Transcript

Linking academic knowledge and professional experiencein using statistics: a design experiment for businessschool students

Corinne Hahn

# Springer Science+Business Media B.V. 2011

Abstract The aim of the empirical study presented in this paper is to explore how studentslink academic knowledge with workplace experience. I carried out a research study with agroup of 36 business school students entering a 3-year masters level apprenticeshipprogramme. In an introductory statistics course, I designed and implemented a four-steplearning activity, based on an Exploratory Data Analysis approach and inspired by anauthentic workplace situation. I report the findings of qualitative research based on therecorded discussions between students and the reports they wrote at each step in theexperience. I found that three different forms of rationality—technical, pragmatic andscientific—led them to shape the problem differently. I observed that they hardly usedstatistical tools because pragmatic rationality which is linked to their experience assalespersons prevails, although access to a managerial approach suggests the use of morestatistical knowledge.

Keywords Statistics . Apprenticeship . Management . Decision making . Rationality

Over the past decades, a number of studies have addressed the problem of the transitionsbetween school mathematics and out-of-school mathematics. The seminal works of Lave(1988) and Nunes, Schliemann and Carraher (1993), drawing on anthropological methods,focus on sociocultural activities in which mathematics is embedded. They analysed out-of-school practices and highlighted the difficulties experienced by subjects in linking out-of-school activities to academic knowledge.

Many researchers have focused their interest on mathematical practices in workplacesand provided a wide range of outcomes from different industries (Bessot & Ridgway, 2000;Hoyles, Noss, Kent & Bakker, 2010; Noss, Hoyles & Pozzi, 2000; Roth, this issue;Triantafillou & Potari, 2010). Beyond the acknowledgement of the existence of twodifferent types of practices (out-of-school and academic) and of the difficulty workersexperience using mathematics, the question is how to help these workers to broaden their

DOI 10.1007/s10649-011-9363-9

C. Hahn (*)ESCP Europe, Paris, Francee-mail: [email protected]

Educ Stud Math (2014) 86:239–251

Published online: 26 November 2011

perspective by integrating mathematical knowledge to their work. Specific tools designedfor adult workers such as technology-enhanced boundary objects (Hoyles et al., 2010) areone possible answer. More generally, researchers often recommend the use of “authentic”situations in educational programmes (Nunes et al., 1993; Steen & Forman, 2000;Triantafillou & Potari, 2010). Nevertheless, introducing work reality into the classroom isnot an easy task, as the epistemologies of work practices related to mathematics differ fromschool mathematics (Noss et al., 2000). At school, reality has to be adjusted by the teacher;problems are drafted in order to fit classroom goals (Freudenthal, 1991). Thus, as claimedby Abreu (2000), there is a need to explore more deeply the relationship between themicrocontext of the mathematics classroom, and the macrocontext of the socioculturalenvironment, in order to gain some insight into the way learners decide on their actions.

Vocational education takes on many different forms in different countries, butapprenticeship is a common form, dating as far back as the Middle Ages. In France, it isbased on a real partnership between school and businesses, a partnership whose terms arestrictly legally defined, both nationally and regionally. One of its main characteristics is thefocus on the learner, seen not as a student or a professional who on some occasions travelsto the other world, but as a full member of both worlds—a difficult position to manage (Star& Griesemer, 1989). Because the French apprenticeship system is based on a dual jointintegration in two worlds, school and industry, it appears to us particularly suitable forobserving the reciprocal influence of the school and workplace on learners' behaviours(Hahn, 2000).

In this article, I present a design experiment (Cobb et al., 2003) whose main goal is toexplore how students link academic knowledge with workplace experience. The researchfield of management education appears particularly suited to the examination of academicdisciplines in real-life context: Although academic disciplines play an important role in thecurricula, their role in the workplace is difficult to grasp, as management is largely based oninformal, collective and unstable situations, and the results of managers' actions are notalways clear.

I conducted the research with a group of 36 business school students entering a 3-yearmasters level apprenticeship programme in order to explore how these students linkedacademic knowledge and workplace experience. To achieve my goal, I implemented, in anintroductory statistics course, a learning activity, specifically designed for this researchstudy, based on the use of an Exploratory Data Analysis (EDA) approach and inspired byan authentic workplace situation.

The first part of this article presents my theoretical framework. The second part describesthe methodology and experimental procedure employed in the experiment. Finally, Isummarise and discuss the results obtained from the experiment.

