutions, and allow viewing mistakes as opportunities, thus encouraging growth, creativity and free expression among the pupils (Mischau & Bohnet, 2014). Concerning the learning and lesson materials we would like to highlight the use of a gendersensitive or gender-inclusive language and the avoidance of stereotyped portrayal or stereotypical representations of e.g. boys and girls, men and women, for example with regard to attributed interests, abilities, and competences (not only in mathematics) or attributed and thus gendered activities or areas of life. Furthermore, learning materials and textbooks should represent the

5 heterogeneity of people beyond any stereotypes based on social constructions of e.g. gender, ethnicity, class, disabilities, sexual orientation, or age. They should offer a heterogeneous composition of persons as role models for pupils and task contexts not based on connotations of gender or other social categories (Mischau & Bohnet, 2014). Lastly, gender-sensitive mathematics lessons or learning environments are committed to the communication of a manifold, meaningful, and holistic image of mathematics by revealing mathematics as part of culture and society (see e.g. Burton, 2008; Mischau & Bohnet, 2014). For our understanding, it is therefore necessary to direct the focus also towards the development of mathematics as a historical and ongoing multicultural project as well as making visible the diversity of individuals/creators and forms of mathematical thinking, knowing, and practicing involved in it. In addition, a gender- (and diversity-) sensitive mathematics education should impart the usability and everyday relevance of mathematics and their correlation to other subjects and sciences, such as arts, architecture, music, nature, medicine and so on. Based on our guidelines and according to the German Mathematics School Education Standards (KMK, 2004, 2005), we have developed several mathematics lessons or learning environments. These are related to various content-related mathematical competencies (according to the five overarching ideas numbers and operations, measuring, space and shape, functional relationship, data and chance) and various process-related mathematical competencies (like mathematical argumentation, modeling, problem solving, use of mathematical representations, mathematical communication), which are part of the school curriculum for pupils of different grades in Germany. Some of our examples are being implemented within the course by simulating a school lesson. This means the students take the role of the pupils and solve the tasks from their point of view and we supervise them in the role of the teachers. Thus, with learning by doing students get the opportunity to gain practical experience in various ways of designing gender-sensitive mathematics lessons or learning environments. For an enhanced understanding, we will present two of the examples in the following. Both examples open up an action-oriented learning, whereby the first focuses on a content-related and the second on a process-related mathematical competence. Our first example is about getting acquainted with prime numbers and connects mathematics with arts, literature, and history. For primary school classes this lesson starts out with one of us reading the passage prima-donna numbers from the book The Number Devil by Hans Magnus Enzensberger, which describes the discovery of prime numbers through Eratosthenes' sieve in a child-friendly manner. Following that, the pupils are being split into small groups and receive prime number spirals printed on posters (with numbers from 1 to 100), colours and the task to use Eratosthenes' sieve to find all prime numbers up to 100. Additionally, they are being asked to colour all numbers they had sorted out, i.e. that are not prime numbers. Afterwards all numbers that were left uncoloured, i.e. the prime numbers, are highlighted with a colour that had not been used so far. Once the pupils are done with their prime number pictures they receive the optional task of finding and highlighting the ten Sophie Germain prime numbers that exist up to the number 100. These special prime numbers are explained in a handout which also contains a picture and short biography of the mathematician Sophie Germain. For secondary school pupils, the knowledge about Eratosthenes' sieve is assumed. The team projects follow the same principle as explained above

6 but the pupils receive several additional tasks about the discovery of additional specific prime numbers besides Sophie Germain prime numbers (e.g. Mersenne s prime numbers, Fibonacci prime numbers, and lucky prime numbers). Their creators are introduced with pictures and short biographies here as well, which puts the discovery of different prime numbers into their historical context. Subsequently both grades receive a power point presentation showing some prime number pictures by various artists to stress the connection of mathematics and arts. Since the criteria for good modeling tasks (open task, complex, containing problems, realityoriented, authentic, solvable by application of a modelling circle) are overlapping with our guidelines anyway and modeling in mathematics also has the intention of creating references to reality and conveying an appropriate image of mathematics, lessons highlighting the competence in mathematical modeling can be shaped as gender-sensitive very well, given the appropriate arrangement of the learning environment. Because of that we developed several gender-sensitive learning environments for modeling in mathematics, one of which we would like to present here. In this example pupils