Renuka Vithal

The End of Innocence: A Critique of 'Ethnomathematics'?

Ethnomathematics originated in the former colonies, in response to the Eurocentrism of the history of mathematics, mathematics itself and mathematics education. It has also found expression in several other contexts. It is a part of the broader framework that elaborates the social and political dimensions of mathematics and mathematics education but especially, the dimension of culture. This focus on culture examined in the unique context of South Africa makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. This paper explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematrics education.

Researching Mathematics Education in Situations of Social and Political Conflict

We explore the thesis that given that our societies are fraught with various social and political conflicts, and that mathematics education is concerned with contributing to the life possibilities of students in that world, then mathematics education as a field of practice and research has to be concerned with the implications of recognising those conflicts. In particular, we explore the implications of considering social and political conflict situations for: the kinds of research questions and agendas constructed; the theories and methodologies adopted; and the criteria used for judging the quality of research in mathematics education. In building our argument we draw not only on international literature in the discipline of mathematics education and outside it, but also on our experiences as researchers struggling with the complexity of conflict contexts.

Project work in university mathematics education: A Danish experience : Aalborg University

This article discusses project work in university mathematics education. The practice perspective is obtained as students and teachers from Aalborg University share their experiences. A theoretical framework is introduced. It includes the following key-terms: Problem-centered studies, interdisciplinarity, participant-directed studies, and the exemplarity principle. The contrasting of this theoretical conception of project work with the practice shows that the original notion of project work has been modified as a consequence of its encounter with practice. The modification can be perceived as both a success and a failure. To discuss this, different perspectives on project work in mathematics are suggested.

Teachers and `Street Children': On Becoming a Teacher of Mathematics

The phenomenon of `street children where youngpeople, for various reasons, live on thestreets of towns and cities is found all overthe world in varying degrees and forms. InSouth Africa, one approach to take care aboutthe plight of these children has been to set upand run what are referred to as `streetshelters. One such street shelter, the onlyone exclusively for girls in the city ofDurban, is Tennyson House. In this paper Idescribe an innovative outreach programmeintegrated with a university curriculum inwhich a group of pre-service teachers takingmathematics education as a major were involvedin teaching mathematics to girls at TennysonHouse. From the vantage point of a mathematicsteacher educator in the programme, I describeand reflect on what was experienced and learnedfrom the intervention in terms of threeaspects: learning about learners; learningabout teaching (mathematics) and learning aboutrelationships.

Differentiation, in contradiction and co-operation, with equity in mathematics education

Abstract This paper theorises the theme of equity and differentiation, which emerged from a study exploring a social, cultural, political approach to the mathematics curriculum. While rooted in empirical data produced from a grade 6 mathematics classroom in which a student teacher attempted to realise this approach, the analysis of the theme, and in particular, the relation of equity and differentiation is explained through a simultaneous contradiction and co-operation best captured in the notion of complementarity. Multiple facets of the theme are discussed as the concepts of equity and differentiation and their connection are developed and deepened.

A Pedagogy of Conflict and Dialogue

In this research I have traveled a journey from the imagined hypothetical situation of a particular theoretical landscape, begun in a university lecture room, to a school mathematics classroom where a situation was arranged. A brief stay with one student teacher in this arranged situation led to the production of a variety of data. These data were organised into a crucial educational case description. Through this description it was possible to invite an interested outsider to participate in the visit to this mathematics classroom, and to produce an analysis. Five dual-concept themes emerged from the analysis. These themes, underpinned by the notion of complementarity, were cast in another sketch that charts the beginnings of perhaps quite a different theoretical landscape.

An Emergent Social, Cultural, Political Approach:

“Education after Apartheid. ” “Education after Auschwitz. ” And what of “Education after Colonialism”; or “Education after Genocides and Ethnic Cleansings”? Indeed, what about an education for living in a world of terror and of war. In juxtaposing these, a global sketching is made of humanity’s continuing inhumanity toward each other. Our joint project must surely be to work toward a world that will never see another Auschwitz, another Apartheid — a world of peace, of fairness, of freedom, respect and dignity for all. We assume that education can and must participate in this larger project. But what of mathematics education?