1 Theoretical framework

1.1 To learn between school and workplace

Although referring to different theoretical frameworks which emphasise either the culturalor the cognitive dimension, some authors agree that learning appears to occur through adialectical process—between conceptualisations in action, embedded in the setting in whichthey occur, and theories or “scientific” concepts—whether these authors stress thecontinuity between these two forms of thinking (Noss et al., 2000) or the discontinuity(Pastré, Vergnaud & Mayen, 2006). A dialectical learning process implies the construction

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of an internal space where different levels of generalisation play, work or compete together(Brossard, 2008). In fact, this means not only different levels of generalisation but alsodifferent conceptual fields, as defined by Vergnaud (1990). His cognitive model ofcomplexity gives an essential role to concepts, seen as a set of invariants used in action.Regional epistemologies (Bachelard, 1970), specific to each discipline, lead to differentlydefined conceptual fields. The problem is to think of their articulation with professionalfields, structured around situations and not around problems: The learner has to selectknowledge from one conceptual field that s/he thinks will be useful in order to perform aspecific action (Pastré, 2007). But how does the learner select this knowledge? We are notonly driven by bounded rationality (Simon, 1991), and the decision-making process is not asimple question of information processing. Our rationality, developed through ourparticipation in different communities, is shaped by values and beliefs of which we aremostly unaware. Not all of this tacit knowledge can be codified and it shapes not only themeans but also the evaluation of the ends (Polanyi, 1966). Scientific rationality as it isdeveloped at school—explicit logical reasoning—coexists with other social forms ofrationality. The way the learner solves a problem depends on what the problem means toher/him. According to Vergnaud, drawing on Piaget, schemes that organise subjects' actionsand allow them to interact with their environment are associated with a set of situations.Thus, in a classroom context, the procedure used to solve a problem varies depending onthe situation with which the student associates the problem, and the personal goal s/hebuilds for the activity. This explains why learners use different strategies in differentenvironments (Hahn, 2000; Säljö &Wyndhamn, 1993). Therefore it seems important tobuild activities that not only refer to authentic work practices but which are also part of thelearner's field of experience (Boero & Douek, 2008).

1.2 Statistics and management

Because of its widespread use in modern society, activities involving statistical reasoningand data can easily provide students with problems inspired by everyday life or professionalsettings. In business schools, statistics is an important subject, as it offers much insight intomany serious corporate questions and issues. But, in fact, most decisions can be madewithout considering any statistical methods and, quite often, managers are not aware of thetypes of rationality underlying the decisions they make, or of the way they could improvetheir decision-making process by using statistical methods (Dassonville & Hahn, 2002). Insales management, statistics offers the possibility of analysing and modelling informationwith very large data sets held by firms about their customers.

Statistics educators recommend using real data and developing an EDA approach inorder to “enculturate” students into statistical reasoning (Gould, 2010; Pfannkuch, 2005).The aim is to give students the opportunity to mine through data, to formulate hypothesesout of the information given and to choose appropriate tools to verify these hypotheses. Inparticular, students are driven to work on notions such as variation and distribution, twofoundation stones of statistics (Wild, 2006).

Nevertheless, if variation and distributions are key statistical concepts, they are hard todeal with at any age or level (Garfield & Ben-Zvi, 2005). Research studies show thatstudents usually study extremes and divide data into subgroups (Hammerman & Rubin,2004), they have difficulty with spontaneous use of summary statistics (Konold &Pollatsek, 2002) and, when they calculate measures, they do not use common sense insolving the problems (Bakker, 2004). Authors stress the importance of dealing with the twoforms of variability, within-group and between-groups (Makar & Confrey, 2005; Garfield &

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Ben-Zvi, 2005). They show that moving from a local (data seen as representing a collectionof individuals) to a global point of view (data seen as a whole), and therefore constructingthe concept of distribution, is a difficult task (Makar & Confrey, 2005).

My aim was to explore how students link academic knowledge with workplaceexperience. The tested hypothesis was that through a carefully designed learning activity, ateacher could gain some insight into this process of problem shaping at the interplay ofwork and school. This hypothesis can be divided into three sub-hypotheses as described insome details below.

