With the introduction of any new initiative into the mathematics classroom, there is often an assumption that it will produce visible and measurable effects in teaching approaches and pupil progress. Yet, there is a body of research that tempers such optimism, drawing attention to a series of mitigating factors, for example, the deep-seated nature of teachers' practices, their implicit or stated beliefs and values, and their lack of detailed awareness of how they perform in the classroom. Rather than make associative links between these factors and the success of the initiative, our intention is to examine the ways in which teachers are trying to interpret what the new scheme requires of them and how in turn, engaging with it causes them to re-describe both their pedagogic understanding and classroom practices relationally to earlier approaches. Employing data from a small project, we seek to examine four teachers' moves to grapple with this attempted shift from one teaching paradigm to another by considering how certain key terms serve to anchor the teachers' conceptions of themselves during this transition and find that their responses can be idiosyncratic and varied depending on the approaches in which they have been previously embedded. By using theoretical ideas from some neo-Marxist writers we examine these discursive shifts and their relevance to conceiving curriculum change. We suggest that the individual's teaching practice develops as a result of it being understood and enacted through a succession of ideological filters, each adding to the cumulative experience of the teacher.

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures. The study to be described was part of an ongoing research programme exploring how spreadsheets might function as pedagogical media, as compared with pencil and paper methods. As a tool for investigation, we asked, how might the study inform our understanding of the ways spreadsheets filter the learning experience? In particular, we asked how might spreadsheets influence learner's perceptions and understandings of mathematical phenomena? One aspect of this programme, to be pursued here, was to identify the ways in which participants approached mathematical investigations. We explored how they negotiated the requirements of the tasks, and how they produced their conjectures and generalisations.We commence by outlining the three core themes and some literature upon which these themes are premised. First, we introduce a hermeneutic theoretical perspective in which the process of understanding mathematical phenomena is seen as oscillating between individual encounter and social discourse. Understanding here is considered to be a function of the learner's interpretation and reflection, where such engagement gets fixed as conceptual phenomena. These concepts, however, evolve through further cycles of encounter as understanding develops. This understanding is thus manifest in what students say, and what they do. It is our contention that through an examination of participants' social interaction and output, we will gain insight into the ways students internalise mathematical understandings.Second, we review literature that underpins our concern with the particular qualities that spreadsheets bring to investigative mathematical processes. This enables us to differentiate patterns in the dialogue and output better, and, as a consequence, pinpoint the influence of spreadsheets on the learner's investigative trajectories. The assumption here is that spreadsheets filter

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