In the last two decades, awareness of students' conceptions of learning has altered the way in which we approach student learning, teaching and academic development. More recently, such 'generic' ideas about learning are being challenged by research on learning in different disciplines. In this paper, we report on our investigations in the area of statistics. We establish connections between how students see statistics as a profession and how they go about learning in statistics. Our argument is based on the analysis of a series of interviews carried out with students of statistics, linking their conceptions of the profession with ideas about how they learn statistics.

Statistics is only one subject area that we have investigated: others include music, theology, design and law. Each shows evidence of an overarching notion of professional work and its connection with learning. This Professional Entity is a manifestation of a strong relation between students' perception of professional work and their conceptions of the discipline and learning within that discipline.

Our investigations have had a profound effect on our teaching and our work as academics. We explore the ways in which our discoveries about learning of statistics in particular, and professional areas generally, have changed our practice in teaching and academic work, and our approach to research. In this paper, we report our findings about statistics students' understanding of their subject area and how they go about learning. We also explore the extent to which our participants 'fit' within the outcome space, especially within the context of the Professional Entity. This report also serves as a case study of the ways in which our own view of research and research planning in higher education have developed using an initial phenomenographic methodology to frame our research practice and learning development activities. As we explore our students' learning of statistics, we learn about statistics learning and learning in general.

In recent years, a sector-wide interest in improving the quality of teaching and learning in higher education has resulted in research that is directly aimed at identifying which aspects of learning are important for the improvement of both learning and teaching. The description of deep and surface approaches to learning and their relations with conceptions of learning (Marton and Saljo, 1976; Marton et al, 1993) formed the research bases for the now widely used text, Learning to Teach in Higher Education (Ramsden, 1992). This text was an integral part of many professional development activities in the 1990s, and ideas stemming from these activities have resulted in the development of curriculum, materials, teaching actions, and learning environments that focus on the quality and diversity of the student experience. The early work that identified "students' conceptions of learning" is now so widely recognised that university promotions committees look for evidence of student-focused teaching and the demonstration of scholarly approaches to teaching as part of their deliberations (for instance, Macquarie University Enterprise Agreement, 9.01.21-24, and UTS promotions guidelines).

Academics entranced by the commonsense aspects of this research base set about uncovering the variety of ways students understand various topic areas in order to design learning environments to specifically target the development of student understanding across the range of conceptions. Studies were carried out in areas such as biological concepts (Hazel et al, 1996), way-finding (Kwan and Gerber, 1994), legal theory (Keyes and Orr, 1996) and the physics of sound (Linder and Erickson, 1989). In turn, this research was supported by studies that looked at students' experience of entire subject areas such as mathematics (Crawford et al, 1998), science (Prosser et al, 1995), music (Reid, 1997; 2001) and even academic development (McKenzie, 1999).

In conjunction with the focus on subject, and ideas contained within a subject, researchers began to explore the ways in which students understood learning in their subject. Prosser and Trigwell (1999) based their text on this approach, as they exhaustively explored each aspect of the students' learning situations to generate a model of an integrated learning theory. They based some of their conclusions on the early work of Biggs (1979) who described the presage-process-product model of learning. Prosser and Trigwell's extensions of Biggs' model were described as a 'constitutionalist model of student learning' (p. 17), implying that a student's learning situation simultaneously included his/her prior experience, approaches to learning, perceptions of the situation and learning outcomes.

Curiously, all of these studies, whilst looking at the subject and the learning of the subject from a student perspective, focus almost exclusively on institutional learning. For instance, Crawford et al. (1994) looked at the ways in which students understood mathematics as an academic discipline, but did not relate this to the work of a professional mathematician. The identification of students' ideas about the nature of professional work and the relation that this perception has with their conceptions of learning and their chosen subject would seem to be an important step forward.

During her PhD studies with music students anticipating a career as professional musicians, Reid (1999) found that students (and teachers) clearly identified ways of experiencing the subject, learning in the subject, and the way this learning was directed towards an idea of professional work (Reid, 1997). This relationship was referred to initially as the 'Music Entity': our and our colleagues' investigations in other areas - theology (Morgan, 1999), design (Davies and Reid, 2001), law (Reid et al.) and statistics (Petocz and Reid, 2001) - revealed that each shows evidence of an overarching notion of professional work and its connection with learning. This 'Professional Entity' (Reid and Petocz, 2002) is a manifestation of a strong relation between students' perception of professional work and their conceptions of the discipline and learning within that discipline.

