Towards Equity in Mathematics Education pp 373-387 | Cite as

# A Socio-Political Look at Equity in the School Organization of Mathematics Education

## Abstract

This paper presents some theoretical tools to help understand the meaning of mathematics education as socio-political practices and the implications of these for researching mathematics education. Taking two cases of schools and students in Denmark and South Africa, the paper illustrates how the theoretical and methodological ideas come into operation when illuminating issues of equity. It is contended that the disadvantaged positioning of some students for participating in mathematics teaching and learning is the result of the routines, ideas, shared meanings, and ways of talking and conceiving mathematics education among the actors in the school organization, inside as well as outside the classroom.

## Keywords

Mathematics Teacher Mathematics Classroom School Leader Mathematics Education Research Private Tutor## 1 Introduction

That mathematics education is political should not surprise many nowadays. In the last two decades, several mathematics education researchers have formulated different thesis about how the teaching and learning of mathematics, a very important discipline in the construction of the modern and contemporary world, is deeply involved in a differentiated positioning of diverse groups of students and people (see, e.g., Keitel 2006). In the practices of teaching and learning mathematics in classrooms at all educational levels, people may construct more or less influential positions for their action in relation to their successful (or less successful) exercise of mathematical competence. In further social action outside of educational settings, the advantaged (or disadvantaged) positioning may persist. Formulations about mathematics education as a means to empower individuals and consolidate democracy, as well as to discriminate and exclude particular groups of children and people, have not only been part of the concern of researchers. Practitioners who care about the effects and consequences of mathematics education on the improvement (or worsening) of students’ lives have also shown interest in thinking about how power is in operation in their teaching practices. Even educational policy makers around the world, for whom all school subjects should contribute actively in the education of citizens, have clearly formulated a desire of making mathematics education strengthen the general competencies of citizens in the twenty-first century. That mathematics education is highly political is part of the current way in which this social practice is conceived at this time in history.

It is not my intention in this paper to go into the details of the general formulations about mathematics education being socio-political practices, nor about how and why mathematics education is related in a positive or in a negative way with the construction of democratic social relations and of critical citizens. Others previously have done this in depth.^{1} My intention in this paper is twofold. On the one hand, I will present some theoretical tools to understand the meaning of mathematics education as socio-political practices and the implications of these notions for researching mathematics education. On the other hand, I will illustrate how the theoretical and methodological ideas come into operation in an empirical study on equity issues in two schools in Denmark and South Africa.

## 2 Mathematics Education as Social and Political Practices: A Theoretical and Methodological Framework

I will start by addressing a series of central theoretical and methodological points when researching mathematics education from a socio-political perspective. First, it is important to clarify the meaning I give to the term “mathematics education.” It refers to the whole series of practices where the meaning of the teaching and learning of mathematics is constituted. Such practices are not limited to the space of the classroom where teachers and students put into play forms of communicating around a particular mathematical content, but also include other spaces where decisions are made and actions are taken around the teaching and learning of mathematics. Sites of practice such as international or national educational policy making in mathematics, teacher education, textbook production, the labor market, and even the very same research on all these practices, among others, are part of the practices of mathematics education. Such a broad and complex collection of sites is what I have called the *network of mathematics education practices* (Valero 2002b).

Second, mathematics education practices are social not only because the act of learning is social and because mathematics is a socially constructed knowledge (Lerman 2006), but also and foremost because the learning and teaching of the subject are embedded in that broad network of practices. Being so, their meaning is constantly created and recreated though history, in particular social and cultural conditions, by all those people involved in shaping what is understood at a particular time and in a particular site by “mathematics education.” This view implies that, for example, the activity of policy makers or the demands of the labor market at particular times in history have an important role to play in providing frames for action in schools when mathematical instruction is being planned and implemented. The actions and meanings constructed in the classroom around mathematics cannot be completely isolated from the actions and meanings constructed in other sites of the network.

Third, mathematics education practices are also political because they are implicated in the functioning and distribution of power in social relations. Among the different ways of conceiving power and relating it to mathematics education, post-structuralist definitions inspired by the work of Michael Foucault (e.g., Foucault 1972; Foucault and Faubion 2000) have been illuminating for many researchers such as, for example, De Freitas (2004), Hardy (2004), Meaney (2004), and Popkewitz (2002). In this view, power is a relational capacity of social actors to position themselves in different situations through the use of various resources. Power is not an intrinsic and permanent characteristic of social actors; rather, it is their capacity to participate by taking and defining the positions and conditions for engaging in social practice. Thus, power is not monolithic; it is distributed in social relations and is in constant transformation. This transformation does not necessarily happen directly in open struggle and resistance, but through the everyday participation of actors in social practices, in the creation of their meaning, and in the constitution of their associated discourses. Power is not openly overt and easy to identify but subtly exercised in and through social action.

