We Offer a Tentative Framework

We Offer a Tentative Framework

Techno-mathematical Literacies in the workplace: Improving workplace processes by making the invisible visible

Arthur Bakker, Celia Hoyles, Phillip Kent and Richard Noss
Institute of Education, University of London

Paper presented at the 5th Annual Conference of the Teaching and Learning Research Programme, Cardiff, 22-24 November 2004

ABSTRACT. As more and more companies are taking part in process improvement and becoming increasingly data-driven, the drive to manage information has brought about an escalating need for employees at all levels to interpret computer outputs. This requires developing Techno-mathematical Literacies (TmL): technically-oriented functional mathematical knowledge, grounded in the context of specific work situations. In this presentation we will report some findings from the first year of our TLRP Phase III project, during which we have carried out case studies of techno-mathematical practices in several manufacturing companies. In many of these companies, it seems that a core capacity to solve problems involves making visible the relationships among processes (between machines, tools, materials, and people). We are beginning to clarify one defining characteristic of TmL as rendering the invisible visible through the production of mathematical signs and developing meanings for action from an interpretation of these signs. Activity theory provides a sophisticated account of how knowledge is acquired in becoming part of a workplace community, but the nature of knowledge at individual and group levels has been less well theorised. This is a significant area which we intend to address theoretically in the light of TmL. We are working on ways to theorise the nature of TmL by using some aspects of Peirce’s semiotic theory to analyse the use of mathematical signs within activity systems to address the issue of invisibility and coming to data-informed decisions.

KEYWORDS: Activity theory, Boundary objects, Semiotics, Computers, Mathematics


The Techno-mathematical Literacies in the Workplace (TmL) project is funded under TLRP Phase III, and commenced in October 2003 for three and a half years. The project is examining mathematical practices in three industry sectors – Packaging, Pharmaceutical Manufacturing and Financial Services. We have coined the term “techno-mathematical literacies” as a way of conceptualising mathematics as it exists in modern IT-based workplace practices (partly, we have felt the need to adopt a new term to avoid the baggage which goes along with the term “numeracy”, and, indeed, “mathematics” itself in this context). It has been evident since the 1980s from studies of mathematical practices in workplaces, that most workers use mathematics to make sense of situations in ways which differ quite radically from those of the formal mathematics of school and college curricula. What emerges from studies in workplaces is that people develop mathematical techniques to carry out their work, which are generally strongly situated according to their experiences, the tools they use and the features and local regularities of the context. These techniques are preferred because they are often quicker and more efficient than general mathematical techniques. Yet it is evident from researching in workplaces, that experienced employees use and interpret mathematical concepts, as “situated abstractions”, which are generalisable within the work context; for detailed discussion of this phenomenon, see our previous research in workplace mathematics (Noss & Hoyles, 1996; Noss, Hoyles & Pozzi, 2002). We believe that this generalised kind of conceptualisation forms a crucial underpinning for the skills base of all types of employees in all kinds of workplaces, as IT increasingly shapes industrial and commercial working practices. In the example below, of a food manufacturing company, we will illustrate how TmL are emerging as core competences for shopfloor employees as the company seeks to modernise and improve its production processes.

Methodology of the research

The project has begun with a phase of interviews combined with ethnographic observation of between two and four companies in each sector, in order to identify and categorise different forms of TmL. Our research has an epistemologicalfocus of inquiry, in that we are investigating the roles played by mathematics, IT and contextual knowledge “at work” for individuals and communities, and how knowledge and understandings develop among these different groups and are communicated between them. This focus distinguishes our methodology from some other studies of workplaces (including some of the projects in TLRP), which are concerned with learning more generally, conceived as a form of social practice in organisations. The consequence of our epistemological stance is that our methodology needs to be “theory-driven”, in the sense suggested by Pawson & Tilley (1997). They contrast “data-driven” research — where the emphasis of inquiry is on collecting data and identifying ideas as they emerge from data— with theory-driven research, where it is the theory of the researchers that steers the inquiry.

The notion of TmL has developed out of our previous research on mathematics in workplaces, and thus, to a certain extent, our data collection is driven by the motive of “looking for” TmL. There is, of course, a necessary balance between “looking at” and “looking for”, particularly in the early work of the project; one technique that we find very productive is to focus initial workplace observations (“looking at”) on situations where routine working practice breaks down, and this brings into view the explicit problem-solving and communication strategies of employees – thus suggesting to us the TmL which might underlie those strategies, and suggesting issues to be looked for in subsequent observations.

