Hahn, 2014. Statistics Business

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Educational Studies of Mathematics

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  • 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 rationalitytechnical, pragmatic andscientificled 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: hahn@escpeurope.eu

    Educ Stud Math (2014) 86:239251

    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 authenticsituations 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 worldsa 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 processbetween conceptualisations in action, embedded in the setting in whichthey occur, and theories or scientific conceptswhether these authors stress thecontinuity between these two forms of thinking (Noss et al., 2000) or the discontinuity(Pastr, Vergnaud & Mayen, 2006). A dialectical learning process implies the construction

    C. Hahn240

  • 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 (Pastr, 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 schoolexplicit logical reasoningcoexists 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; Slj &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 &

    Linking academic knowledge and professional experience 241

  • 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 authenticbased 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' conceptio...

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