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Presentation 2E3. Are Statistical Meanings Contingent on Setting? The Case of Nursing

Celia Hoyles (UK)
Richard Noss (UK)


Presentation Abstract

Our recent work with a variety of professionals in work settings has convinced us of the superficiality of the (widespread) view that most professional life has little mathematics in it. There does exist a rich seam of mathematical activity which people exhibit in their working lives, if we know where and when to look, and if we do not rest content to equate reality with the stories people tell about it. So our starting point has been that by studying carefully the kinds of problems professionals actually solve, we can begin to make visible a range of activities that can usefully be described as mathematical, in terms of their participation - at least at some level - in the manipulation and interpretation of quantitative and spatial data and relationships. This kind of mathematics seldom comes in what Jean Lave calls "boxed products of calculation". On the contrary, it turns out that there is almost invariably a subtle and reciprocal mediation of both professional and mathematical knowledge.

Researching in this field has proved a challenge, as we were wary of taking as a starting point any simple classification of the 'visible mathematics' that we could see, but which might merely represent our own, as opposed to our subjects', orientation. Nevertheless, as our research progressed, we became aware that it was possible to make a provisional epistemological classification of some of the activities we were observing, and that it made sense to analyse them in terms of what they represented from our mathematical point of view, as long as this was made explicit. This analysis could then be augmented, synthesised and compared with the practitioners' viewpoints.

In this paper, we report the outcome of one such classification, in which the visible mathematics was the collection, recording and interpretation of data, and, the less visible part, the concepts underpinning the judgements made. The context was a study of paediatric nurses and how they made sense of clinical data, focusing on the concepts of average and variation. Our findings illustrate that the nurses' understandings of average are, from a mathematical point of view, webbed together with their practical and professional expertise. This knowledge is not 'a conception of average', to be transferred as a whole to a new situation. Rather it consists of pieces of knowledge about average - its use in practice, finely-tuned sets of 'rules' which may work only in limited domains - which, in the new situation of the teaching experiment, became coordinated in new ways to develop new meanings. This is the heart of the idea of situated abstraction, a theoretical construct which will be elaborated. The crucial idea is that individuals' sense of situation and the tools they have to hand, provide support for making meaning, and also the means for reconstructing these pieces in new ways (or developing new knowledge pieces).


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