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International Seminar on Learning and Technology at Work, Institute of Education,
London, March 2004 www.lonklab.ac.uk/kscope/ltw/seminar.htm
Techno-mathematical Literacies in Workplace
Activity
Phillip Kent, Celia Hoyles, Richard Noss and David Guile
Institute of Education, University of London
[email protected]
www.ioe.ac.uk/tlrp/technomaths
ABSTRACT. The changing nature of workplaces and the ubiquity of computer-based
systems for the automation and control of processes and the management of information,
has brought about the need for employees at all levels to engage with these systems, to
interpret their outputs and to make sense of the abstract models on which they are based.
This means developing competence in Techno-mathematical Literacies (TmL):
technically-oriented functional mathematical knowledge, grounded in the context of
specific work situations. We will draw on observations and interviews in manufacturing
workplaces to present a characterisation of TmL in terms of activity systems, and
boundary objects which enable communication between different activity systems where a
shared purpose is negotiated. We wish to develop an explicit cognitive dimension in our
analysis, in which boundary objects serve as artefacts which mediate mathematical
understandings for the individual and his/her community within the activity setting, and
which enables these meanings to be generalised beyond it – a key characteristic of TmL.
Our longer-term objective is to develop principles for designing interventions to equip
experienced employees who have a limited mathematical background with the TmL
appropriate to their workplace, using boundary objects in the training process which
enable employees to acquire TmL in ways which are consistent with their prior
experience while stretching beyond it to a greater generality.
Draft
Introduction
The changing nature of workplaces, such as the transition in the manufacturing and
service industries from modes of mass production to modes of “mass customisation”
(Victor & Boynton, 1998), and the ubiquity of IT-based systems for the control of
processes and the management of information within those different models of
production, has brought about the perceived need for significant groups of employees at
all levels to engage with these systems, to interpret their outputs and to make some sense
of the abstract models on which they are based. We do not claim here that ubiquitous IT
is an entirely new source of change in workplace practices — IT-based systems have
been common in workplaces since the 1970s, and methodologies of process improvement
originate even in the 1930s. Rather, once it has been widely introduced, IT can be
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International Seminar on Learning and Technology at Work, Institute of Education,
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modified constantly to support changes in strategies and practices — hence the wellrehearsed argument throughout the social sciences that IT intensifies the pace and degree
of change in workplaces. One consequence of this potential for IT to be constantly
changed according to production goals is that workers throughout an organisation, not
just the minority of trained engineers and designers who are directly involved with IT
development, need to develop some appreciation of the IT-based models on which work
processes are based. This is a competence which we have termed Techno-mathematical
Literacies (TmL) — technically-oriented functional mathematical knowledge, grounded
in the context of specific work situations. For example, in a manufacturing context there
are often IT systems for process monitoring and process improvement — the latter
underpinned by statistically-based process control techniques. The way that some
companies express the need for new skills to support improvement in their production
processes takes the form: “we can only improve our process so far with a workforce that
does not understand the workings of process improvement”. The research literature on
workplaces has also in recent years increasingly recognised that in order for workers to
deal with the changing nature of production systems, they need to be involved and
informed about processes; one version of this argument is the idea of “work process
knowledge” (Boreham et al, 2002). Our research1 is concerned with the particular form of
work process knowledge that is at least partly informed by “techno-mathematics” and
thus we are building a more specialist interest on the general insights provided by the
literature.
Draft
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. Rather than striving towards
consistency and generality — the hallmarks of “mathematical thinking” as conventionally
conceived — what emerges from studies in workplaces is that people develop
mathematical techniques to carry out their work which are generally strongly “situated”
in their knowledge and experience and which exploit features of the context and its local
regularities. These techniques are preferred because they are often quicker and more
efficient than general mathematical techniques. Yet it is evident from looking at workexperienced employees that a “generalised” mathematical ability which operates across
contexts can emerge through experience in particular contexts. For example, in a study of
nurses that we carried out (Hoyles et al, 2001; Noss et al, 2002), the nurses exhibited an
understanding of the concept of (drug) concentration in which the mathematical and nonmathematical elements of workplace calculations were organised by the artefacts and
discourse of drug dosages, and in this form were usable by them to think about drug
concentrations more generally. A striking further observation was the fragility of the
nurses’ knowledge: when the “anchors” of the workplace context were removed from our
discussions with them, we suddenly saw fragmented strategies (often vaguelyThis paper reports on work-in-progress from a current research project, “Techno-Mathematical Literacies
in the Workplace” (2003–2007).