For each company that we have studied, interviews and observations (including artefacts collected) from workplace visits are written up as detailed transcripts. Starting from these raw data, our analysis has proceeded by developing a preliminary categorisation and description of TmL in order to identify significant work episodes that exemplify one or more TmL. These work episodes are written up collaboratively by the project team, discussed and revised. Similarly the emerging TmL categorisation and descriptions are iteratively discussed and revised. The analysis schemes for the work episodes have various dimensions: routine or non-routine situation, the nature and role of the models, tools and artefacts used or available, and the ways that TmL are mobilised (or not) to communicate between different groups or to make decisions. Note that, in general, we do not code individual “chunks” of data, such as individual interview responses, since the understanding of how a TmL is being used in practice requires a synthesis of different viewpoints and data sources.

We describe our observational methodology as ethnographic, meaning that we spend periods of time in workplaces, observing and talking with people there, but we should be careful to say that we do not attempt the kind of engagement which is typical of ethnography amongst professional anthropologists (immersion of the researcher in the community under investigation over periods of months or years). We have, therefore, to adopt a realistic perspective that sidelines some of the issues that are much discussed in the literature of ethnography (e.g. Hammersley & Atkinson, 1995) about the intervention of the researcher and its effect on the “culture” which is to be observed: in fact, we explicitly present ourselves as “outsiders” and observers, and we believe that the mathematical processes we wish to observe are rather robust, even if “tacit” (i.e. embedded within artefacts of the practice). We do, however, acknowledge the need to gain the confidence of research participants, and to be open in our dealings, which is crucial to encourage participants to initiate discussion of the mathematics that they actually do, rather than the mathematics that they think we (as mathematicians and educators) want to hear about.

Triangulation is a key concern for our research (cf. Hammersley & Atkinson, 1995).In collecting data, we continuously seek to triangulate different views of the same workplace activity, seeking the perspectives of employees including shopfloor operators, supervisory managers, process engineers and process improvement specialists, stock controllers and schedulers, maintenance engineers, and more senior managers. In analysing data, we triangulate interpretations of the raw data (audio transcripts, photographs of workplaces, artefacts in the form of paper documentation) amongst the project team. We further triangulate our findings by appealing to experts in the particular industrial sector that the data come from, by means of consultation (including the project’s advisory group) and validationmeetings in which sector experts are invited to learn about project findings, comment on their validity and generality, and suggests ways forward for the research. In the next phase of the project, which involves the iterative design of training materials, the triangulation of research findings will effectively continue as we gain feedback on our data analysis from the prototyping of materials.

Activity theory and knowledge

One theoretical framework of our project comprises the view of organised, technologically-mediated social activity suggested by activity theory (Engeström, 2001; Kuutti, 1996). We have found the basic premise of activity theory — that people working to realise an object of activity people mediate their actions through the use of artefacts, for example computers and the information that they provide — very helpful in coming to understand the role of TmL in workplaces. We interpret workplaces as a complex arrangement of interacting activity systems each characterised by their own object of activity (i.e. the purpose of work), mediated by artefacts and located in a context characterised by a specific “division of labour”, sets of “rules” and inter-related workplace “communities”. For example, it is evident from analyses of our observational and interview data that shopfloor workers and managers can often inhabit different Activity systems with different goals expressed with different tools and following different rules (see Hoyles et al, 2004, for an example). Moreover, the notions of boundary object and boundary crossing that have recently been explored in the activity theory literature (Tuomi-Gröhn and Engeström, 2003; see also Star, 1989; Star & Griesemer, 1989) have helped us to explain the role played by signs, such as numerical data and graphical information, as boundary objects that mediate communication between, and within, different activity systems.

From an activity theory perspective, the learning processes of an individual must be considered in a meaningful context of goal-directed, socially-situated activity. Yet although activity theory provides a sophisticated account of how knowledge is acquired in becoming part of a workplace community, the nature of knowledge at individual and group levels has been less well theorised. Guile and Young (2003) argue that in socio-cultural approaches to learning, the wider question of knowledge tends to be subsumed into the knowledge shared by particular communities, and the analysis of knowledge development tends to focus on the social practices of “communities of knowers”. Because the focus of our project is on TmL, we are coming to see that the question of knowledge and, in particular, mathematical concepts within workplace settings, has to be addressed by a more elaborate theoretical account of the role of TmL in workplaces.

The role of TmL in making the invisible visible

We are beginning to clarify one defining characteristic of TmL as making visible the relationships among processes (between machines, tools, materials, and people). In routine practice, people are making sense of their piece of the system and its relation to the overall process when necessary. In practice, workers seamlessly mobilize a mixture of contextual and mathematical knowledge. Yet there is plenty of evidence (see, for example, Noss, Hoyles & Pozzi, 2002) that this knowledge is built from a complex web of abstraction on the one hand and situational specificity on the other. These situated abstractions are woven into the practice, and do not – in general – employ any external sign system that we might recognise as mathematical, other than those invisibly embedded in the artefacts and tools of the practice. Abstraction in the form of conceptualizing relationships within the work process are certainly made, but they do not in general involve abstracting away from the situation. In fact, the reverse is mostly true: the “noise” of the practice appears to be decisive in generating meaning.