Viewing power in this way invites analysis of the microphysics of power in mathematics education practices; that is, investigating how the everyday interaction among the different social actors that participate in the practices of mathematics education, inside and outside educational institutions, bring into life ways of talking and viewing the teaching and learning of mathematics. Such an analysis makes evident the mechanisms through which different actors get positioned as more or less influential participants and thereby get included and excluded.

Fourth, all the previous considerations about the nature of mathematics education practices have implications in the way the researcher approaches the study of those practices. A very first implication has to do with the delimitation of the site of study. In mathematics education research, the individual learners and teachers and the classroom have been privileged sites of study. Few studies have considered, for example, the school organization, the sites of policymaking, the working place, or the family. Mathematics education research with a serious concern and commitment with evidencing the political and social nature of mathematics education practices needs to open up its focus of study; and the school organization is an important site and unit of research (Skovsmose and Valero 2001, 2002). A second implication that follows is the necessity of considering the site as part of the network of mathematics education practices. This means that the researcher is invited to analyze the relations among different actors within the site, as well as the connections between it and its context. The complexity of mathematics education practices at any site can only be understood through an analysis that links in significant ways the construction of meaning for mathematics education at micro- and macro-levels of social practice. Such methodological challenges, among others, are some of those facing researchers adopting a socio-political perspective on mathematics education.

In what follows, I intend to illustrate the previous points by concentrating on an empirical study that allowed discussing student’s participation in mathematics education and disadvantage, one of the core issues addressed by research concerned with equity.

## 3 Studying Equity in the Network of School Mathematics Education Practices

In Valero (2002b), I engaged in formulating a language of interpretation to talk about mathematics education reform within the school organization and from a socio-political perspective. I built on the work of Perry and collaborators (Perry et al. 1998; Perry et al. 1996) who developed the notion of *institutional system of mathematics education* (ISME). The ISME is a model that views the functioning of the teaching and learning of mathematics inside a school as a system in which at least three types of actors intervene: the school leaders, the group of mathematics teachers in the school, and the teacher as an individual in his or her classroom.^{2}

Three case studies in three schools—Nyspor School, a primary school in Denmark, Rajas Secondary School in South Africa, and Esperanza Secondary School in Colombia—were carried out with the intention of being an empirical ground for triggering reflection, challenging, and reformulating the ISME model. The three qualitative case studies (Stake 1995, 2005) were conducted in order to get a detailed understanding of the functioning of the ISME in the three schools selected to be the cases. A number of methods—such as classroom observation of the group of mathematics teachers in each school, observation-based interviews with teachers on their teaching practice, observations of staff meetings, observation-based discussion with school leaders and other relevant staff members, documentation of national and local educational policy, and mathematics education related policy in the school, among others—were used for collecting information about the functioning of the ISME in the three schools. The information was used to construct a series of critical episodes, presented in the form of vivid stories of practice, addressing relevant aspects of the functioning of school mathematics in the school organization.^{3}

The analysis of the critical episodes concentrated around the exploration of five clusters: (1) the significance of *the context of schooling* in mathematics education change (for details see Valero 2007); (2) the conception of *the mathematics learner* as a fully social and political human being constituted within the practices of school mathematics education (see Valero 2002a, 2004); (3) the role of *school leaders* as navigators in organizational contradictions when dealing with the transformation of mathematics education practices in the school; (4) the constitution of *professional communities of mathematics teachers*; and (5) the realization of the *school mathematics teachers* as socio-political beings who contribute to the creation of the meaning of school mathematical in the classroom and in the whole organizational environment outside of it. The overall analysis led to the formulation of the notion of the *network of school mathematics practices* as presented in the previous section of this paper.

Part of the discussion about the conception of the mathematical learner emerged from the observations in the three schools from students who seemed to be marginalized from active participation in classroom activities. Processes of inclusion and exclusion of some students have been the central concern of most of the research studies and policy formulations arguing in favor of more equitable and democratic mathematics teaching and learning practices. Digging in the network of school mathematics practices and discussing existing research literature and policy documents opened the way for allowing insights into how these processes operate and how advantaged/disadvantaged positioning of students come into being in mathematics education. In what follows, I will enter that discussion, starting with two snapshots from Nyspor School in Denmark and Rajas Secondary School in South Africa.

### 3.1 The Lonely Girl

Mette, a young, novice female Danish teacher, and I walked to her eighth grade classroom together. Carrying a pile of photocopies with the activities she had planned, she entered the classroom, which was organized in a typical matrix of three rows and three columns of students’ desks. Students sat in pairs. There was only one individual desk, right in front of the teacher’s table. As students slowly moved to their places, the shelves with books, dictionaries, pencils, paper, and notebooks became more visible and suddenly seemed to get ready for doing some mathematics. It took some time before the 18 students got ready to work. Mette’s soft voice became clearer as there was silence enough for her to deliver the photocopies with the tasks for the whole week. Students complained but finally got started, solving the problems in pairs, as they were sitting in the class. Mette attended those who called for assistance, and I concentrated on observing and talking to the girls sitting at the front.