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International Seminar on Learning and Technology at Work, Institute of Education,
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remembered legacies of school mathematics) replacing the confident use of workplace
techniques.
It is worth elaborating two distinguishable elements of TmL. We have adopted the term
“techno-mathematics” to emphasise that the visible mathematics of the workplace, the
mathematics recognised in textbooks or formal training procedures, is only part of a more
broadly-defined and technologically-shaped mathematics, which remains largely invisible
and embedded within the routines of working practice. A crucial characteristic of technomathematics, therefore, is that it can bring new “analytic power” to workplaces (at all
levels) by making mathematical knowledge and techniques more usable by more people
than before the existence of ubiquitous IT (for example, consider the sophisticated
statistical techniques nowadays pre-loaded in everyday spreadsheet programs) – provided
that users are equipped with the understanding necessary to take control of that power
and use it responsibly. TmL consist of the tools and techniques that underpin such
understanding.
A second element of TmL is that it takes the form of “literacies”, in the same sense that
conventional literacy is understood as something possessed by a literate person – one
who is not only competent in the technology of reading and writing but also has a broad
appreciation for cultural forms (literature), such as novels, poetry or drama, which are
expressed through that technology. Thus, we want to emphasise TmL as an element of
the cultural forms of a workplace, and TmL, like literacy, should be regarded as being
both individually powerful and a source for social transformation. (For extended
discussion of mathematical literacies and their inter-relation with technology, mainly in
the context of school-level education, see Noss (1998) and diSessa (2000)).
Draft
Workplaces as activity systems
In order to find out about the mathematical practices of different workplaces, our research
method is to carry out ethnographies of workplaces, visiting sites to observe work
happening and to interview operators, shopfloor supervisory managers and more senior
managers. We have sought to understand how different companies deploy IT-based
systems, the forms of knowledge required by employees to operate effectively and the
managerial and human resource strategies adopted by the company. The basic premise of
activity theory — that in 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 — is helpful in understanding the role of TmL in workplaces. The analysis of
organisations and learning is of course a well-established field of activity theory research
(see, e.g., Engeström, 2004). Consequently, we begin by explaining our particular
interpretation of activity theory in this context.
The concept of an activity system is best thought of as a “theoretical lens” that represents
the smallest and most simple unit that preserves the essential unity and integrated quality
behind any human activity (Russell, 2002). 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” (see, eg, Kuutti, 1996; Engeström, 2001).
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A useful form of description for the complexity of goal-orientated and artefact-mediated
activity in workplaces is Leontiev’s three-level scheme (cf. Kuutti, 1996):
Activity
Objective


Action (chain of actions)
Goal


Operation (chain of operations)
Conditions
In this scheme, the activity – which in our research might be the production of different
types of packaging in a factory (cf. TmL examples below) – consists of actions or chains
of actions, which in turn consist of operations. Actions are conscious tasks to satisfy an
immediate goal, which taken together generate the overall activity which must satisfy an
overall objective: for example a step in the production of a plastic bag is the printing of a
company name or logo onto a roll of plastic film that will become several thousand bags,
followed by a separate action of splitting the film into bags and sealing the individual
bags. Operations are habituated routines which together support the performance of an
action, for example, the “routine” steps a print machine operator must take to check on
the accuracy of the printing process, or the steps taken by a bag machine operator as each
bag is sealed (standard checks in this case are length, width and strength of the bag
against bursting).
Draft
The critical insight that activity theory offers, which is missing from many other
frameworks used to analyse workplaces (see, for example, Boreham et al, 2002; Luff et
al, 2000) is the reciprocal links between activity, actions and operations. In the case of
collective activity in a factory, the activities of the teams of workers are broken down
through the division of labour into sub-activities with the result that for each participant
there is a combination of actions and operations which underpins their personal activity.
In paying attention to learning in the workplace, there is a crucial relationship between
action and operation in that operations must be learnt – they begin as conscious actions
and through practice become fluent and routine2. Also, the operation may (in Leontiev’s
terminology) “unfold” back into a state of conscious action, where the conditions for the
operation are changed, and thus there is a need for re-learning. Where the operation
involves underlying mathematical concepts, then the re-learning will entail some
development of TmL, as the discussion of contradictions and breakdowns below will
elaborate.