Methodological “Theoretical Tools” for Researching a Social, Cultural, Political Approach

The story that I tell is about a student teacher, and it is told through her attempt to give meaning to a particular approach to teaching and learning mathematics in a classroom. A second underlying hidden story that often remains largely untold is the researcher’s journey and her struggle in all that comprises the research endeavour. It is the “messiness” of classrooms and the successes and failures of teachers’ and learners’ lives in those classrooms that is usually revealed but seldom the parallel scenarios played out in the work and lives of researchers. Just as the theoretical landscape developed through the research, so too did the methodology. As I write this chapter, I do not want to present what I did and why I did it in a way that implies that it was all clearly thought out methodologically and theoretically. What I know now is so different from what I knew when I planned and produced the data. So in this chapter, I try to chart my own growth and journey as a researcher with respect to this emergent methodology, as I work through the many conflicts and dilemmas of doing research in South Africa and try to ground the methodology theoretically.

Crucial Description of a Social, Cultural, Political Approach:

In this chapter the data from the arranged situation, as it was pedagogically organized for research, is represented. It begins with “Day 3”, the lesson in which the project work ideas were presented to the class by Sumaiya following her preparatory work done earlier, described in the last chapter. The projects of individual groups of pupils as they unfolded in the classroom then follow and are discussed separately, together with initial reflections that arise from each of the five group projects. To construct the description, data from each lesson was “chunked” and re-clustered but maintained in a continuous sequential thread so that the workings and dynamics in each of the groups can be followed. The classroom video/audio data of the lessons are “smoothed” to facilitate reading but preserve the sequence of events in their entirety through the “Days”. The data chunks are introduced with comments, which offer an orientation to the particular reading I am making of events. The data selection is made to preserve as far as possible the natural environment of the classroom and what happened in the groups, and also to highlight aspects that developed in the reflections that followed in the attempt to constitute a crucial description. Implicit in any description, is an interpretation and analysis. The reflections continue an initial grassroots analysis, providing a means to organise additional data gathered from the teachers and pupils; and hence offer multiple perspectives and interpretations on the happenings in the classroom. In this respect they contribute to a democratic participatory validity. Any attempt to understand what happens in classrooms always produces only a slice of that reality. Many different readings can be made. It is a partial view because of where the researcher’s lens focuses and it is also partial in that it is coloured by the lens of the theoretical landscape through which the data are being interpreted. The perspective I bring to the data, the language of description, is that of a social, cultural, political approach to the school curriculum which integrates a critical perspective.

Methodological Challenges and Criteria for Researching a Social, Cultural, Political Approach

In this chapter I address the question of what is an appropriate methodology for researching an approach which foregrounds a critical perspective. I raise several issues which I consider to be necessary (but by no means sufficient) in seeking such a methodology and do so by referring to three broad well-known categories, which serve as a map for the rest of the discussion and for locating the research process and description. These distinctions quite commonly made between different research approaches in educational and social science research literature are: i) the empiricalanalytical, logical positivist or behaviourist paradigm; ii) the interpretive, hermeneutic, phenomenological or symbolic paradigm; and iii) the critical paradigm, drawing from earlier work by Habermas (1972) (e.g. Bredo and Feinberg, 1982). Such classifications are not in any way exhaustive, we need only refer to the growing research debates related to feminism, postpositivism, postmodernism and poststructuralism (e.g. Neuman, 1997; Guba and Lincoln, 1998), and these categorisations have themselves been critiqued (e.g. Carspecken, 1999). Nevertheless, they have been variously imported into research discussions in mathematics educationi (e.g. Ernest, 1998; Romberg, 1992; Nickson, 1992; Kilpatrick, 1988). Further, it is possible to observe and argue that the first paradigm has dominated mathematics education research, though in recent years, with the strong emergence of constructivism, the second paradigm has also gained much ground (Vithal and Valero, in press).