Quite soon, Gitte, a Danish teenager with colored hair and fashionable clothes, attracted my attention. Two girls sitting by the window needed a sharpener and a ruler. “Gitte, give us the sharpener and the ruler,” said one of them. “Here they are,” Gitte replied. Other girls dropped a pencil on the floor. “Gitte, can you pick up the pencil?” “Yes,” Gitte replied, picking it up and passing it to them. From time to time the girls behind her also asked her similar things. Gitte was solving a different working sheet. She was sitting alone in front of the teachers’ desk. I started wondering… I offered her assistance but she refused it. The rest of the class was chatting, sometimes more about the weekend than about drawing lawns and fences, and calculating areas, and perimeters. Gitte, the lonely girl, suddenly stood up and left the room. After a while she came back and sat staring at the girls sitting by the window. “Stop looking and do your work” was the answer to Gitte’s friendly smile. She turned back to her desk and did her exercises until the class finished.

Back in the staffroom, Mette commented on her difficulties with this class. As a novice teacher, it had been hard for her to convince them to engage in doing some work in mathematics. She had to adopt a low profile in front of these problematic students. I asked Mette directly about Gitte. She explained that this girl had some learning problems. She was allowed to be in the school and do as much as she wanted. Mette had tried to help her, but it was time consuming and the other students also demanded attention. “It is important to give her a hand,” I insisted. “But you see, it is difficult, with the messy class, I cannot give her more time. I make special copies for her. Besides, she has serious problems, some members of her family have also studied here and they have also had difficulties in learning, so when there is a case like this, what can you do?”

### 3.2 They Are Creeping into…

African students were together, always together with their African peers in Rajas Secondary School. In the mornings, groups of uniformed students walked some kilometers up the hill to reach the school. Many of them started walking from the main avenue where the white “black taxis” dropped them. In the schoolyard, they walked and talked only with other African students. In the classrooms they also sat next to each other, in pairs or in groups of four, scattered in the room, never all in the same spot. Very seldom did they ask a question or raise their hand to answer the teachers’ questions. Only few times I heard them speaking in their native languages in the midst of the sea of English words that flooded the school. Teachers seemed not to pay much attention to them, even though teachers recognized that many of these students had difficulties. At least their marks in mathematics assessments and exams were systematically low. For an outsider like me, African students constituted a silent minority inside the school, with the same formal rights to be members of it, but also with high and thick invisible walls around them. The walls did not let them approach others neither to be approached.

Breaking those walls was one of the challenges of Rajas School in the era of the “New South Africa.” Mr. Ruikar, the acting school principal, when talking about the composition of the student body, referred to the change from an Indian segregated school to an integrated school with a mixed racial composition. Legally, the school was compelled to open places for students from other racial groups. In a new, democratic South Africa all should have the same opportunities, and accessing better schooling constituted one of the big achievements for the most disadvantaged although larger group, the African population. But making democracy is not only a matter of opening seats in a more advantaged school. For Mr. Ruikar, there were problems of access to resources, but especially the “Blacks’ learning culture” needed transformation. For Arun, one of the mathematics teachers, language was the greatest barrier.

The invisible wall around African students was a double-sided fortification built with bricks of misunderstandings along the very many years of racial segregation and struggle. African students in Rajas resembled intruders who are slowly creeping into a forbidden place. I wondered about how and when they could become legitimate insiders…

### 3.3 Entering the Discussion of Equity in Mathematics Education Research

These two episodes invited me to take up the issue of equity in consideration. In “The lonely girl,” Mette tries to do her teaching in the best possible way. In many respects, she brings into practice some of the curricular recommendations of the moment (Undervisningsministeriet 1995) such as engaging all students in learning, by meeting them at their own individual level. The principle of “differentiated teaching” encourages teachers to deal with the diversity of students’ competency and to provide support to students’ individual development. Although Mette does her best, she finds difficult to deal with Gitte, who has the right to basic education and to be taken care of by teachers in a school. She gets some attention from Mette and she does special mathematics tasks at her own pace. She interacts with her classmates in a condition of “inferior”: While they do the mathematics tasks, Gitte picks up pencils and rulers from the floor. The episode was shocking since it illustrated the predicaments of equity: disadvantage is being built even at the heart of an educational system that has inclusion and democracy as an organizational principle; the predicament lives right in the middle of the mathematics classroom.