Activity, production and technology
2
A similar idea which is gaining currency in mathematics education research is the notion of
“instrumentation”, which describes the transformation of tools into “instruments”, as the user of the tool
develops mastery in fluent use of the tool. (see Rabardel, 2002; Guin et al, in press)
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One major issue for organisations is to decide how to use IT-based systems to enhance
the work process. Computers are, of course, “number crunchers” par excellence, and this
has led to the development in industry and commerce of enormously complex software
systems for information management and process control, a trend which first began
mainly in companies whose business is abstract “information” (such as financial services)
and which has been spreading gradually into physically-based manufacturing industry.
Wherever the introduction of information systems takes place, decisions need to be made
about different users’ relationships with the information system: to what degree is the
user required to possess a model of the internal workings of the system in order to use it?
How is the “interface” designed that mediates between the computer’s model of the
workplace and the actual physical operation of the workplace?
Although activity theory is sensitive to the ways that the different modes of deployment
of computers will affect the division of labour, rules and communities that characterise a
specific activity system, it does not provide a conceptual language to distinguish between
different modes of deployment of computer technology. Zuboff (1988) has usefully
depicted this issue in terms of the dual potential of information technology to automate
and to informate, that is, on the one hand the potential of technology to be deployed to
replace human work, and on the other hand its potential to inform human work by
making information more accessible and usable:
Draft
computer-based, numerically controlling machine tools or microprocessor-based sensing
devices not only apply programmed instructions to equipment but also convert the current
state of equipment, product, or process into data. … The same systems that make it
possible to automate office transactions also create a vast overview of an organization's
operations, with many levels of data coordinated and accessible for a variety of analytical
efforts. … Information technology … introduces an additional dimension of reflexivity: it
makes its contribution to the product, but it also reflects back on its activities and on the
system of activities to which it is related. Information technology not only produces
action but also produces a voice that symbolically renders events, objects, and processes
so that they become visible, knowable, and shareable in a new way. (Zuboff, 1988, p. 9)
Zuboff’s claim that IT in workplaces renders processes more visible needs, we think,
some refinement. Whilst some objects and processes do indeed become more visible, it is
evident that other processes, and especially mathematical processes, become less visible
or even invisible when the mathematics becomes performed by IT. In such cases, the
nature of the mathematical skills required becomes changed — indeed, this is the heart of
our claim for the importance of TmL: the shift in requirement from fluency in doing
explicit “pen and paper” mathematical procedures to a fluency with using and
interpreting output from IT systems and software, and the mathematical models deployed
within them, to carry out mathematical procedures in order to informate workplace
judgements and decision-making.
Any “computerisation” of a workplace requires choices to be made about which
processes to automate, and to what degree, and which processes will benefit more (in
terms of efficiency or productivity) by informating the employees involved. This is not an
either-or choice: it is a matter of striking a balance for any particular process. Zuboff
provides detailed case studies of IT implementations during the 1970s-80s, and notes how
the importance of informating was often missed, leading to alienation of employees and
flawed implementations. In our own observations of workplaces, it seems evident that
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International Seminar on Learning and Technology at Work, Institute of Education,
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companies today are much more careful in the design and scoping of IT systems, and
marrying IT development with employee development; none of the companies with
which we are involved is undertaking developments of the pace and scale which, for
example, Zuboff describes in her case studies. For example, several companies that are
introducing integrated information systems (eg. SAP software) have the new system
running alongside established paper-based systems and this will continue for several
years. However, where change is more gradual, this can lead – as we shall see later – to
hidden or neglected effects with regard to skills.
Another way of looking at the implementation of IT systems, and one which brings us
closer to our concern with techno-mathematics, is in terms of models. How do workers
build on workplace experience, mediated through IT systems, to develop cognitive
techno-mathematical models of workplace processes? To automate/informate a process
requires different models of that process to be constructed by different actors: the
designers of the IT system must create a “computer model” of the process which can be
implemented in the hardware and software. At the same time, the users of the system
must develop “mental models” of the system in order to engage with it, mediated by the
artefacts of the IT system and the explicit operating procedures of the workplace, and
working in tandem with the “tacit” knowledge of workplace practices that individuals and
teams possess.
Draft
It is useful to adopt a proposal by Wartofsky that models are not just “entities” (that is, a
static notion – a representation of a system), but should be regarded in general as modes
of action, in the sense that the models are embodiments of purpose and instruments for
carrying out such purposes (Wartofsky, 1979, p. 142). In our terms, then, a “technomathematical literacy” is, in part, the mathematical element of a mode of action — but it
is also, as the activity theoretic viewpoint underlines, determined by the “cultural forms”
of the workplace.
