Questioning (in) school mathematics : lifeworlds and ecologies of practice
The nature and experience of participation in school mathematics classrooms is considered through the analytical frames of community of practice theory (Lave and Wenger 1991; Wenger 1998) and the lifeworld by focussing on interactions generated by verbal teacher questioning of the whole class. The thesis reports on an explorative, personal inquiry that complements theoretical reflection with research material generated through interviews with learners of mathematics and by participant observation in school mathematics classes. The methodology is qualitative, hermeneneutical and engaged, and influenced by the principles of participative action research and co-operative inquiry in the context of post-modernist thought. The concept of usual school mathematics is developed to describe dominant social practices in mathematics in schools. Through an analysis of teacher questioning and the learners' experiences of it, the meaning of participation is problematised. The nature of marginal rather than legitimate peripheral participation in usual school mathematics classrooms shows that they are not communities of practice and are better described as regimes of practice. 'Ecologies of practices' is proposed as more flexible construct that allows the diversity of networks and practice in classroomsto be theorised. The nature of particular ecologies can be described(and researched) using similar dimensions to community of practice theory and this is illustrated by a case study which contrasts usual school mathematics practices with those that foster greater engagement by participants. The concept of the lifeworld supports understanding of the different experience of participants in ecologies of practice of mathematics and teacher questioning. The entities in mathematical lifeworld of learners of mathematics are not just simpler versions or a smaller subset of those in teachers' lifeworld but are existentially and ontologically different and this requires investigation. A case study of a mathematical lifeworld shows school mathematics can be deeply existentially alienating and marginalizing for learners. Students' views on ways of increasing engagement in questioning practices are presented and the implications of the research for engaged, transformative and democratic classroom practice with regard to teacher questioning is considered. Key conclusions of the thesis are: The analysis of the participation of participants in usual school mathematics practices as marginal demands that such practices be questioned; An ecological perspective allows the complexity of the variety of forms of participation, enterprises and engagement in classrooms to be analysed; The concept of the lifeworld supports an understanding of the diversity of meaning that arises for participants in the same ecologies; There are questioning practices that foster fuller participation by learners.
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