2 Methodology

2.1 The pedagogical device

The first part of my theoretical framework led to the design of an activity centred on asituation that should make sense at three levels: At the learner's level, this situation must berelated to her/his field of experience; at the discipline's level, it must focus on fundamentalconcepts; and at the workplace level as it must be “authentic”—based on informationcollected in the field.

In order to support the dialectical learning process, I assumed that the activity had toinvolve intermediary phases related to school practices or to work practice as well as a finalphase of decision making during which students would connect knowledge from bothworlds. Because students must confront their conceptions, I also wanted the activity toinclude discussions among students, intended to provoke such a confrontation.

Drawing on the statistics education research results quoted above, I designed a four-stepdevice based on a story, inspired by observations made in workplaces I had visited and byinterviews with sales managers. The story was about a firm, “T”, which sells officeequipment, hiring a sales manager. Students were asked to choose which of three sales areasthey would prefer to manage. They had to make their decision according to informationthey were given about a group of customers (businesses) located in different regions (withdifferent group sizes in each region). This information, presented in an Excel file, includeda set of one categorical variable, date of first purchase; one ordinal variable, evaluation ofcommercial relation (a grade from 0 to 10); and four quantitative variables: previous year'samount of sales (of the client), distance (from the client to “T” location), staff (of theclient), and number of different items (sold to the client in the past year). Distributions ofvariables were carefully designed in order to present specific characteristics. For example,in the three regions, the variable “sales” had the same mean but different variances andmedians; in area A and B there were linear correlations between numerical variables but inarea C no correlation; in Area A outliers played an important role. Of course, none of thethree regions could be considered the “absolute best”.

First, each student was provided individually with the distribution of one variable fromone sales area (a different distribution for each student per class); subsequently each studentwas asked to write a brief summary of the information he or she received (step 1). Next, Iformed groups of three students, with each of them having studied the same variable in adifferent area, and I asked each group to summarise the information it had received bycomparing the three distributions of the same variable in the three different samples (step2). In this way, they were able to consider two types of variability, within a group andbetween groups. Then I built new groups of six students, each of them having differentinformation about one variable (among six) in all three sales areas (step 3). In the final

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phase, I asked the students (in groups of three, as in step 2) to make a final decision aboutthe area they would choose by analysing all available data simultaneously (step 4).

I assumed that steps 1 and 2 were closer to school practice, and steps 3 and 4 were closerto professional practice, with step 3 more typical of a situation faced by a salesperson andstep 4 being a situation typically faced by a manager. Thus I expected that, consistent withmy hypothesis, students using results from steps 1 and 2 (the “school part”) would be led toconfront both types of knowledge at steps 3 and 4 (the “professional part”), and that thiswould enable me to gain some insight into the way they linked statistical knowledge withworkplace experience.

More specifically, I assumed that:

(H1) Students would refer more to school knowledge at steps 1 and 2 and more toprofessional workplace knowledge at steps 3 and 4;

(H2) Passing from step 1 to step 2, but also from step 3 to step 4, would help students tomove from a local to a global point of view;

(H3) Step 4 would lead students to integrate both types of knowledge, as they had tomake their final decision according to what they had done at steps 1 to 3.

2.2 Experimental procedure

Since I wanted to gain insight into students' conceptions and the way they negotiatedmeaning, I needed to design a qualitative procedure. My device was first tested with 36students (15 women and 21 men, 20 to 24 years old), engaged in a 3-year masters levelprogramme of an average level business school that regularly includes several periods ofinternship. Most of these students (n=34) completed a 2-year commerce degree prior toentering the masters programme and had work experience, mostly as salespersons. All ofthese students had a secondary education in mathematics and all had previously completedat least a basic statistics course during their post-secondary curriculum.

Two questionnaires were given to the students at the beginning of the school year by theteacher in charge of the business course. The first questionnaire focussed on their formerexperiences and future projects, the second on their statistical knowledge: Given a list ofstatistical concepts, they were asked if they had met these at school and if they knew how touse them.

The experiment took place during the two first sessions (3 h each) of acompulsory statistics course during the first year. I split the group into twosubgroups located in two different classrooms for space and organisational reasons.Each subgroup followed the same procedure. At each step, the students were able touse their personal calculator or computer. There was no intervention by theresearcher during the sessions. Two colleagues helped to manage the organisation:They were present in the classrooms to answer questions on practical matters and tomonitor the activity.