Impetus for changes in production: Breakdowns and contradictions
We analyse the impetus for change in terms of two inter-related concepts, the breakdown
and the contradiction. One of the advantages of using the concept of an activity system as
a unit of analysis to analyse changes in workplaces is the firm emphasis placed in activity
theory on the central role of contradictions as sources of change and development.
According to Engeström (2004), new qualitative stages and forms of activity emerge as
solutions to the contradictions of the preceding stage. There is an implication in this
definition of contradiction (with its roots in Soviet psychology, stemming from Marxist
thought) that there is an inescapable need for companies to address the contradictions
they are experiencing. In practice, however, companies tend to live with the long-term
effects of contradictions for some considerable time, because, for example, there are not
the resources available to resolve the contradiction, and it may not be possible for
departmental managers to quantify the problem sufficiently (for example by a cost benefit
analysis) to demonstrate a quantifiable payback to senior management. In such a
situation, there may be a process of gradual “technologising” of the workplace activity in
an attempt to improve competitiveness without considering the extent to which the
process changes made are introducing a hidden, or sometimes intentionally ignored,
contradiction of a “knowledge gap” in the workforce, which may cause a critical
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contradiction in production months or years later. Where a gap is recognised, it may be
that a skills problem is shelved – the company recognises a training need to informate the
workforce, but decides that it does not have the resources to deal with it. We have noted
several examples of this in the companies that we have visited, and in a later phase of our
research we will be concerned with devising effective forms of training to enable
companies to address knowledge gaps related to TmL that they are experiencing. As we
noted above, we believe that as companies increasingly seek to balance the
automation/information of their production, mathematics is becoming a particularly
significant area of concern, not least because mathematical processes may be “invisible”
within the IT system.
In contrast to the contradictions that companies must deal with, the idea of breakdown is
an attempt to explain the type of challenges confronted by individuals within workplaces.
This concept originally emerged from the work of Heidegger and in the context of
organisations it has been described as “the interrupted moment[s] of our habitual,
standard, comfortable ‘being-in-the-world’ … breakdowns serve an extremely important
cognitive function, revealing to us the nature of our practices and equipment, making
them ‘present-at-hand’ to us, perhaps for the first time” (Winograd & Flores, 1986, pp.
77-78). For us, breakdowns for individuals are potential causes of, and consequences of,
contradictions at other levels in an activity system: a breakdown at the level of
action/operation may be the result of, and can be the cause of, a contradiction at higher
levels of the activity:
Draft
CONTRADICTION AT ACTIVITY LEVEL


BREAKDOWN AT INDIVIDUAL/ACTION LEVEL
Thus, a breakdown is primarily an issue at the level of the individual worker and his/her
actions, that generates a reappraisal of those actions, whereas a contradiction implies a
transformation of the whole activity system (cf. Koschmann, Kuutti & Hickman, 1998).
Breakdowns are important moments where operations and actions may unfold, potentially
bringing to explicit attention the results of previously hidden contradictions.
Boundary objects, models and activity
Our current thinking about how to conceptualise the relation between the purpose of
activity and the actions and operations undertaken to realise that purpose, is influenced by
the debate in activity theory about “boundary-crossing” and “boundary objects” (TuomiGröhn and Engeström, 2003). The notion of boundary objects that we have adopted —
objects which are shared between different activity systems, and used to communicate
information between them for shared purposes — is informed by the work of Star (1989)
and Star & Griesemer (1989). It is worth remarking that our view of boundary objects
appears to be more broad than that taken in much of the activity theory literature.
Engeström (2001), for example, describes how two or more activity systems interact
through boundary objects. For us, boundaries are also present within the same activity
system, in which a boundary object is an “open” object for sharing. Also, for Engeström,
a boundary object usually has the purpose of changing the system(s) where it is involved,
whereas our purpose with boundary objects is to understand at a finer level of detail the
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role of boundary object in how a team operates in routine activity, and small-scale
change, as well as major change (transformations) in the activity system. This is similar
to the difference in scale between breakdown and contradiction, as described above.
