The first aim of this paper is to present a characterisation of techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory, specifically to the notions of boundary object and boundary crossing. In this paper we draw on ethnographic research in a pensions company and focus on data derived from detailed analysis of the diverse perspectives that exist with respect to one symbolic artefact, the annual pension statement. This statement is designed to facilitate boundary crossing between company and customers. Our study showed that the statement routinely failed in this communicative role, largely due to the invisible factors of the mathematical-financial models underlying the statement that are not made visible to customers, or to the customer enquiry team whose task is to communicate with customers. By focusing on this artefact in boundary-crossing situations, we identify and elaborate the nature of the techno-mathematical knowledge required for effective communication between different communities in one financial services workplace, and suggest the implications of our findings for workplaces more generally. This paper presents findings from our ongoing research aimed at characterising the use and development of mathematical knowledge at work. We are concerned with how the mathematical aspects of workplace artefacts (particularly computer inputs and outputs, and other documents containing symbolically-expressed information) are understood by individuals and teams, and how these understandings are communicated. Our focus is on data drawn from a range of industrial and commercial workplaces, with a principle concern in this paper on data from a large pensions company. Over the last two decades, the nature of mathematical knowledge required in workplaces has been influenced by two significant changes. The first change has been a dramatic increase in the deployment of information technologies as a pervasive, mediating presence within workplace practices (Felstead, Gallie, & Green, 2002; Kim, 2002 ). An early study of "computerisation" of manufacturing and service industries by Zuboff (1988) describes the dual potential of IT to automate and to informate; that is, on the one hand the potential of technology to replace human work, and on the other hand its potential to inform human work by making information more accessible and usable. In 2 order to be "informated" individuals are increasingly forced to ask questions about the data generated by the computerisation of the work process, for example, "What is happening?" and "What does this mean?" (ibid, p. 196). Answering the type of questions that arise from working in a symbolic medium, Zuboff argues, raises issues of communication and collaboration in the workplace, and accomplishing work comes to depend more upon a capacity for "theoretical" or "system thinking" in which workers are able to identify what an automated IT system is doing and what follows from it, rather than simply upon acting out a process based on know-how derived from experience (cf. Guile, 2006) . The second significant change in workplaces is the shift from focusing largely on production of identical mass-produced outputs to one prioritising response to customer requirements on a more individual basis (Victor & Boynton, 1998) . In the financial services context that we will describe later, this shift is connected to a business perception that competitive advantage comes from offering customers a far greater degree of flexible communication. Taken together, these two changes have impacted on the nature of the mathematical skills required in modern workplaces. For example employees at most levels in any company need to understand some elements of what is behind the interface of the IT system, so they can communicate with others in different parts of the workplace, and with customers who are demanding more information and more transparency. Thus, new work practices increasingly involve quantitative or symbolic data processed by information technology, as part of the interactions between employees, and between employees and customers. We seek to characterise and develop the forms of mathematical thinking that enable these data to be interpreted and their meanings negotiated. Mathematics is widely considered a problematic subject in workplaces and employers have for a long time been reporting "skills deficits". National governments in many countries have put forward waves of policy and curriculum innovations to address the problem in the school and vocational education system as well as in lifelong learning (Coben, 2003; Coben, in press; Fitzsimons, Coben, & O"Donaghue, 2003). The debate has been focused on the notion of "numeracy" (Fitzsimons, 2002 ; for a critique of "numeracy" see Noss, 1998) and, more recently in the UK, on the specification of core functional mathematical skills (Wake, 2005) . In our own research on mathematics in workplaces over more than a decade, we have studied the practices of professional, technical and intermediate grade workers in a wide range of service and manufacturing industries, such as finance, nursing, commercial airlines, civil engineering, pharmaceutical manufacturing, tourism, food processing and packaging (Hoyles, Wolf, Molyneux-Hodgson, & Kent, 2002; Kent & Noss, 2000; Noss & Hoyles, 1996a , 1996b . This work has shown the need to characterise more precisely the nature of mathematics used in the workplace, and leads us to argue that much of the discussion around "skills gaps" and the non-transferability of school mathematics misses the essential characteristics of the knowledge required in technology-mediated work. As workplaces have become more and more organised around IT systems, mathematical processes have tended to become less visible -the mathematics becomes embedded within the IT models. This means that there has been a shift in requirement from fluency in doing explicit pen-and-paper calculations, to fluency in using and interpreting outputs from IT 3 systems