In the workplace: learning as articulation work, and doing articulation work to understand learning

This paper offers an account of a methodological approach to understanding and developing learning that has been successfully used in a research project on mathematical skills in workplaces. The approach is based on the concept of articulation work, which is concerned with the processes of coordination and integration by which different social worlds intersect and negotiations take place between them, and the role of symbolic boundary objects as mediators for negotiation

The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. We question the validity of this metaphor, and make the case that engineers do in fact use mathematics as more than a set of passive tools—that mathematical models for phenomena depend critically on the settings in which they are used, and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and we think it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways

The mathematical components of engineering expertise: the relationship between doing and understanding mathematics

this paper are extracts from our interviews with engineers.) Where, then, is the complex mathematics that certainly exists in modern engineering? Throughout all aspects of engineering design, computer software has an overwhelming presence. Also, in the particular firm that we visited, there a small number of analytical specialists (a few per cent of the professional engineers employed) who act as consultants for the mathematical/analytical problems which the general design engineers cannot readily solve. (In general in structural engineering, such specialist work is often carried out by external consultants, eg. academic researchers

On the integration of digital technologies into mathematics classrooms

Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics

Situating graphs as workplace knowledge

We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use, and more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the notion of transparency to characterise instances of graph use by highly educated scientists in cases where the context was familiar: the scientists were able to read the situation "through" the graph. This paper explores the limits of the validity of the transparency metaphor. We present two vignettes of actual graph use by a factory worker, and contrast his actions and knowledge with that of a highly-qualified process engineer working on the same production line. We note that in neither case were the graphs transparent. We argue that a fuller account that describes a spectrum of transparency is needed, and we seek to achieve this by adopting some elements of a semiotic approach that enhance a strictly activity-theoretical view

Improving work processes by making the invisible visible

Increasingly, companies are taking part in process improvement programmes, which brings about a growing need for employees to interpret and act on data representations. We have carried out case studies in a range of companies to identify the existence and need of what we call Techno-mathematical Literacies (TmL): functional mathematical knowledge mediated by tools and grounded in the context of specific work situations. Based on data gathered from a large biscuit manufacturing and packaging company, we focus our analysis here on semiotic mediation within activity systems and identify two sets of related TmL: the first concerns rendering some invisible aspects visible through the production of mathematical signs; the second concerns developing meanings for action from an interpretation of these signs. We conclude with some more general observations concerning the role that mathematical signs play in the workplace. The nee

Attributing meanings to representations of data: the case of statistical process control

This article is concerned with the meanings that employees in industry attribute to representations of data and the contingencies of these meanings upon context. Our primary concern is to characterise more precisely how the context of the industrial process is constitutive of the meaning of graphs of data derived from this process. We draw on data from a variety of sources including ethnographic studies of workplaces and reflections on the design of prototype learning activities supplemented by insights obtained from trying out these activities with a range of employees. The core of this article addresses how different groups of employees react to graphs used as part of statistical process control, focussing in particular on the meanings they ascribe to mean, variation, target, specification, trend and scale as depicted in the graphs. Using the notion of boundary crossing we try to characterise a method that helps employees to communicate about graphs and come to data-informed decisions

Techno-mathematical literacies in the workplace: a critical skills gap

There has been a radical shift in the mathematical skills required in modern workplaces. With the ubiquity of IT, employees now require Techno-mathematical Literacies, the mastery of new kinds of mathematical knowledge shaped by the systems that govern their work. The education system does not fully recognise these skills, employees often lack them, and companies struggle to improve them. This project has developed prototype learning resources to train a variety of employees in the mathematical awareness and knowledge that today’s employment require