“They are creeping into…” shows the situation of African students in a predominantly Indian school in South Africa. In a time of national reconstruction and democratization, changes in policy allowing access of African students to more advantaged schools such as Rajas Secondary School was a challenge. The historical walls of apartheid were thrown down in laws and regulations but pretty much existed in the experience of people when meeting other racial groups. School administrators and teachers recognized that there were “problems” with the African students but in spite of more or less conscious efforts the walls were still there, even in the mathematics classrooms. The episode called my attention and invited thinking about the actual possibilities of throwing the thick walls down. Was there ever a chance to do it?

Gitte in Nyspor and the African students in Rajas represent students at risk of disadvantage in mathematics education. How to interpret the students and their apparent disadvantage? Research literature dealing with issues of equity and disadvantage in mathematics education had identified gender, ethnicity, language, social class, and ability as key factors related to the differentiated access and success in mathematics learning (e.g., Burton 2003; Keitel 1998; Rogers and Kaiser 1995; Sriraman 2007; Zevenbergen and Ortiz-Franco 2002). There have been different approaches in researching why and how mathematics education becomes a gatekeeper for particular social groups. A first trend of essentialist explanations related differentiated mathematical performance to genetic factors (for a critique of this type of studies see Ginsburg 1997). In a second trend, attention has been then given to students’ psychological characteristics—such as affection, self-esteem, confidence, motivation, and persistence—and how these influence low performance and participation when engaging in mathematical learning (e.g., Fennema 1995; Leder and Forgasz 1998). This trend has been criticized for being “attributionist” (Boaler 1998) and not going into the mechanisms for the construction of exclusion. A third trend has built on the assumption that equity is a socially constructed phenomenon; that is, differentiation is not the result of intrinsic, genetic deficiency, or personal characteristics, but of larger social inequalities that are also visible at the level of individuals and of collectivities. Studies have recognized that the problems of inequity reside in the organization of mathematical instruction in the classroom. Patterns of interaction and teachers’ attention to particular students, teachers’ differentiated mathematical demands, the learning styles privileged by different types of instruction, the pedagogical discourses in mathematics classrooms among others are factors that give an account of the creation of disadvantage (e.g., Boaler 1997; Licón-Khisty and Chval 2002; Zevenbergen and Flavel 2007).

An examination of the situations described above suggested that students’ disadvantage in mathematics trespassed the boundaries of individual attributes and of instructional organization in the classroom. Disadvantage and equity could be reformulated in terms of positioning within the relations and practices that constitute mathematics education in the school.

### 3.4 Examining the Construction of Disadvantage in the School Organization of Mathematics Education

How is an advantaged and disadvantaged position for participation in mathematics education constructed in the network of mathematics education practices within the school organization? Let us consider the episodes again.

Gitte, the “lonely girl” in Nyspor School, seems to have a position of a student with learning difficulties in mathematics. Such position, however, is not given by the fact that she may have some kind of genetic or psychological deficiency.^{4} Whether she has it or not is in fact unknown to the teachers. However, the series of interactions between Gitte and other actors in the school clearly isolate her more than her own possible difficulties. How is it then that Gitte’s environment constructs her “deficient” position? First of all, Gitte’s position is evidently marked physically: Her desk is placed just in front of the teacher’s desk. She sits alone while all other students sit in pairs. This very physical setting marks her as being different. Her classmates also relate to her in a particular way. Gitte can be disturbed to pick up pencils from the floor, and passing sharpeners and rulers. Given the organization of the primary and lower secondary school in Denmark where students stay in the same class and with the same teacher for many years, students in the class have known Gitte for some years, and in their everyday interaction with her have also contributed to reinforce her being “lonely.” Mette, the teacher, has identified Gitte’s difficulties. She has created a way of interacting with girl that clearly gives her the place of a lower achiever and a slow learner in mathematics. The sets of special and easier problems given to Gitte function both as a help and as a marker of Gitte’s difficulties. All these interactions in the classroom are only one of the elements in constructing Gitte’s position as a less able student in general and in mathematics. Mette mentioned Gitte’s belonging to a family with learning difficulties. Mette has been in the school for only 2 years, and it is the first year that she had that class. In the classroom, she may see that the girl does not perform as the rest of the students. But how does she know that Gitte’s problems are common to other members of her family? In her socialization as a new teacher in that school she came to know from colleagues that Gitte had problems, but also that her learning difficulties was some kind of “genetic” deficiency. Gitte’s previous mathematics teacher had identified a lack of (mathematical) ability in Gitte, in her passing from first to eighth grade, which coincided with the deficiency of her relatives. Other teachers, in diverse spaces of interaction, have also commented about both the girl and her family. Probably not only Mette but the teachers in other school subjects also position Gitte in this way, given their shared idea on her disability.