and software, alongside some appreciation of the mathematical models deployed within them, in order to informate workplace judgements and decision-making. Thus, rather than traditional notions of numerical skill and competence, we find more relevance in the concept of "mathematical literacy" (see Coben, 2003, p. 15, for a review of the literature on this concept). For example, the OECD"s Programme of International Student Assessment (PISA) defines it as follows: Mathematical literacy is an individual"s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual"s life as a constructive, concerned and reflective citizen. (OECD, 2003, p. 24). However, the developments discussed above indicate that a specific characterisation of mathematical literacy is required that takes account of the character of the workplace in which IT is pervasive. We have therefore adopted the term "techno-mathematical literacies": the prefix, "techno", emphasising the mediation of mathematical knowledge by technology, and the plural form of "literacies" pointing to the breadth of knowledge required in the context of contemporary work. By using the term "literacies" we intend also to stress the importance of engagement that goes beyond symbol manipulation to an appreciation of how the same symbols are constitutive of different meanings across different contexts. In this paper, we present evidence of the techno-mathematical literacies needed in the financial services sector. Our evidence is drawn from a study in a pensions company, but we are confident of its generalisability as we have noted similar needs in other types of financial services companies, such as banks and mortgage companies. To assist in identifying the nature of techno-mathematical literacies, we have employed activity theory as a "theoretical lens" (Russell, 2002) to analyse workplaces as being characterised by their own object of activity (i.e., the motive or purpose of work), mediated by artefacts and located in a context characterised by a specific division of labour, sets of rules of discourse and inter-related workplace communities (e.g., Engeström, 2001; Kaptelinin & Miettinen, 2005; Kuutti, 1996) . From this perspective, it is evident that employees and managers have different engagements with the object of activity, use diverse tools (or the same tools for different purposes) and follow distinct rules, in their attempt to realise that object. Hence any attempt to understand what employees are doing simply in terms of lists of generic, context-independent competencies 1 , fails to take account of tool mediation and how technologies fundamentally alter the activity system of the workplace, and -above all -the knowledge required for the effective use of technology. By focusing on techno-mathematical literacies we intend to address this issue. One of the merits of the literature on cultural-historical activity theory is that it has drawn attention to forms of learning and development that previously have not been well 1 As Rothwell & Lindholm (1999) observe, a typical approach is to define sets of competences and programmes to develop them in generic terms. 4 described, such as horizontal learning (Engeström, 2001) . Nonetheless, Guile and Young (2003, p.79) have argued that "the role of scientific concepts seems to have got lost in recent developments in activity theory with their stress on activities, context and horizontal development". Our research aims to restore some balance with respect to knowledge, while simultaneously taking into account recent insights derived from activity-theoretical approaches. Thus we use the concept of an activity system, not so much to characterise the mediated relationships between the object of activity, tools and communities in areas of work, but rather to help us focus on the role of technomathematical literacies. As we have already suggested, the knowledge underlying the sites of technomathematical activity in an IT-based workplace is under the surface of the computer systems and software. We have found that the use of mathematics most readily becomes visible in activity when the artefacts in use involve the expression of mathematical symbols, and are used to communicate information between different communities. Such artefacts include graphs, tables, charts and diagrams. We are interested in how such artefacts might be employed to allow diverse groups of employees to achieve shared objects of activity. The notion of boundary object (Star & Griesemer, 1989) and its more recent elaboration in the activity theory literature (e.g., Tuomi-Gröhn & Engeström, 2003) proves useful for this purpose. We note that the term "object" here is distinct from the idea of object as motive of activity: "Boundary objects are those objects that both inhabit several communities of practice and satisfy the informational requirements of each of them" (Bowker & Star, 1999, p. 297). Star and Griesemer originally introduced this notion for analysing the heterogeneous nature of scientific practice. They describe how boundary objects in the form of specially-designed data-recording forms for collecting field information on insects helped both amateur naturalists and professional scientists, groups that often existed in tension and limited mutual understanding, to coordinate their perspectives of studying insects in the state of California. The idea of a boundary object as a way to analyse the heterogeneous nature of the knowledge at play in workplaces has been further developed by Wenger (1998) . He used the notion to describe the role of medical claim processing forms as boundary objects, helping to coordinate the different communities of practice involved in medical claims (the client and the different departments within a medical insurance company). He also suggests that not all objects are boundary objects, since not all objects help to coordinate the perspectives of different communities (ibid, p. 107). In information-driven industries such as financial services, an