Stefano Pozzi

Proportional Reasoning in Nursing Practice

We investigate how expert nurses undertake the calculation of drug dosages on the ward. This calculation is error-critical in nursing practice and maps onto the concepts of ratio and proportion. Using episodes of actual drug administration gleaned from ethnographic study, we provide evidence that experienced nurses use a range of correct proportional-reasoning strategies based on the invariant of drug concentration to calculate dosage on the ward instead of the single taught method they describe outside of the practice. These strategies are tied to individual drugs, specific quantities and volumes of drugs, the way drugs are packaged, and the organization of clinical work. The centrality of mathematics to school curricula has been justified partly in terms of its importance for the world of work, and many researchers have attempted to articulate the relationships between school-taught mathematics and the mathematics found in occupational and everyday lives. We believe that the study of mathematics in work provides a particularly fruitful setting for illuminating fundamental issues concerning the construction of mathematical meanings more generally. In essence, it offers an opportunity to focus attention on the ways in which professional discourses shape mathematical meanings and, reciprocally, on how the use of mathematics-however defined-structures the discourse of work. One might hope that such insight will afford leverage on didactical strategies within and beyond workbased settings. Until the middle of the 1980s, research in this field was undertaken largely within a framework in which the researchers assumed that mathematics was unproblematically visible in workplace settings and that it consisted mainly of calculation (see, for example, Fitzgerald, 1981). Later, researchers, for example Wolf (1984) and Harris (1991), adopted methodologies that were considerably more sensitive to the complexity of the practice/mathematics relationship. Yet all using such approaches encountered a fundamental obstacle: Most employees did not describe their activities in mathematical terms, and they often declared that they used very little mathematics in their work. The fundamental difficulty, it seems, is that the math

Tools in practice, mathematics in use

We seek to analyse the notion of structuring resources and their role in shaping mathematical activity, and more broadly to add to our understanding of mathematical epistemologies in workplace settings. Our analysis is of two nursing activities – drug administration and fluid balance monitoring – based on data collected in an in–depth study of paediatric nurses on the ward. In the first activity, we examine ways in which nurses conceptualise ratio and proportion problems, while in the second, we provide a case study of two nurses discussing conflicting strategies when monitoring the fluid balance of a patient. We discuss the ways in which the available resources give mathematical and professional meanings in these situations and draw out some implications for the design of viable didactical strategies in vocational mathematics teaching.

Working Knowledge: Mathematics in Use

In this chapter, we explore how mathematics is used and described in work in the context of investment bank employees, paediatric nurses and commercial pilots. We distinguish the visible mathematics of the workplace, that is the mathematics referenced in textbooks and by experts, from the mathematics observed in ethnographic observations of the practice. Our conclusions are that practitioners do use mathematics in their work, but what they use and how they use it may not be predictable from considerations of general mathematical methods. Strategies at work depend on whether or not the activity is routine and on the material resources at hand.

Interdependence and autonomy: aspects of groupwork with computers

Abstract This paper presents case studies of two groups of six pupils undertaking three research tasks involving mathematical ideas and incorporating work with computers. We attempt to characterize effective groupwork and analyze the importance of developing a synergy between pupil interdependence and pupil autonomy. We examine the interrelationship between task, group as a social system and the role of the computer in establishing good group practice and identify the need for a pupil-teacher role within such a practice.

Learning Mathematics in Groups with Computers: reflections on a research study

Abstract This paper traces a methodology for analysing groupwork with computers, together with some of the findings. The theoretical underpinning of the research is outlined along with how this theory informed the design of the study. In order to make explicit the research process, reflections on the project revolve around a detailed description of how the data were analysed and the phases through which the analysis progressed. This includes how decisions were made in order to cope with large qualitative data sets, the choice of appropriate quantitative techniques, and how qualitative and quantitative methods were combined. Advantages and limitations of this analysis are considered, and finally generalisations on the role of groupwork with computers in mathematics education are explored.

Towards a methodology for analysing collaboration and learning in computer-based groupwork

Abstract This paper presents a methodology for researching effective groupwork within computer environments, developed as part of the Groupwork with Computers Project. The research involves eight groups of six mixed-sex, mixed-achievement pupils, undertaking research tasks using both the Logo programming language and a database program. Our aims are to identify factors influencing effective computer-based groupwork in terms of both group outcome and individual learning. Two groups working on a Logo-based task are described to focus attention on how our methods of analysis address the relationship between group processes, individual progress and group outcome, and some emerging considerations are discussed.