are assigned the task to support a heterogeneous group of 5 pupils (named Karin, Ayla, Peter, Yilmaz, Toni) from Berlin in planning a trip by city train and underground their visiting partner class from Hamburg wished to do. For the planning, the pupils receive a map of Berlin, a BVG (Berlin public transport) map, a computer for research, and a wish list sent by the pupils from Hamburg containing eight Berlin sights they would like to visit. Additionally, they receive information about where the trip is supposed to start and to end and how long it is supposed to last. The pupils are expected to come up with a solution process using the placemat method (to strength their communication during the working process), apply it and afterwards present their excursion programme on posters. This example is applicable to varied grades, since the focus is on acquiring/expanding the process-related competence mathematical modelling and the pupils are free to shape the step mathematising and working mathematically according to their existing content-related competencies. Accordingly the resulting excursion programmes vary a lot and the pupils experience that also in mathematics the development and applications of solutions may be different and not only right or wrong. Once the students have become acquainted with our examples they are given the opportunity to put their acquired knowledge into practice by planning a gender-sensitive mathematics lesson within the framework of a study project. More concretely, students form pairs or small groups which then work together for two or three weeks. Every team chooses a mathematical topic or competence based on the curriculum for mathematics in primary or secondary school in Berlin. According to the abovementioned criteria, each team creates the complete learning environment autonomously by selecting an appropriate method and by developing the worksheets, tasks, handouts or other materials that they would need in order to implement their lesson in school. As in our examples, the lessons designed by the students are played out during the course. The respective teams take the role of the teachers while the other students and we take the role of the pupils. After that simulation the different lessons are reflected on collectively, so the teams can optimise their drafts according to the feedback they receive. At the end of the course students create a short booklet about their lessons. That way we can hand out the compilation of the booklets to all students, who can draw a lot of suggestions and examples for their professional practice out of it.

7 Conclusions From our point of view, the only way to break the vicious circle of reproduction of gender differences in mathematics is to adopt a constructivist approach which presumes that not only gender but also mathematics are social constructions and that both processes of construction are linked. Only then will mathematics teachers be able to understand how mathematics education at school functions also as an arena of doing gender by doing mathematics and to identify traps of co-constructions e.g. in their own attributions, forms of teaching structures, patterns of interaction, as well as to develop strategies to change their behavior and teaching practice to avoid possible (unintended) gender-biased effects. Therefore, regarding our underlying construct of gender competence it is important to stress that the four described dimensions are systematically intertwined and that gender competence cannot be regarded as formula knowledge but relies on the idea of teachers as reflective practitioners (Blunck et al., 2014). This means, we cannot strengthen gender competence of (prospective) mathematics teacher without taking account all four dimensions within their academic education as we try it in our program. Certainly it will take a few years until we will be able to tell to what degree the intentions and desired effects of the program, to contribute to overcoming gender bias in mathematics, could be realized, because these are long-term processes and not short-term reachable or measurable effects. An important prerequisite is, of course, the students continuous implementation of the things learnt during the program and their further development of self-reflectivity in their later teaching practice. The acquisition of gender competence, that the above described program makes possible, at least lays a foundation for this. But although changed educational policy as mentioned in the beginning of this paper underlines the importance of gender competence as an occupational key qualification for teachers, so far the program is only a pilot project. Actually we have intensified our efforts on achieving a sustainable implementation within the regular curricula of teacher education, but currently we could not say whether we will be successful. References Blunck, A., Mischau, A. & Mehlmann, S. (2014). Gender Competence in Mathematics Teacher Education. In W. Ernst & I. Horwarth (Eds.), Gender in Science and Technology. Interdisciplinary Approaches (pp ). Bielefeld: transcript. Burton, L. (2008/1995). Moving towards a feminist epistemology of mathematics. ZDM Mathematics Education 40(4), Curdes, B. (2007). Genderbewusste Mathematikdidaktik. In B. Curdes, S. Marx, U. Schleier & H. Wiesner (Eds.), Gender lehren Gender lernen in der Hochschule. Konzepte und Praxisberichte (pp ). Oldenburg: BIS-Verlag. Coradi Vellacott, M., Denzler S., Grossenbacher S. & Vanhooydonck S. (2003). Keine Lust auf Mathe, Physik, Technik? Zugang zu Mathematik, Naturwissenschaften und Technik attraktiver und geschlechtergerecht gestalten. Aarau: SKBF.