The debates between students during steps 2, 3 and 4 were audio-taped; in addition,the teachers and I took field notes and collected reports written by the students at eachstep. Students were told that we wanted to keep track of the discussions in order tohelp us to adapt the course to their needs, which I actually did after the conclusion ofthe research. They were allowed to stop the recorder if they wanted, which happenedoccasionally during breaks. The recordings include snippets of personal discussionswhich were not to the classroom activity. I assumed that the students, eventually, forgot

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about the recorder. I transcribed all discussions between students and analysed theircontent.

I first studied the use of statistics by students from their written work at each step. Someof the findings are summarised in the first part of the results section. Then I transcribedeach of the debates between the students (steps 2, 3 and 4) and made a first coding,according to standard methodology in qualitative analysis (Miles and Huberman, 1984). AsI assumed that discourse is shaped by and helps to shape the activity, I used amethodological framework based on a sociocultural type of discourse analysis whichBernard and Ryan (2010) identify as “language in use” and distinguish from the linguistictype “grammar in use” and the critical type.

Given my hypothesis, I focused on two themes: the reference to statistical tools and thereference to students' personal experiences. Initially, I identified how and when studentsrefer to statistics tools. The results are presented in the second part of the results section.Then I searched for simultaneous occurrences of these two themes and selected all theelements of dialogue where I had found one of these occurences. I analysed these transcriptexcerpts and made conjectures about patterns. These conjectures led me to propose aninterpretative framework for the way students linked their experience to both the problemthey had to deal with and to statistics. I present below a synthesis of the main findings,illustrated by typical segments of the transcripts selected through pile sort method (Bernard& Ryan, 2010).

3 Results

3.1 The use of statistical tools in the written reports

I describe in this section of the article results concerning the ordinal variable and the fourquantitative variables (30 students studied these variables, six students per variable at firststep). I focus on the use of the mean, median and standard deviation because there werevery few occurrences of the use of other tools, such as graphs.

Table 1 compares answers to the questionnaire (what students claim to know) andcontent of the reports at step 1, for 30 students out of the total of 36 (the six remainingstudents dealt with the qualitative variable). It seems that students were accurate in their selfrating—although they also seem to underestimate their capacity to calculate a mean and amedian.

Although very few students calculated or used measures of variability, many of themexpressed an intuitive conception of variation, as evidenced by their references to the shapeof the distribution. As I had expected, as it is a natural process (Hammerman & Rubin,

Table 1 Comparison between answers to questionnaire and answers at step 1

Questionnaire Step1

Taught inschool

Met out-of-school

Know howto calculate

Know howto get theresult fromspreadsheet

Know howto use itout-of-school

Calculated(without mistake)

Calculated(wrongly)

Mean 30 16 16 20 18 24 2

Median 18 5 6 7 6 10 5

Standarddeviation

24 2 1 4 2 1 3

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2004), many students divided the data into subgroups. Nevertheless, I found two differenttypes of strategies. At this stage, 19 students out of 30 built subgroups based on thedistribution (use of mean or median, or discontinuities in the data set) and 10 builtsubgroups referring to a “social norm”: the decimal system (hundreds), economic typology(size of firms), or a “school norm” (a good grade must be 5 or above). So the observations Imade at step 1 are consistent with the results from the literature review, although theliterature refers mostly to younger students.

I had predicted that the students would refer more to school knowledge at steps 1 and 2than at steps 3 and 4 (H1). Indeed, at step 1, many students tried to apply statisticalknowledge learned at school and calculated as many summary statistics as they could; 11without any mention of the task context, even to recall the name of the variable.Nevertheless, 12 of them already integrated elements of their personal experience of thesituation context at this stage. Strategies seemed to depend on the task context (Wedege,1999) and not only on the distribution of numbers: Similar strategies were used for thesame variable (e.g., all students who dealt with sales and distance calculated percentages forsubgroups). I mostly found references to the situation context for sales and distance (mostimportant for a salesperson, according to our interviews with professionals).

At step 3, when groups of six students had to draw a conclusion about one area fromtheir individual study of each of the variables, I noticed in the reports that the use ofmeasures of variability was less frequent and, as in step 2, dependent on the task context(see Table 2). They indicated standard deviation for only two variables, staff and items.Those who did not relate their work to their personal experience in the workplace calculatedstandard deviation for variables where it made no sense for them to consider the context.One group went back to a local strategy by numbering customers.

At step 4, when groups of three were supposed to decide on the area they would like tomanage, I found almost no occurrence of the use of measures of centre or variability: Onlytwo groups (out of ten) used the average for distance and grade in their writtenargumentation. Their reasoning was based on commercial arguments and mostly built oncomparison of percentages within subgroups.

I assumed (H2) that steps 2 and 4 would help students to move from a local to a globalconception—in particular by using multiplicative strategies (as sample sizes were different).That was obvious in the reports made in step 2: Each student who had previously made listsor rankings of customers abandoned them. This seems to indicate a shift towards a globalpoint of view, although they used few summary statistics. While at step 3 there is a return tothe study of individuals one by one, at step 4 reports indicate a shift back to a global pointof view: Students did not focus on particular firms, and used expressions like “in general”or “globally”.

Table 2 Use of summary statistics at step 3 (ten Groups)

Sales Staff Items Distance Grade

Mean 3 3 4 4 3

Median 1 1 2 2 1

Standard deviation 0 2 2 0 0

Use of effective commercial context 5 0 0 5 5

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3.2 The reference to statistics in the discussions

The written report is the result of the debates between students, and only provides arestricted picture of the richness of these discussions. For example, the recordings showedthat, during step 3, students mentioned the standard deviation several times, although thisdid not appear in the reports. In the following extract (step 3, group 3),1 two students triedto explain to their group how standard deviation was calculated. The ultimate lack ofapplication of standard deviation in the reports suggests that these students failed toconvince the others of its relevance to the problem.

S4 Standard deviation it is with average, how much most of the firms deviate…S6 Yes it is variations. You see for example, here [he shows his paper], there are a lot of

numbers, so average is here… Not here because it is very, very small but as there aresome that are high and this modifies average. Then standard deviation is high becausethere are values that are very far from the others. When it is small, this means that allvalues are close. For example if average is 10 and you have only tens we will say thatstandard deviation is 0.

To calculate an average is an easy task, but interpreting the result according to thesituation context is not so straightforward, as it requires adoption of a global point of view.This can be discerned from the following extract (step 3, group 3):

S5 7 is a good grade!S4 Yes but in general we have good grades as the worst is 4.S6 The average is 6.76.S5 But I think that 7–8 is a good grade.S6 You have to compare to the average. If, for example everybody has between 16 and

20, then average is 18.S5 And then you will say that you got a bad mark?S6 Compared to the average. For example if you got a 16.3, compared to the average…S5 Even compared to the average it is still a good mark.S4 The regular average is 5. We got 6.76.S5 But you decide you got a good mark if it is above average? In the example she gave, if

I have 16 and if it is the worst mark I will still say I got a good mark.S4 But listen you talk about a school test, we are talking about a firm.S5 But it is the same. Whenever you talk about school or grade given to a firm, it is the same.

S5 struggled with the interpretation of the mean. Although she identified the conceptacross situations, she did not take into account the distribution of values. She drew anindividual, local analysis, based on her experience as a student when S6 positioned thevalue comparatively to the whole set of values. S4 used a more intuitive strategy: shecompared the value they had found (7) to an extreme (the minimum, 4), and then comparedthe average to the anchor value (Tversky & Kahneman, 1974) 5.

In most of the cases, step 3 led students to formulate a hypothesis about the relationshipbetween two variables. They looked for potential links (or no link) from particular cases orbased on assumptions growing out of their experience, as seen in this extract (step 3, group 2):

1 Quotations from students' recorded discussions are numbered by the step (2, 3 or 4) and the group number(1 to 6 for step3, 1 to 12 for steps 2 and 4).

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S1 If it is a small firm then the sales must be low.S2 Look at this one, it has high sales and a staff of only forty…S3 You must look in general; there is always a single case…S1 Staff does not go with distance.S1 We must connect everything to sales, sales is still the main criterion.S2 We see if it grows in proportion.S1 In general, we see that grades grow with sales. Distance, the same.

The assumptions formulated by students mostly reflected their lack of knowledge aboutpossible statistical tools. Students kept summary statistics when they were able to agree ona common interpretation, dropping those that they could not make sense of. This explainswhy they hardly used summary statistics in their written reports: “We are going to stick tothis kind of knowledge, like this percentage [of customers] is satisfied, this number [ofcustomers] put the max score, because this kind of information is clear (step 4, group 8)”.