An example of our understanding of the role of boundary objects is in the communication
between different areas of a factory, or between the “shopfloor” (where the
manufacturing is physically performed) and the “management structure”. We put these
terms in quotes, because although they represent the traditional dominant division of
manufacturing workplaces, the transition to new modes of manufacturing means that
management functions operate to an increasing extent on the shopfloor (see TmL
Example 2, below). Along with new kinds of work organisation, we should in general
expect to see new kinds of boundary objects. In this case, the boundary objects would be
various kinds of production information: specifications (norms) and targets which pass
from the management to the shopfloor, and actual production information which is input
from the shopfloor to the management structure, and is increasingly dealt with directly by
shopfloor managers. The shared purpose here will typically be not only the matter of
producing products, but also a matter of process improvement (the goal of producing
“more for less”). Then, a boundary object such as a process chart may mediate the
communication between, say, the “operator’s model” and the “manager’s model” of
production. Where a process is not changing, there may well be little motivation for the
process to be explicitly communicated between different employees; where a process is
changing, in terms of needing to identify and solve problems and inefficiencies in the
process, then there is a strong requirement for communication. The manager’s model
(assuming he/she has a technical/engineering background) will tend to be based on
formal mathematical models; the operator’s model is far more based on the physical
experience of production, and it is in this kind of situation that we see the need emerging
of a TmL-based understanding, grounded in the process, which allows the operator to
interact with the boundary object, which mediates communications with other people.
Draft
Another example of boundary object figures in the relationship between the activity
system of the employee in the workplace, and the same employee in the activity system
of a training course, where there arises a need for boundary objects which “carry”
meanings from working practice into the training context, and back again. For example, a
boundary object might be a set of numerical tables and charts which describe production
data, representing both routine and breakdown situations. Our hypothesis is that
boundary-crossing activity is central for employees to develop TmL – that is, to work
with the boundary object in different activity systems (the workplace as viewed by
different employees, and from the viewpoint of the training course), and to examine
routine and breakdown situations, in order to develop an appreciation of “abstract”
explanations for, for example, the sources of inefficiency when a product is
manufactured.
Of course, different employees will need to develop these capacities to different degrees
– we are particularly interested in the needs of those who are promoted from shopfloor
operations to first-level management (see TmL example 2 below). Given the typical
educational backgrounds of these workers (often, in term of formal qualifications, only
basic school-leaving level) they can be expected to find the abstract techno-mathematical
demands of working with IT-based models particularly challenging.
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The TmL of complex modelling
The current focus of our research is on manufacturing industry – in the sectors of
packaging (i.e. the manufacture and deployment of boxes, bags, cartons, cans, etc.) and
pharmaceuticals manufacture. A form of workplace activity that we have encountered
almost everywhere, initially identified in previous research (Hoyles et al, 2002) and
which is indicative of TmL being involved, is what we call complex modelling, in which
employees are required to manipulate qualitative and quantitative data to diagnose
problems, search for solutions and carry out process improvement. Complex modelling
requires some understanding of the sophisticated concepts of variable and functions,
however not in an abstract (mathematical) sense but situated in the workplace context,
and supported by intuitions for the meaning of these concepts. In the following we
present two brief examples of complex modelling, drawn from our observations in
different companies. One notable thing about these examples is the different degrees of
articulation of the models involved, and the consequences of this for the development of
TmL – in the first case, the models are personal and largely unarticulated, and in the
second case, the models are shared and highly articulated.
Draft
Example 1: The Works Manager
In one packaging factory, which prints cardboard cartons in very high volumes on a
contract basis for clients such as supermarkets, we interviewed a Works Manager whose
job is to oversee several of the areas of production, reporting to the general manager of
the whole factory. The Works Manager’s responsibilities are: to monitor performance of
production against targets, to look for process improvements, to communicate production
information “upwards and downwards”, and to communicate “outwards” with clients
(negotiate and cost contracts).
We took a particular interest in the kind of thinking that underpins the costing of
contracts. Effective costing relies on understanding the variables of raw materials (costs,
availability) and the capabilities of the printing machines (e.g. some risk assessment of
having to deal with complicated art work, which may lead to a high rejection rate), as
well as knowing what competitors may be working on, and the prices they are currently
quoting. Evidently this is a highly complex set of variables, and obviously accurate
calculation is very important when there is a narrow divide between quoting too high and
losing the contract to a competitor and quoting too low which would lead to an
unprofitable contract; much relies on being able to manipulate numbers, within models,
in the negotiation process.
