Conceptualising numerical workplace task performance as a cultural practice
Clive Kanes
Griffith University
Paper presented at Fourth International Conference 'Vocational Education and Training Research', University of Wolverhampton, 16-18 July 2001
This paper focuses on activity surrounding particular tasks in a workplace setting. It is devoted to illustrating how numerical workplace tasks are actually performed. In attempting this, it uses a framework derived from the Vygotskian inspired cultural historical activity theory of Engeström and others. Its main conclusions will be that numerical workplace task performance is very much a local-cultural practice; and that in relation to this, numerical knowledge as an abstracted structure has limited direct significance.
A “trick” question sometimes asked in schools is as follows: 90 students are going on a school excursion in 4 buses, how many will travel on each bus? Students who give the numerically correct answer of 221/2 for each bus usually laugh when the teacher asks how can you fit half a person on one bus and the other half of a person on another? Any volunteers? As the lesson goes, mathematical procedures, however well understood, do not necessarily carry over into sensible recommendations for practice in real life situations. Once we have chosen an effective mathematisation of the problem and are able to implement the mathematical concepts correctly, we still need to ensure we are able to interpret our mathematical results in the light of the context in which the problem arose, before any valid solutions arise. That is, we need to bridge the gap between where we are (or could be) as workers of mathematical ideas and where we need to be as workers managing industry referenced tasks.
This matter, of course, is usually conceptualised by cognitive psychologists as the issue of ‘transfer’; and, over the last generation, a large amount of very fruitful research has been developed around this topic (Gott, 1994; Salomon & Perkins, 1998; Stevenson, 1999). Instead of this approach, however, I want to investigate how the “gap” referred to above is bridged in actual practice. What I aim to show, is that the way numeracy is applied is shaped by the workplace context as well as by the logical apparatus of numeracy itself, and that this fact gives grounds for reconceptualising numeracy as a situated, rather than abstracted, kind of knowledge. The first of these points is important because it shows how difficult it is to plan a curriculum event for the application of numeracy; the second point is important because it suggests that 'numeracy' and 'application of numeracy' need to be considered together in curriculum contexts.
In presenting this material the paper outlines first steps in developing a cultural historical activity theory theorisation of numeracy. This aims to afford an understanding of numerical workplace competency from the perspectives of the multiple mediation of numerical knowledge by situated artefacts, and the reconstitution of numerical knowledge within the trajectory of numerical knowledge use. In working towards these goals, a schematic overview of the activity theory approach is presented in the following section. Then, in the next two sections, analysis draws on data obtained from authentic workplaces settings to explore the way situated artefacts shape the use of numerical concepts and shape the concepts of numeracy. The paper concludes with brief remarks concerning implications of this work.
Cultural historical activity theory
As stated previously, cultural historical activity theory (Leont'ev, 1981; Wertsch, 1981; Engeström, 1987; Cole, Engeström & Vasquez, 1997;Scribner, 1997) is the theoretical paradigm adopted in this study. On the view of this theory, human endeavours are divided among activities (driven by a common motive or object, historically given and relatively long lived), actions (driven by goals purposed to advance the driving motive) and operations (necessary to implement actions). In engaging each of these the subject (the worker, say) makes use of culturally-historically given artefacts, including tools and instruments (both physical and psychological), rules and procedures, management organisation and conventions and customs of the community sharing the common motive. Relations among these are depicted in Figure 1.
Figure 1: Engeström’s model of an activity system
Central to the activity theory approach is its allegiance to the concepts of: historical and cultural development; transformation driven by contradictions or tensions within and among elements of an activity system at any given time; multivalence of domains mediating activity; and the two way action of mediation whereby activity both utilises artefacts and, in turn, is shaped by artefacts. As the object of an activity resolves inherent tensions within the system at one given historical moment, the activity is re-mediated. This means the activity proceeds via the encompassment, reconstitution and generation of old and new artefacts. By this means the activity is said to attain a developmentally more advanced form.