When something is wrong in the production process or the process is undergoing improvement, key variables have to be identified, coordinated and, where possible, quantified. These data on the process have then to be analysed in order to make visible the cause of any problem or “bottleneck” in maximising output. Inevitably this analysis is achieved through the production of mathematical signs with a view to developing meanings for action from an interpretation of these signs[1]. These signs however cannot be interpreted in isolation from the context to which they refer, and the tools through which they are expressed. (See Noss & Hoyles, 1996, for further discussion.)

Due to increasing use of technology, processes in the workplace have become both more visible and more invisible. On the one hand, technology allows measurement and analysis of hundreds of parameters in real-time and the display of relationships graphically in ways that were previously impossible. On the other hand, employees tend, as a consequence, to have less direct contact with the production process, which is increasingly mediated by computer interfaces that can obscure key determinants of the process and their interrelationships. Thus what may be lost is accessibility by simple observation, but what is gained is the possibility for operators to employ mathematical techniques to perform their jobs more effectively. (In Hoyles et al., 2004, we illustrate the tensions that can emerge as operators, and their managers, try to resolve the different information provided by the physical perceptions of the operators and the technologically-mediated perceptions.)

Thus one of the trends we observe is that more and more companies are becoming data-driven – and generally wishing to become more so (the manager of a food manufacturing company commented that for a long time people in the company had considered themselves involved in the “art” of making food, whereas his view is that the company is “an engineeringbusiness that happens to make food”). With all the data that have become available by using new technologies, it has become potentially easier to make decisions based on data. This potential does not however, necessarily make it easier to come to an informed decision. Our contention is that with so much data to analyse, informed decision-making depends on employees developing relevant TmL mediated by the available tools,in order to identify and compare the effects of key variables and the relationships between them.

When we have asked managers how they recruit and develop new employees, they often speak of looking at processes and making decisions. What is needed, said one manager, is “the ability of people to look at things and react.” From a semiotic perspective this implies that people need to interpret signs and know what to do in response. Another manager said: “people will be able to make more decisions from the data at their fingertips. And they will need more skills to do that – not really computer skills, more decision-making skills.” This stresses that what is needed is not simply fluency with the technology or some particular statistical knowledge to interpret data, but the capability to make decisions from multiple sources of data, whose interpretation is contingent on an appreciation of relevant details of the workplace context.

In the following, we present some empirical findings from a food manufacturing company to suggest what it means in practice to make visible key variables in the production process, to see what is important to be seen and to act accordingly, i.e. actually solve the problem. We analyse the data from a semiotic perspective and point out how the analysis suggests the need for a theoretical framework which can address more adequately the role of knowledge in activity. This expanded framework will be discussed in detail in future publications.

Example: Using data to solve problems in food manufacturing

This example concerns a programme of process improvement work that is being carried out in a food manufacturing company[2], with the overall goal of improving efficiency (less wastage, more production) and hence increasing profitability. Among the aims of the programme are:

  1. dealing with obvious process deficiencies
  2. building in the long term a culture among employees of thinking about process improvement, and simultaneously upskilling employees at all levels to support this change.

One part of the programme is the formation of “process improvement teams” (PI teams), which spend several weeks working full-time on one particular production line. Each team consists of volunteers who occupy different roles across the company – managers, maintenance engineers and shopfloor operators – with the idea that by interacting in detail with the managers and engineers, the operators will become stakeholders in process improvement.

The PI team that we observed began with several days of classroom training.Then the first problem-solving activity of the team was to collect data about the whole production line and assemble it into a single chart, known as the “capacity profile chart” (Figure 1). The intention of this chart was to reveal any “bottlenecks” in the production process, so that the PI team could prioritise a programme of tasks to remedy the most important sources of inefficiency. However, the meanings drawn from reading this chart are not unproblematic. From the point of view of the PI team, the chart was to serve as a problem-solving tool. We want to interpret the chart in our research as a boundary object, since we conjecture that different team members read the chart differently based on their different everyday roles in production (i.e. operators do the manual work on the production line, engineers maintain the machinery and infrastructure, managers work to monitor and maintain the whole process of production). For example, it was reported to us that operators tend to lack an overview of the process: “operators don’t want to think about what they are doing, not bother about what type of biscuits goes through, so long as it goes through – just worry about their own section where they work.” And: