This article reports on research into primary student teachers' understanding of mathematics and its teaching undertaken at the Manchester Metropolitan University and funded by the Economic and Social Research Council. The research set out to investigate the ways in which non-specialist student teachers conceptualise mathematics and its teaching and how their views evolve as they progress through an initial training course. The study has shown how the mathematical understanding of such students is, in the first instance, embedded in a strongly affective account of their own mathematical experiences in schools, where mathematics was often seen as difficult and threatening. College training successfully nurtures a more positive attitude to mathematics as a subject, albeit couched in a pedagogically oriented frame. In later stages of training however, their conceptions of mathematics and its teaching are subsumed within the organisational concerns of placement schools and school experience tutors, and shaped by commercial schemes. It is suggested that alternative conceptions of mathematics assumed at different stages of this training appear incommensurable. A theoretical framework is offered as an approach to reconciling this conflict. This demonstrates how three potential dichotomies, phenomenological/official versions of mathematics, discovery/transmission conceptions of mathematics teaching, and perceptual/structural understandings of the mathematics teacher's task can be seen as productive dualities harnessing both qualitative and quantitative perspectives.
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
This article seeks to contrast two constructions of teachers and teaching in England. The first construction is to be found in government documentation, which privileges a technical‐rational approach. The second is to be found in film and advertising for the profession, where the teacher is represented as an altruistic and charismatic subject. In their contrasting ways, both these constructions can be regarded as fantasies for teaching held by the government and wider society, which the teacher has to deal with. The article examines both constructions and the tensions that have been created by their presence in Teacher Training Agency ‘texts’, by drawing on data from trainee interviews as well as examples from the media which give rise to these disparate fantasies. Employing psychoanalytic theory, the article seeks to examine the ways in which teachers and trainees are faced with the paradox of fulfilling both seemingly contrasting fantasies while in the meantime the Government works to annex personally felt fantasies into its codes. It is suggested that trainees need to be educated into these tensions and that practitioners overall need to maintain their fantasies for teaching as well as accommodating these codes.
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