explicit goal for artefact design, as we shall see, is to produce artefacts that can serve as boundary objects. Engeström (1999, 2001) employs a further notion of "boundary crossing" in his intervention methodology, the Change Laboratory (1999) or the Boundary Crossing Laboratory (2001). His aim with these interventions is to contribute to change in activity systems by transforming the object of activity. One example was the reorganisation of work in a city healthcare system, which led to a different patient record form for the handling of patients. In this case, the record form that emerged from the Laboratory, was named by Engeström as an instrument, but served as a boundary object in the sense of Star and Griesemer (1989) . One common link between these various approaches is that boundary objects have an explicit role to facilitate boundary crossing between various communities, communicating across different perspectives and facilitating shared decision-making. In the following detailed workplace example, we will describe our own use of the notions of boundary object and boundary crossing. While this follows from the analysis above, it adds our specific concern, which is to make visible the epistemological role of symbolic boundary objects in situations in which people from different communities use common artefacts with the intention of communication. Specifically, we will ask under what circumstances these artefacts actually become boundary objects, and how they may facilitate effective communication between and within work teams and between work teams and customers. The case study presented in this paper was gathered as part of the "Techno-mathematical Literacies in the Workplace" project 2 . Here we present a very brief overview of our methodology: for details see Hoyles, Bakker, Kent, & Noss (8 January, 2006) . The industry sectors covered in this research are Financial Services, Pharmaceuticals Manufacturing, Packaging and Automotive Manufacturing. In the first phase of the research, we have carried out ethnographic case studies in ten companies, three of which were in financial services, in order to identify the existence of and need for technomathematical literacies. Methods used included workshadowing and conducting interviews around symbolic artefacts. In the second research phase, we have carried out design experiments (cf. Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003) to support employees in developing the techno-mathematical literacies identified in the first phase, and to illuminate further their characteristics. In the two research phases, we adopted three slightly different notions of boundary crossing, while retaining a common essence, namely that successful boundary crossing involves reaching some consensus as to the epistemological nature of the boundary object, which derives from the mathematical symbolism used or the mathematical structures underlying the object (invariably produced or mediated by technology). In the ethnographic phase, the main role of boundary crossing occurred as we learned about the mathematical and contextual reasoning that characterised communication around artefacts in use. The second form of boundary crossing (largely the focus of this paper) occurred as we analysed how the artefacts stood between community boundaries and how different views of the artefact were or were not coordinated. A third form of boundary crossing occurs where we design tools and activities with the purpose of developing employees" techno-mathematical literacies, through reconstructing the mathematical artefacts from workplace practice with the help of computer tools, and opening them up for exploration and discussion. We should stress that in all these forms, boundary crossing takes place in two directions: we learn about the companies" practices by talking about the purposes of the artefacts, while employees begin to adopt our language of techno-mathematical literacies and 2 Website: www.ioe.ac.uk/tlrp/technomaths 6 develop a different awareness of the epistemological underpinning of the artefacts. Similarly, in the design experiments, we do not present ourselves as experts who are going to "train" employees in modelling or mathematical reasoning. Rather we collaborate with managers and workplace trainers to produce "learning opportunities" for employees and in so doing, open windows onto their perceptions of techno-mathematical ideas. This third form of boundary crossing is not the topic of the present paper; for general background see Noss and Hoyles (1996b)  The data that we present in this paper is derived from the following situation. A pensions company annually sends out pension statements to inform its customers about the current and projected values of their funds. However, we learned that the pension statement is not always understood by customers, nor is it always well-understood by customer service employees, who often find it difficult to answer technical queries from customers. In these cases, the statement clearly did not function as a boundary object, and we studied why this was the case, and what might be done about it. We report on the new artefacts created by the company to enrich the communicative potential of the pension statement, and the extent to which this aim is fulfilled. After a general description of the company, we focus our analysis on a characterisation of the techno-mathematical knowledge that needs to be mobilised by the company in order for customer queries about their pension statements to be answered more effectively.
Another way of thinking about the relationship between knowledge maturing and organizational learning is to look at the boundaries between different communities of employees in an organization and the artifacts, e.g., documents, graphs, computer software, that are used to communicate between communities REF .
Characterizing the Use of Mathematical Knowledge in Boundary-Crossing Situations at Work
Mind, Culture, and Activity
Sociology