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