At step 4, even if the comparison of their work with what had been written by othergroups during previous steps aroused students' curiosity, they quickly abandoned theirdesires to exploit it, given the complexity of the task. Most students simply characterisedareas in a simplistic manner, such as “Area A—dangerous, Area B—risky, Area C—morehomogeneous” (step 4, group 7).

In general, I observed that as students moved forward in the experiment they left theirstatistical knowledge behind. An interpretation could be that they did not find it practicalenough for the objectives they had set themselves.

3.3 Forms of rationality

Considering the references to the situation context, sometimes even at step 1, it seems thatstudents very quickly built a representation of the problem as a commercial problem. Thisled them to interpret data differently, as we can see in this extract of the discussion thatoccured in one of the two groups dealing with grade at step 2 (group 9):

S7 You did not calculate the average for your area? For your twenty customers, how many?S8 I told you that there were ten [customers who gave a grade under 5] out of twenty.S7 Yes, but the total average?S8 But I told you, it is 10.S7 But the average grade, how much?S8 I told you.S7 You did not calculate it?S9 The addition of grades divided by the number of grades.S8 Oh this, I did not do it.S9 The average is 6.76 in my area.S8 Is this good or not?S9 This is not so simple… the average is 6.76…S8 But how many have a grade above 5, this I am sure you did not do it?S9 No, I did not.S7 In my area, there are thirty-one customers, the general average is 5.S8 Exactly 5?S7 Yes, there are thirteen whose business relationship is under 5, which represents 42%,

and there are eighteen whose relationship is above 5, which represents 58%. Then theend result is positive but not good enough.

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S8 In my area, eleven customers reach average 5, so we must improve commercialrelationship and try to find out during appointments what they really need and adaptcommercial policy to improve their satisfaction.

We could claim that the three students were at different stages of understanding but it seemsto me that they are not solving the same problem. The problem is shaped by the objective theyset for themselves: S7 seems to plan a comparative study in order to understand differencesbetween areas, S9 is solving a school problem to answer the teacher's request, and S8 alreadywants to answer the question “which is the best area?” at this early stage. Then, of course,strategies differ. S7 referred to what seems to be a scientific rationality: to comparedistribution and use statistical concepts. S9's actions are based on technical rationality (Schön,1983): He applied techniques learned at school, but did not know how he can use the result toanswer a question. S8's reasoning is pragmatic; he used a simple, intuitive strategy.

Pragmatic rationality seems to be linked to students' experiences at work while technicalrationality seems to refer to school practices. Students using intuitive strategies frequentlymention their experiences as salespersons. The recordings showed that they raised questionsabout information not given in the file. For example, at step 3, while studying distance,students wondered about qualitative factors such as type of road or the amount of traffic.When, in one group, a student asked, “What is the grade you think is good?” anotherstudent answered: “5. Between 5 and 6 it is a grade where nobody objects to you, the guy ismore sympathetic. Below 5, he is with you but if another supplier visits him then he willleave.” (step 3, group 5). The reference to the anchor value 5 implies anticipation linked toa reference point and led students to construct a rule of action as a salesperson to achievethe goal they had set (i.e. so keep the client).

Students who refer to technical rationality see the goal as a response to a command by theschool. Some students mentioned the teacher or “people” and referred to the perceivedrequirements: “People know what is right or wrong with a sentence like that” (step 3, group 2).The problem is primarily academic, but it is not a statistical problem, rather a business problem,as students often talked about tools they learned in the business course: “I do not remember theformulas to calculate small ratios, to give numbers” (step 3, group 5). The aimwhen they lookedfor links between the variables was primarily to verify relations learned at school, that is, to findthe answer hidden in the data by the teacher.

At step 4, students had to compare the three areas and decide which one they wanted tomanage. This was not an easy task as there was, of course, no single right answer. Iexpected (H3) that students would use knowledge from different origins—the statistics andbusiness course, their personal experience—and articulate it. However, I observed that, atthis step, pragmatic rationality mostly prevails. Nevertheless, some students tried to makesense of statistics as in the following extract (step 4, group10):

S11 The issue is that you're the sales manager and you must choose the area you want todevelop. They let you choose what is most important to select an area.