The municipal and school policy on support to students with special needs have also impacted the way in which the school master and teachers have organized the possibilities for providing students with difficulties—and Gitte in particular—with additional help. The decisions on how to deal internally in the school with the support to mathematically weak students concern the school leaders, the teachers, and the students’ parents. The emphasis that local authorities put on bilingual students leaves few resources for students such as Gitte. Therefore, most of the help given to her has to go through Mette and her strategies for differentiation of teaching and meeting students’ different ability levels in the same class. Besides, the fact that Gitte is a quiet, well behaved girl may distract the attention of the teacher to other students whose evident misbehavior is considered in the school culture as a sign of being “problematic” and, therefore, in need of special attention.

It is clear that in the interaction among leaders, other teachers, and Mette, collective ideas about ability, in general, and of mathematical competence in particular students such as Gitte, are built. The resulting decisions made and actions taken in the school organization and in the classroom contribute in constructing Gitte’s positioning as a low-ability, female (mathematics) learner.

In the case of the African students in Rajas Secondary School, how is it that the walls around African students come in place? Are they only built in the classroom? A very first answer to this question could be that the position of African students in an ex-Indian school in South Africa is the result of apartheid and the deep structural inequalities of that regime. However, such an answer does not allow seeing the instauration of mechanisms of inclusion/exclusion in the everyday functioning of schools and mathematics education in them. It is necessary to dig into the constitution of practices in the school about mathematics education and how those position African students.

*Rajas School Constitution*, it is stated that one of the aims of the school is to “educate and prepare learners to accept and manage the challenges and demands of a changing society based on equality and freedom and the eradication of all other forms of unfair discrimination” (Rajas Secondary School 1997, p. 2, unpublished data). Formally, there is an institutional commitment against discrimination and racism, in accordance with the national democratic transformation in South Africa and with specific policies of affirmative action, which intend to favor African population as a way of balancing the historical racial unbalance and discrimination. Although in Rajas, a predominantly Indian school, there is no explicit policy for the admission of children belonging to other racial groups, the criterion of “first come, first served” has opened the doors to African students who make up 20% of the school population. Most of the African students live in townships far from the school area and must find and pay for their transportation to and from school. Although these students are allowed in the school, it is also evident that they perform poorly. Mr. Ruikar, the school’s principal, mentions the difficulty of these students to cope with school mathematics. The difference in “culture of learning” between the school and the African students is the reason of the poor results:

[…] if you take like specially the Blacks, you will find the Blacks are in a fairly quite hopeless community when it comes to mathematics results or in fact in any other subjects. In their culture of learning [unrecognizable] whatever they can do, they use to do it in the school. Now, when these Black students are coming to Indian schools, for us, homework is always there. In fact we’ve got a special homework timetable, where they [students] are suppose to have about 45 minutes of homework per day or every second day. And we insist on homework because the time that is allocated to the subjects during normal class hours is not sufficient. So we do the basics in class and they have to go home and consolidate in the form of examples and so on. But the Blacks are not doing the homework. And only now, in these Indian schools by being forced, they are slowly attempting or learning to do the homework (Mr. Ruikar, Interview 1).

Mr. Ruikar: […] when you give homework to a child, one from a deprived community and one from the elite, that child has got computers at home. When he goes and speaks to the parents and looks at the questions and what they are expected to do, the child can afford to go to the bazaar and buy certain types of aids, and pictures and other things in order to enhance the assignment. Whereas in a poorer home, the child just is being assisted. He hasn’t got even the daily news or the daily paper from which he can take certain cutting and he can paste it.

Paola: And the parents probably don’t even have the time to check the homework.

Mr. Ruikar: Maybe they didn’t even go to school. They haven’t got the ability to help the child even if they want to help the child they haven’t got the knowledge. So this is the situation that we are facing (Mr. Ruikar, Interview 1).

Mr. Ruikar’s explanations resemble the attributionist views of equity mentioned in the previous section. Nevertheless, in the first quotation, he pointed to the fact that the organization of instruction in the school has settled the practice of homework making it an important part of the activities that students are expected to do in order to learn. In this fragment of conversation with Mr. Ruikar, it is evident that the organization of teaching and learning installs a practice, central to the learning of mathematics, which disadvantages African students. Disadvantage is partly constructed by the way in which instruction happens, although it is perceived as a problem of the students for not sharing an important part of the “learning culture” of the dominant Indian community in the school. Mr. Ruikar identifies this as a problem, but still does not foresee possibilities for overcoming it with introducing changes to the “Indian learning culture.”

[…] And so my experience with all the people we teach is that they realize they must work hard. And the mark gets better, you would never believe they did badly in grade 9 because they reached that level where they know. And the mark has got very good […] But some of them think that automatically they go for tuition, automatically they will get good marks. It doesn’t happen, they have to work hard (Seema, Interview 1).