As one might expect, it proved difficult to get a good handle on how the manager that we
interviewed did think about this task. Indeed, there is a general difficulty for
understanding workplace expertise: employees have difficulty to verbalise the procedures
of “doing the job”. But also, from a mathematical point of view, there are differences of
interpretation about what is mathematical: mathematics which is used tends to be
appropriated and categorised within other knowledge domains – often it is the maths
which is not used that is categorised as “maths”.
An important way of addressing the hidden-ness of mathematical practices is to examine
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cases where there is a problem in performance, that is, situations in which there are
breakdowns and contradictions. In this example, the general manager of the factory
described a former Works Manager who could not “concretise” data or “abstract”
information from data:
We had somebody who had been in the section a long, long time. He could not manage
the six machines, the complexity of it… He found it very difficult to be able to juggle the
dynamics of what was happening …. He could do the mechanics of it because he knew
how to do that... but he was not able to interpret it, to transform it into a trend or a
problem solving analysis. He wasn’t able to really use the information in a well
constructed argument. He could not present an argument which was fact-based, by using
the numbers and the information that we do collect. …not really understanding what that
data means or how it impacts on the business.
This example illustrates the interaction of breakdown and contradiction introduced above:
the breakdown of individual performance leads to a contradiction for the company, in the
form of a problem of skills development and the emergence of “skills gaps” as IT is
introduced. As the complexity of the Works Manager role increases, so does the
complexity of how to develop that role within the company.
Draft
Example 2: “Data, data, data”
Our problem-solving is all based on data, data, data, no-one can walk into my office and
tell me ‘there’s a problem’, they’ve got to say ‘my OEE has gone from 73% to 71%’, then
we can talk about the problem (Production manager, Packaging manufacture)
In another packaging factory that we have visited, there is a huge effort on process
control and process improvement. A derived measurement called the OEE (Overall
Equipment Effectiveness) is used as a critical tool. This is a generic measure, pioneered
by Japanese industry in the 1950s, that can be applied to any manufacturing process: it is
simply the product of three numbers: Availability, Performance and Quality. Availability
is the percentage of time that a machine is “up” and running, relative to the total available
up-time; this might be 20 hours out of 20 hours expected, which is 100%. Performance is
measured in terms of the rate at which the machine is expected to produce, say a machine
could produce ideally 100 items per minute, that would be a Performance of 100%, but
the target may be only 60%. Quality says, of the items made, what fraction were of
merchantable quality; typically 95% might be expected. The OEE is then the product of
those 3 numbers [e.g. 1.0 x 0.6 x 0.95 = 0.57 = 57%], with 85% being typical of a “world
class” business.
OEE is used as a tool for process monitoring and improvement at different levels of the
factory – the machine, the line, the unit, the plant.
We’re all obsessed with OEE. Here is the plan of what we’re going to do this year, going
through month by month, so in this particular area we started the year at 71% OEE and
we plan to end the year at 80.9%. There is a huge focus on understanding why in any area
the OEE is what it is now, and then taking actions to lift it.
(Production manager)
Furthermore, OEE information is cascaded down to all levels of the company:
If you go into the manufacturing areas you will see lots of graphs telling people ‘on this
shift you were at 75% OEE’. The levels of understanding of that are varied, some people
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will struggle with percentages and multiplying them together, but we try to visualise as
much as possible, nice bright-coloured charts. So, ‘don’t worry about the numbers, just
see if it’s going down or going up’.
Notice how, compared with Example 1, this situation was much easier for the interviewee
to verbalise, and for us as outside observers to gain an understanding of it. We would
argue that this is to a large degree because of the role of the OEE measure (and the
boundary objects which incorporate it) as an abstraction of the manufacturing process,
which allows for the taking away of detail in order to focus on the essential
characteristics of production as a process (Key Performance Indicators are another
version of this kind of measure.)
The factory has a medium to long-term programme of “upskilling” in mathematics:
The requirement for mathematics is getting more rigorous. I would not employ anyone
today [on the shopfloor] without the ability to do basic calculations, whereas I would have
done 10 years ago. We have a numeracy test as a minimum filter, but I expect within the
next few years we’ll need a more demanding test, because the current one gives us people
who won’t be able to fulfil our future job requirements.
Draft
The mathematical skills required shift to a greater level of complexity for the pivotal role
of first-level manager, called team leader in this company, who is a kind of intermediary
at the boundary between the “management” and the “shopfloor” (simplistically speaking,
as if management exists in an abstract world of numbers, and workers in the physical
world). Typical complex modelling tasks for the team leader are: satisfying OEE targets
set by more senior managers – making numbers come out in reality; using many
representations of data, and communicating data for different purposes. A much greater
degree of responsibility is nowadays attached to this role compared with the past.