8 Forgasz, H. J., Becker, J. R., Lee, K.-H., & O.B. Steinthorsdottir (Eds.) (2010). International perspectives on gender and mathematics education. Charlotte, NC: Information Age Publishing. Hyde, J. S., Lindberg, S. M., Linn, M. C., Ellis, A. B. & Williams, C. C. (2008). Diversity: Gender similarities characterize math performance. Science, 321(5888), Jungwirth, H. (2003). What is a gender-sensitive mathematics classroom? In L. Burton (Ed.), Which way social justice in mathematics education? (pp. 2 26). Westport, CT: Praeger. KMK (= Standing Conference of the Ministers of Education and Cultural Affairs of the States in the Federal Republic of Germany) (2004). Bildungsstandards im Fach Mathematik für den Mittleren Schulabschluss (Jahrgangsstufe 10). Neuwied: Luchterhand. KMK (2005). Bildungsstandards im Fach Mathematik für den Primarbereich (Jahrgangsstufe 4). Neuwied: Luchterhand. KMK (2014). Standards für die Lehrerbildung: Bildungswissenschaften. Online: Standards-Lehrerbildung-Bildungswissenschaften.pdf KMK (2015). Educating teachers to embrace diversity. Online: Empfehlung-Vielfalt-englisch.pdf Langfeldt, B. & Mischau, A. (2011). Genderkompetenz als Bestandteil der Lehramtsausbildung im Fach Mathematik zu innovativ für deutsche Hochschulen? Zeitschrift für Hochschulentwicklung, 6(3/4), McCormack, M. (2013). Mathematics and Gender. In D. Leslie & H. Mendick (Eds.), Debates in Mathematics Education (pp ). London: Routledge. Mendick, H., Moreau, M.-P. & Hollingworth, S. (2008). Mathematical Images and Gender Identities. A report on the gendering of representations of mathematics and mathematicians in popular culture and their influences on learners. Research Report Series for UKRC No. 6. UK Resource Centre for Women in Science, Engineering and Technology (UKRC) and London Metropolitan University. Mischau, A. & Bohnet, K. (2014). Mathematik anders lehren und lernen. In I. Rieken & L. Beck (Eds.), Gender Schule Diversität. Genderkompetenz in der Lehre in Schule und Hochschule (pp ). Marburg: Tectum-Verlag. OECD (2014). PISA 2012 Results: What Students Know and Can do: Student Performance in Mathematics, Reading and Science. (Volume I, Revised edition, February 2014). OECD Publishing. OECD (2012). PISA 2012 Results: Ready to Learn: Students' Engagement, Drive and Self-Beliefs. (Volume III). OECD Publishing. Wilz, S. M. (2008). Geschlechterdifferenzen Geschlechterdifferenzierungen. In S. M. Wilz (Ed.), Geschlechterdifferenzen Geschlechterdifferenzierungen: Ein Überblick über gesellschaftliche Entwicklungen und theoretische Positionen (pp. 7 17). Wiesbaden: VS Verlag.