Because you may reach a point in your life, even in school, when you get highly frustrated of students not cooperating […] But at the end of the day when you look at what is important, the pupil is important and they need to produce a result based on knowledge and your duty is to impart that knowledge and also take care of them for their future […] So you find that you come to a class when half of them may not do the work. At first, your initial reaction is to yield. But then you look at the other and those are the students we work for. Don’t worry about the other half. And then the other half who don’t do it, they get the message eventually […] But then I usually look at the kid who sat until 10 last night and did the work. So I always maintain that there is at least one kid who benefits form it, that is enough. But that shouldn’t be the goal. You should try to get everyone to that level (Mahesh, Interview 1).

Both Arun and Vijay, the other mathematics teachers, also expressed their expectations about students doing their homework, reading the textbook, doing the exercises in it, and completing additional work that they prepared about topics they recognized as difficult. Students have to study hard in order to successfully cope with the examinations. If they fail it is because, as Vijay said, “they don’t want to learn anymore.” The group of mathematics teachers led by Seema value hard work and connects it with success in mathematics. They all expect that students are able to do a considerable amount of additional activities so that they can cope with the demands. As Mr. Ruikar pointed out, more “well-off” students have the resources—material and parental—to do so. But the possibilities of doing all the extra work needed may not be within the reach of most African students. Lack of material resources may restrict access to textbooks, additional materials, and free time—some students have to do work at home or outside to help supporting their families. Parental support is also a restricted resource that limits students’ possibilities to fulfill all expectations concerning hard work.^{5}

The teachers and the principal in Rajas identified private tuition—see Seema’s comment above—as an important support to perform well in examinations, particularly when approaching the end of secondary school and the national tests when leaving school. Even some of these teachers service students from other schools as private tutors in their free time. An organization of mathematics education in a school which requires additional, paid tuition may certainly be in the disadvantage of less affluent students, among them most of the African youngsters attending this school.

^{6}For Arun, one of the mathematics teachers, language was a serious problem:

Arun: […] Now from 94 with all the transformations, you have different cultures in the classroom.

Paola: And which kinds of problems do you see in this integration of cultures, in your classroom, for example, with Black children?

Aarun: The main problem is really communication. Black students have problems because the medium of instruction here is English and they have been used to a culture where the medium of instruction is Zulu or one of their languages, and now they come to an English-Indian school, and the main problem is the communication. For example, in maths, you do a lot of things with words, and if they may not follow the problem, they won’t pick it […] (Aarun, Interview 1).

It was evident that teachers recognized the difficulty of having several cultures and languages in the classroom. However, there was not an explicit institutionalized effort in addressing the difficulties. On the contrary, the decisions made concerning instruction in a time of shortage of resources accelerated the pace of teaching in order to cover the mandated syllabus; the result of that being a very compact and pressed school day which made it difficult for students who are not very proficient in English to cope with the teaching.

The organization of school demands, the valuing of hard work, the expectations of extra home work and eventual private tuition, and the language of school mathematics are part of the institutional practices of school mathematics in Rajas Secondary School. These practices have implications for teaching in the classroom, but are definitely not limited to it. They are built and exercised in the school organization where mathematics teachers as a collectivity, in relation with other teachers and with school leaders, create ways of talking about what is valued in teaching and learning mathematics. These ideas are many times the grounds for decision making about the organization of a type of instruction that construe a disadvantaged position for African students.

## 4 Power and Equity in Mathematics Education Research

One of the tasks of mathematics education research as an international field of study is bringing an understanding of the complexity of the practices of mathematics education. Identifying key predicaments in those practices is part of the scientific endeavor. In my trajectory as a researcher in this field, it has been important to open the research scope in an attempt to contextualize mathematics teaching and learning practices in the broader social space in which they live. In this paper, I have outlined some of the key ideas that make part of my socio-political perspective and have illustrated how those ideas are the theoretical and methodological tools for researching mathematics education practices.

I used two cases, Gitte in Nyspor School and the African students in Rajas Secondary School, to bring forward a discussion of equity in mathematics education. Issues of equity, social justice, and democracy have been a concern of many mathematics education researchers who acknowledge the fact that performance in mathematics is used in many school systems as a gate-keeping and selection mechanism from entering into socially valued educational and working possibilities. It is argued that not being able to learn mathematics effectively diminishes students’ capacities to act in powerful ways in the current global society. From a broader socio-political perspective, understandings of exclusion and inclusion are incomplete if no attention is paid to the practices of mathematics education outside of the classroom, but that make part of the network of routines, ideas, shared meanings and ways of talking and conceiving mathematics education among the actors in the school organization, and even outside of it. Digging the network of school mathematics education practices in Nyspor School and Rajas Secondary School allowed evidencing that the possibilities of participation that Gitte and the African students have in their mathematics classrooms are constructed in the school. The micro-physics of power of mathematics education point to the school as the arena where differentiated positioning, and thereby access, is constructed.