Team leaders have to come and present to me a lot of analytical data about what happened
in their shift. 5 years ago it didn’t happen. Now, they’ve got to understand it to make
things happen. I have a programme every few months of spending half an hour with every
team leader, and at that meeting they have to give me loads of information. Some team
leaders are graduates, most are not, some college qualifications, some only O levels, but
they have lots of experience. Increasingly, we’re making the selection process for team
leaders very rigorous, lots of tests, a 2-day residential assessment course, looking at
leadership, communication, analytical problem solving, technical skills. Year on year, it’s
becoming more technically-oriented.
Team leaders have certain OEE targets to satisfy, and are challenged to make this bunch
of numbers come out in reality. They need a lot of skills, and many of these we would
associate with the TmL of complex modelling. It seems to be a very demanding role,
especially in a company which is pursuing continuous improvement. There does seem to
be a process of natural selection, in that prospective team leaders appear in the pool of
operators and are spotted and taken upwards. But we think there is a case for asking what
is it that these people have which the others don’t? Are we right in suggesting that there is
some kind of mathematical understanding, that is various kinds of TmL, alongside the
people management and other competences which make up the overall competence of the
team leader? It seems like companies should have a pragmatic interest in this as well, as a
way towards developing more effective routes for the development of team leaders.
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International Seminar on Learning and Technology at Work, Institute of Education,
London, March 2004 www.lonklab.ac.uk/kscope/ltw/seminar.htm
Conclusions
In this paper, we have made a case, to be substantiated by further research, for a
changing, and generally increasing, role of mathematics in workplaces, with the
emergence of a need for model-based understanding at levels of organisations where it
has not been expected previously — especially for first-level managers based on the
shopfloor. Moreover, the “techno-mathematical” models involved are likely to be
different than models as conventionally-understood: not mediated by formal
mathematical symbol systems and artefacts, but mediated by “situated” technomathematical artefacts. This throws up considerable implications for skills development
in individuals, and what forms of training can be appropriate for this kind of situation.
We are at an early stage in our research to characterise the nature of TmL in detail, but
the research done so far suggests a basic distinction that can be made about the place of
the “techno” in TmL, in that technology is not necessarily a mediating artefact. It seems
that TmL may be placed in two broad categories:

for thinking about the technology, but not mediated by it — the individual
recognises what the technology does, but does not use it to perform procedures

thinking through the technology (using technology “to think with”) – eg. the
Works Manager in Example 1 who uses spreadsheets to do “spreadsheet algebra”,
and the use of OEE data in Example 2 (especially at higher levels of management)
Draft
The emergence of a TmL as think about or think through depends on division of labour.
Traditionally, there is an assumption that shopfloor employees are not sufficiently
knowledgeable with models and modelling to think through – hence the imposition of
procedural rules imposed for them to engage with the “black box” of analytical
procedures. How does the ubiquitous presence of IT modify this relationship? In one
packaging factory that we have visited there is a controller on the shopfloor (a timeserved employee, and a non-graduate) who monitors 5 simultaneous computer screens of
data (where numbers on the screen are simultaneously sensors of current values and
controllers to change those values). We know that designers of the system and
presumably process managers have sophisticated, generally mathematical models of the
process (very likely expressed in algebraic and other symbolic terms) – the issue is to
what extent the work-experienced controller thinks through the technology on the basis of
personal techno-mathematical models which are mediated by the technology and the
concrete experience of the work.
We will be able to report more substantially on these ideas as our current research project
progresses, particularly as we begin to test the use of prototype training materials in
workplaces.
Acknowledgements
The research project “Techno-mathematical Literacies in the Workplace” is funded by the
UK Economic and Social Research Council as part of the Teaching and Learning
Research Programme [www.tlrp.org], Award Number L139-25-0119.
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International Seminar on Learning and Technology at Work, Institute of Education,
London, March 2004 www.lonklab.ac.uk/kscope/ltw/seminar.htm
This paper was originally prepared for the International Seminar on Learning and
Technology at Work at the Institute of Education, London, March 2004 [see
www.lonklab.ac.uk/kscope/ltw], and we are grateful to the participants of the seminar for
their criticisms of the paper.
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