Thus, in the activity theory approach, using numerical knowledge is conceptualised as the re-mediation of numerical knowledge goal. According to this view, workers are seen as being engaged in a cultural-historical activity whose motive or object assumes the form of a trajectory shaped by the playing out of contradictions among its defining motive, the conflicting interests of its stakeholders and component communities, the institutional and other imposed rules and norms, and various technologies of production (both physical and psychological) (Kanes, 1999). It thereby mirrors postmodern concerns constructed around concepts of multivalency and multivocacity (Lyotard, 1984; Kanes, 2000). In Engeström’s (1987) terminology, the object of activity expands as it grapples with the prevailing tensions and contradictions indicative of its historically given moment.
The following sections illustrate these ideas with reference to actual workplace situations involving numerical knowledge.
Shaping the use of numerical concepts
Data analysed takes the form of transcripts of operations observed on the front desk within selected motels within the Brisbane metropolitan area. (Note, these were collected as part of a larger study reported in Stevenson (1996).) In exploring the workplace tasks of this site, transactions among motel staff, customers and researchers were recorded by video camera and transcribed. In this paper I have focussed on operations which have as their common theme financial management – specifically, balancing financial records indicating customer purchases (Episode A) and managing the construction of billing accounts (Episode B).
In Episode A, a motel staff member (RS) is in discussion with a member of the research team (RA).
Episode A
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13 / RA: So what are you doing just now?
RS: Just totaling up everything I've got in here to see how it goes against my balance. Balance is in Menu 4. No. 5 `Cashier Shift Balance'. It's now totaling everything I've done under my code. I've written down everything I think I’ve done and this'll now tell me if I'm right or wrong.
RA: So do you do that a few times through the day or?
RS: No. Once you've done this and you do it correctly then that's your balance and that like closes off that section and then you start afresh. You can do ten balances - its stupid to do that - I like to do one as soon as check-outs have all gone, and they're pretty much all gone now, and then the rest of the shift ... because you won’t post as much in the rest of the shift as we did this morning.
So see, that's wrong. I don't know why, but it'll print out and tell me why that's wrong.
RS re-adds totals while the error report is printing.
Using Engeström's model of an activity system as depicted in Figure 1, RS, the Subject, is engaged in the action of balancing a set of financial records - this is the Object. The goal of this action is to generate a set of accurately reconciled records. The Outcome is the finalised set of records. Mediating RS’s actions are instruments such as a handheld calculator, key board controls and the software package. In addition, specific rules for proceeding with and organising work are applied. For example, in line 3 we see procedural rules for operating the software tool “Balance is in Menu 4 No 5 ‘Cashier shift Balance’”. These relations are set out in Figure 2.
Figure 2: Model of the action of ‘balancing’ financial records (remodelling Kanes (1999))
At first sight, this episode appears as a straightforward account of numerical knowledge transferred to the workplace. Concepts of numeration ("just totalling up", line 2), data management, tabulation and balancing (seen as mathematical relation between two independently derived quantities), and so on, are illustrated. Looked at more closely, however, it offers insights into the way the use of numerical concepts have been shaped. In order to illustrate this, I offer two examples which will analyse more closely the rules governing the balancing actions taken.
Example 1: In mathematical terms, the concept of ‘balance’ is a relation between two arithmetical expressions. However, in stating “I’ve written down everything I think I’ve done and this’ll now tell me if I’m right or wrong” (line 4), RS makes it clear that for her balancing is to be understood as a comparison between actual and supposed procedures whereby “what I think I have done” is considered against “what I have actually done”. Moreover, this procedural view of balancing contrasts with a relational concept of balancing, as its focus is not the comparison of arithmetic values but a comparison based on the implementation of procedures. Moreover, the nature of balancing as a procedure and the character of the procedural actions themselves are determined within the specific workplace culture, rather than as transferred knowledge. This example therefore shows how the use of numerical concepts are shaped according to the particular specifications of the context in which work takes place.