Addressing equity issues in mathematics education research and in practice demands the broader type of understanding presented here. Without it, any attempt at tackling exclusion within and through mathematics teaching and learning will fall short in making a substantial difference for students such as Gitte or the African children in South Africa.

## Footnotes

- 1.
Ole Skovsmose’s paper here in this number provides a good overview on this issue.

- 2.
Such an approach shares many points in common with the recent work of Paul Cobb and collaborators (Cobb et al. 2003) on viewing mathematics teachers’ instructional practices as part of the school community of practice.

- 3.
More details on the methodology and analysis of data in the empirical studies can be found in Valero (2002b).

- 4.
The case of Gitte could be interpreted within the research on mathematics education for children with special needs. For a discussion of this trend see Magne (2001).

- 5.
- 6.

## Notes

### Acknowledgements

This paper makes part of the project “Mathematics Education and Democracy” which Ole Skovsmose and I are engaged with, at the Department of Education, Learning and Philosophy, Aalborg University.

## References

- Adler, J. (2001a). Resourcing practice and equity: A dual challenge for mathematics education. In B. Atweh, H. Forgasz, & B. Nebres (Eds.),
*Sociocultural research on mathematics education. An international perspective*(pp. 185–200). Mahwah: Erlbaum. Google Scholar - Adler, J. (2001b).
*Teaching mathematics in multilingual classrooms*. Dordrecht, Boston: Kluwer. Google Scholar - Boaler, J. (1997).
*Experiencing school mathematics. Teaching styles, sex and setting*. Milton Keynes: Open University. Google Scholar - Boaler, J. (1998). Nineties girls challenge eighties stereotypes: Updating gender perspectives. In C. Keitel (Ed.),
*Social justice and mathematics education. Gender, class, ethnicity and the politics of schooling*(pp. 278–293). Berlin: IOWME—Freie Universität Berlin. Google Scholar - Burton, L. (Ed.). (2003).
*Which way social justice in mathematics education?*Westport: Praeger. Google Scholar - Cobb, P., McClain, K., de Silva Lamberg, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and district.
*Educational researcher: A publication of the American Educational Research Association*,*32*(6), 13–25. Google Scholar - De Freitas, E. (2004). Plotting intersections along the political axis: The interior voice of dissenting mathematics teachers.
*Educational Studies in Mathematics*,*55*, 259–274. CrossRefGoogle Scholar - Fennema, E. (1995). Mathematics, gender and research. In B. Grevholm & G. Hanna (Eds.),
*Gender and mathematics education*(pp. 21–38). Lund, Sweden: Lund University Press. Google Scholar - Foucault, M. (1972).
*The archaeology of knowledge*(1st American ed.). New York: Pantheon Books. Google Scholar - Foucault, M., & Faubion, J. D. (2000).
*Power*. New York: New Press; Distributed by W.W. Norton. Google Scholar - Ginsburg, H. (1997). The myth of the deprived child: New thoughts on poor children. In A. B. Powell & M. Frankenstein (Eds.),
*Ethnomathematics: Challenging eurocentrism in mathematics education*(pp. 129–154). Albany: State University of New York Press. Google Scholar - Hardy, T. (2004). “There’s no hiding place”. Foucault’s notion of normalization at work in a mathematics lesson. In M. Walshaw (Ed.),
*Mathematics education within the postmodern*(pp. 103–119). Greenwich: Information Age. Google Scholar - Keitel, C. (2006). Mathematics, knowledge and political power. In J. Maasz & W. Schloeglmann (Eds.),
*New mathematics education research and practice*(pp. 11–22). Rotterdam: Sense. Google Scholar - Keitel, C. (Ed.). (1998).
*Social justice and mathematics education. Gender, class, ethnicity and the politics of schooling*. Berlin: IOWME—Freie Universität Berlin. Google Scholar - Leder, G., & Forgasz, H. (1998). Single-sex groupings for mathematics: An equitable solution? In C. Keitel (Ed.),
*Social justice and mathematics education. Gender, class, ethnicity and the politics of schooling*(pp. 162–179). Berlin: IOWME—Freie Universität Berlin. Google Scholar - Lerman, S. (2006). Cultural psychology, anthropology and sociology: The developing ‘strong’ social turn. In J. Maasz & W. Schloeglmann (Eds.),
*New mathematics education research and practice*(pp. 171–188). Rotterdam: Sense. Google Scholar - Licón-Khisty, L., & Chval, K. (2002). Pedagogic discourse and equity in mathematics: When teachers’ talk matters.
*Mathematics Education Research Journal. Special issue: Equity and Mathematics Education*,*14*(2), 154–168. Google Scholar - Magne, O. (2001).
*Literature on special educational needs in mathematics. A bibliography with some comments*. Malmö, Sweden: Department of Educational and Psychological Research—Malmö University. Google Scholar - Meaney, T. (2004). So what’s power got to do with it? In M. Walshaw (Ed.),
