A BSTR ACTIn this paper, the culture of the mathematics classroom is inspected throug h the lens of one teacher and one class of school students. The intention here is to privilege the voices of the participants, particularly those of the young people themselves, whose views and experiences are sometimes absent from educational studies. A metaphor of spaciousness is invoked in drawing together curriculum, pedagogy, epistemology and classroom practices and relationships. In the classroom under study, the students developed connected and authoritative understanding s abou t the nature of mathematics; they linked these to the classroom relationships and linked these in turn to the curriculum. The comments from the students suggest that a reappraisal and renegotiation of what it means to be a teacher in the secondary mathematics classroom is timely.

In this article, drawing on extended interview data collected as part of a larger study, a model of the ways of knowing of beginning mathematics teachers is elaborated. Central to the model is the construct 'authority' which links authoritative knowing and the authorship of knowledge. Four epistemological perspectives are described: silence, external authority, internal authority and the authority of self and reason. These are linked to two different traditions in mathematics classrooms -'school maths' and 'inquiry maths' -and to the commitment of beginning mathematics teachers to working for emancipatory change in education.Frances called in to use the Resources Collection at our Mathematics Education Centre and stopped for a chat. She did not yet know that I thought teachers' ways of knowing were important in understanding their classroom practice and their commitment, or otherwise, to working for change in education. She had herself read science at University and had been a student on our 2-year postgraduate initial teacher education (mathematics conversion) course. She volunteered this comment. She said: I've been teaching science this year and doing it so badly. It shows that there really is something in teacher training. With science all the knowledge is here [gestures] in my head and I haven't got a clue how to proceed. With maths, the maths is all out there in the classroom with them and I'm very happy with that. (Based on personal research notes, May l995)This article is concerned with the elaboration of a model of the ways of knowing of beginning mathematics teachers. I start with this moment involving one of the participants in the research upon which this paper is based (Povey, 1995) because this incident was something that I noticed, something that I saw differently, because of the model which I had constructed as a result of my enquiry. Here was someone saying that WAYS OF KNOWING 329

No abstract

No abstract

This article rehearses the argument that being a critical mathematics educator is associated with a particular epistemological stance, one which views the truths of mathematics as historically located, influenced by the knower and mutable. Case study data, collected in England, is offered which exemplifies this connection between epistemology and openness to equity issues in the thinking of some beginning secondary mathematics teachers. Teachers' responses are analysed around four themes: their beliefs about the nature of mathematics, how those beliefs affect their pedagogy, how they explain student failure, and their views on initial teacher education. These are linked to their commitment to social justice in and through mathematics. The links between subject studies in teacher education and equity issues in the classroom are discussed.