Example 2: In a further instance, in lines 7-10, RS indicates that within this activity system actions which are performed too early are deemed "stupid" and wasteful of time and effort. It can therefore be concluded that not only technically accurate actions, but timely actions are the required actions of this workplace. In order to achieve timeliness of action, RS indicates that at the appropriate moment, a judgement needs to be made that guests are "pretty much all gone", and only once this is decided is the balancing procedure ('rules') followed. Further, line 9 implies, knowing "how to balance" depends only in part on knowledge of the procedures of balancing themselves. What else is required for this knowledge relates to the custom and usual practice of the workplace site - knowledge of when and precisely when necessary actions are required. This knowledge cannot be transferred to this site, as it necessarily belongs to it; but, because she concludes that in her judgement it would be "stupid to ignore it", RS deems this knowledge crucial to the correct implementation of the account balancing task. This example therefore also shows how the use of numerical concepts are shaped according to the particular specifications of the context in which work takes place.
In both the examples above we see hinted that the achievement of the designated action involves the resolution of contradictory tensions. In Example 1, these were a conflict between the relational and procedural concepts of ‘balancing’; in Example 2, these were the competing points of focus afforded by demands for action at a specific time on one hand, versus the nature of an appropriate ‘balancing’ action on the other hand. These examples have shown how the activity system outlined has been engaged in shaping the use of numerical concepts.
In the next section the focus is on shaping the concepts of numeracy.
Shaping the concepts of numeracy
In the following episode we glimpse RS actions aimed at managing and constructing customer billing accounts.
Episode B
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1 / RA: Do you do much in your head or you use that a lot?
RS: Oh, well to tell you the truth I’ve got a lot better. Because on check-out when people are telling you, when I say “what did you have for minibar?” “Oh I had a packet of chips, two cans of coke and a beer” - see you haven’t got time to get the calculator out you’ve got to go, $3.00 + $2.80 + $1.40 so you can do it in your head.
RA: So you don’t enter each of those items into
RS: Oh no - you just enter minibar total amount - you’ve got to do it that way - it would take too long if you entered - I mean some of them drink like fishes so you could end up with 15 or 20 entries for the mornings minibar - it’s not worth it. So you do get better - you don’t even mean to - it just happens that way. And I find actually, if its quiet like this I work best under pressure - I mean I work fine now, but when things are all happening I find that you don’t have time to think, your brain just does it - like when they say that you just know
FB: But you are thinking because you’ve still got to prioritise that task
RS: Oh yes - but I mean - like with maths, if I started adding up those numbers I’d be sitting here thinking, thinking, thinking. Whereas, if he said to me “I just had two beers a drambuie and a packet of chips - you just kinda know what it is”...
OK and now we’ll try the balance again.
This episode illustrates how numerical concepts are reconfigured in situ. Two kinds of numerical knowledge are illustrated. The first kind is demonstrated in lines 3-5 where we see RS canvassing the application of the numerical addition of the prices of minibar items such as chips, cans of coke and beer. RS explicitly states that constructing a customer account in such a case involves the addition of prices using a calculator (eg “$3.00 + $2.80 + $1.40”). Because this kind of numerical knowledge is associated with the use of a numerical calculator, I call this ‘tool-referenced’ knowledge (see Figure 3). The second kind of numerical procedure is depicted in lines 15-16 in which operations appear to be performed directly on items of merchandise, as in “if he said to me ‘I just had two beers a drambuie and a packet of chips’ - you just kinda know what it is”. Because this kind of knowledge is associated with the implementation of an addition rule related to purchased items, I call it ‘rule-referenced’ knowledge. Whereas tool-referenced numerical knowledge makes use of the calculator as a tool and operates on numerical values being the item price of merchandise; rule-referenced numerical knowledge makes use of a protocol for calculation which operates on the names given to merchandised items.