*Mathematics education within the postmodern*(pp. 181–200). Greenwich: Information Age. Google Scholar - Perry, P., Valero, P., Castro, M., Gómez, P., & Agudelo, C. (1998).
*Calidad de la educación matemática en secundaria. Actores y procesos en la institución educativa*. Bogotá: Una empresa docente. Google Scholar - Perry, P., Valero, P., & Gómez, P. (1996). La problemática de las matemáticas escolares desde una perspectiva institucional. In P. Gómez (Ed.),
*La problemátca de las matemáticas escolares. Un reto para directivos y profesores*. México: Una empresa docente y Grupo Editorial Iberoamé rica. Google Scholar - Popkewitz, T. S. (2002). Whose heaven and whose redemption? The alchemy of the mathematics curriculum to save (please check one or all of the following: (a) the economy, (b) democracy, (c) the nation, (d) human rights, (d) the welfare state, (e) the individual). In P. Valero, & O. Skovsmose (Eds.),
*Proceedings of the third international conference on mathematics education and society*(pp. 29–45). Copenhagen: Center for research in learning mathematics. Google Scholar - Rajas Secondary School (1997).
*Constitution of Rajas Secondary School*. Unpublished manuscript, Durban. Google Scholar - Rogers, P., & Kaiser, G. (1995).
*Equity in mathematics education: Influences of feminism and culture*. London, Washington: Falmer Press. Google Scholar - Setati, K. (2005).
*Power and access in multilingual mathematics classrooms*. Paper presented at the fourth international conference on mathematics education and society, Gold Coast, Australia. Google Scholar - Skovsmose, O., & Valero, P. (2001). Breaking political neutrality: The critical engagement of mathematics education with democracy. In B. Atweh, H. Forgasz, & B. Nebres (Eds.),
*Sociocultural research on mathematics education. An international perspective*(pp. 37–55). Mahwah: Erlbaum. Google Scholar - Skovsmose, O., & Valero, P. (2002). Democratic access to powerful mathematical ideas. In L. D. English (Ed.),
*Handbook of international research in mathematics education. Directions for the 21st century*(pp. 383–407). Mahwah: Erlbaum. Google Scholar - Sriraman, B. (Ed.). (2007).
*The montana mathematics enthusiast*. Monograph*1*:*International perspectives on social justice in mathematics education*. Missoula: Department of Mathematical Sciences—The University of Montana. Google Scholar - Stake, R. (1995).
*The art of case study research*. Thousand Oaks: Sage. Google Scholar - Stake, R. (2005). Qualitative case studies. In N. K. Denzin & Y. S. Lincoln (Eds.),
*The sage handbook of qualitative research*(3rd ed., pp. 443–467). Thousand Oaks: Sage Publications. Google Scholar - Undervisningsministeriet (1995).
*Matematik. Faghæfte 12*: Undervisningsministeriet. Google Scholar - Valero, P. (2002a). The myth of the active learner: From cognitive to socio-political interpretations of students in mathematics classrooms. In P. Valero & O. Skovsmose (Eds.),
*Proceedings of the third international conference on mathematics education and society*(2nd ed., Vol.*2*, pp. 489–500). Copenhagen: Center for research in learning mathematics. Google Scholar - Valero, P. (2002b).
*Reform, democracy and mathematics education. Towards a socio-political frame for understanding change in the organization of secondary school mathematics*. Unpublished Ph.D. thesis, Danish University of Education, Copenhagen. Google Scholar - Valero, P. (2004). Postmodernism as an attitude of critique to dominant mathematics education research. In M. Walshaw (Ed.),
*Mathematics education within the postmodern*(pp. 35–54). Greenwich: Information Age. Google Scholar - Valero, P. (2007). In between the global and the local: The politics of mathematics education reform in a globalized society. In B. Atweh, A. Calabrese Barton, M. Borba, N. Gough, C. Keitel, C. Vistro-Yu, & R. Vithal (Eds.),
*Internationalisation and globalisation in mathematics and science education*(pp. 421–439). New York: Springer. CrossRefGoogle Scholar - Vithal, R. (2003).
*In search of a pedagogy of conflict and dialogue for mathematics education*. Dordrecht, Boston: Kluwer. CrossRefGoogle Scholar - Zevenbergen, R., & Flavel, S. (2007). Undertaking an archaeological dig in search of pedagogical relay. In B. Sriraman (Ed.),
*The montana mathematics enthusiast*. Monograph*1*:*International perspectives on social justice in mathematics education*(pp. 63–74). Missoula: Department of Mathematical Sciences—The University of Montana. Google Scholar - Zevenbergen, R., & Ortiz-Franco, L. (Eds.). (2002).
*Mathematics education research journal. Special issue: Equity and mathematics education*, 14(2). Melbourne: MERGA. Google Scholar