S10 It depends of the salary you want at the beginning! […]S11 (to S12) What are you looking for?S12 Averages.S11 There are about the same. [average sales were almost the same in the three areas]S12 So the argument [for the existence] of a leader is irrelevant because we do not have the

same number of customers. What I am saying is that at first you see that the sales in AreaC are huge compared to the sales in Area A, but in fact area A has fewer companies.Presumably if it had the same number of customers it would have had the same sales.

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S11 That is it, because area C is already well developed… At the same time we are notsure that firms in area A would ask us to equip their offices…

S12 I am wondering…S10 In fact, you do not really want to work in a firm!

The debate between S11 and S12 addresses potential development areas. S12 focussedon the size of the samples. He not only pointed out that they are different, as did manystudents, but decided that the area with more companies and the highest amount of salesmust be the best one. His thinking led him to exploit the concept of mean in a verymeaningful way: if the areas had the same average sales then it should be possible todevelop the smallest area. The concept of mean is linked here with the concept of businessdevelopment. In contrast, S10 positioned himself at a different level, as an operationalperson who does not ask too many questions, except about his salary.

It seems that S12 articulated two conceptual fields (Vergnaud, 1990) that is, two spacesof problems, trade and statistics, involving, for each of them, a set of related concepts, andthis led him to build a more managerial approach to the problem. He seems to question andto link knowledge of different origins by emancipating himself from the roles and identitiesthat he had previously constructed. But his questioning was stopped by S10, who wasdriven by a more pragmatic purpose. I observed this phenomenon in other groups duringstep 4.

4 Conclusion

As apprentices in a masters level business school programme, the 36 students in this studybelong simultaneously to the two different worlds of school and workplace. In order to getsome insight into their learning processes, I implemented a pedagogical device in anintroductory statistics course. This four-step device, based on an EDA approach, placedstudents in a school-type situation, followed by a workplace-type situation, and focussed onthe well-documented learning obstacles of variation and distribution.

The results seem to confirm the hypothesis that the device would facilitate theconfrontation of knowledge of different origins through the use of an “authentic” situationcontext, and linked to students' personal experiences as salespersons. Very early in theexperiment, even sooner than I expected, I found occurrences of students referring topersonal experiences of the workplace. This phenomenon apparently parallels thedisappearance of the use of statistics in the workplace itself (Dassonville & Hahn, 2002).

I claimed that different knowledge confronted by students was associated with what Isuggested to be different forms of rationality: technical (the application of techniques whichare not put into perspective), pragmatic (the use of intuitive strategies to meet a limitedshort-term objective) and scientific (the integration of theories to enlighten the problem).These forms of rationality led students to construct and answer different problems. I foundfew occurrences of what is usually called scientific rationality, the kind of rationality towhich teachers typically refer. As students progressed through the activity, pragmaticrationality, tied to their experience as salespersons, prevailed. This form of rationality didnot prevent students from asking questions, but they worked most of the time withoutreference to statistical knowledge. In drawing upon statistical knowledge, students wereusually trying to meet what they felt to be the teacher's intention. Thus, their actions oftenmade no sense regarding the actual goal of the activity (i.e. to choose the best area). Thesestudents quickly abandoned what I called technical rationality to adopt a pragmatic point of

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view and addressed the activity from the perspective of salespersons. This potential effect isinherent in the use of so-called authentic situations at school, something of which teachersshould be aware.

Students tried to compare areas by articulating their workplace experience with statisticalknowledge but they usually could not go very far due to a lack of mastery of statisticaltools. The capacity to make sense of statistics seemed to be linked to more managerialbehaviour. In particular, the difficulty in moving from a local to a global point of viewreflected the difficulty of shifting identity from a salesperson to that of a sales manager; asalesperson deals with his/her customers more individually than a manager, whose roleimplies the need to mobilise more statistical knowledge. As Cobb and Hodge (2002) claim,an understanding of statistics and personal identity seem to be linked. As cognitive aspectsare linked to social identity, the resistance in using some specific knowledge can beexplained by the fact that some identities are less valued than others (Abreu, 2000). Indeed,if I look at the results of the experiment, it seems that, for the students I worked with, theidentity of salesperson is much more valued than the identity of student. The challenge is tomake them understand that both identities must converge if they are to gain access to theidentity of manager.

This question of identity goes far beyond the fields of vocational education: The identityof a student is not as obvious nor clearly defined as in the past, and, considering theimportance of mathematics in the selection process in most countries, identity andperceived mathematical abilities are strongly implicated in one another—for masters levelbusiness studies students at least.

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