In this paper we examine the links between statistics students' conceptions of statistics, learning statistics and their perceptions of work as a statistician. We do this by firstly describing the categories that show the qualitatively different ways in which statistics, and learning statistics are experienced, and then show how these categories fit within the Professional Entity. We use substantial quotes from students to demonstrate these relations. Finally, we discuss how research of this type affects our work as academics.

In order to uncover the range of different ways that students understand learning, statistics and the work of a professional statistician, we used a phenomenographic approach. This approach enables researchers to conduct a series of in-depth interviews that allow enough scope for students to explore and describe their own experiences (Bowden, 1996; Dortins, 2002). The interviews are then transcribed and analysed as a whole. Using this method, researchers keep in mind the analytic focus and explore the question: "What are the differences that emerge between one person's experience of a phenomenon and the group's experience?" It is the structure of these differences and the nature of the relations between them that become the 'outcome space' and are described as 'conceptions'.

Phenomenography is a qualitative orientation to research that takes a non-dualist perspective and is often used to describe the experience of learning and/or teaching (Bruce and Gerber, 1995; Prosser and Trigwell, 1997). This means that learning and teaching are seen as a relation between the person and the situation that they are experiencing. Phenomenography defines aspects that are critically different within a group involved in the same situation. It is these differences that make one way of seeing the situation qualitatively different from another.

In this project we interviewed 20 students from two classes: a first-year introductory statistics class and a third-year class in regression analysis. All these students were undertaking a degree in mathematical sciences, with possible specialisations in statistics, finance or operations research, leading to professional work in these areas. The interviews were transcribed verbatim and labelled with pseudonyms to avoid identification of individual students: they formed the raw material for our study. The study was approved by the Human Research Ethics Committee of the University of Technology, Sydney.

Since the intention of phenomenographic research is to report on the variation that emerges from the whole group's understanding of the phenomenon - in this case, the notion of statistics, learning statistics and professional work as a statistician - the range of questions was designed to focus students' awareness on different aspects related to their experience of statistics. These questions were followed by probing questions which responded to the students' answers. Each interview was conducted by one of the principal researchers who did not have academic involvement with the students, or by our research assistant for the project. According to the protocol set out in the ethics approval for this study, students were selected at random by the research assistant from the first and third-year class lists. These students were invited to participate in the project and were aware of the research questions and aims. The interviews lasted between 30 minutes and 1 hour, and were concluded when the student indicated that they had satisfactorily explored the research questions.

We have previously reported outcome spaces for conceptions of learning statistics (Petocz and Reid, 2001) and conceptions of statistics (Reid and Petocz, 2002). In this paper, we examine the relations between conceptions of statistics, learning statistics and professional work, and illustrate these relationships by quotes from the transcripts. In this regard, we are extending the usual phenomenographic method. We need to use each individual student's complete transcript to identify the conception of statistics and the conception of learning statistics that he or she seems to be manifesting at the time of the interview: then we need to make connections between these conceptions, and illustrate these connections by means of representative quotations. Our aim is not to classify individual students as holding this or that conception (and anyway such conceptions are not static or free of context) but rather to identify the range of variation of the pair of conceptions in a two-dimensional sense.

These conceptions of learning statistics were first described in Petocz and Reid (2001). Here, we present the summary of the categories without quotes from the transcripts. This and the following section are a necessary precursor of any discussion of the joint range of conceptions of statistics and learning statistics.

(A) Doing: learning in statistics is doing required activities in order to pass or do well in assessments or exams. Here, students focus on activities they have to do as part of their subject, and which they think are sufficient to 'pass'. They approach their study by attending lectures, reading, doing labs, repeating questions or examples until there are no mistakes, or doing previous exam papers. They aim simply to do well in assessment tasks and the exam.

(B) Collecting: learning in statistics is collecting methods and information for later use. Here, students focus on gathering information, absorbing methods, increasing knowledge, and stockpiling examples or ideas. Students with this conception understand statistics to be about a group of techniques that need to be acquired in order to be used 'later'.

(C) Applying: learning in statistics is about applying statistical methods in order to understand statistics. Here, students believe that doing the practical activities provided will enable them to understand the subject of statistics. They focus on doing practical things like examples, checking results and getting problems correct. The students' intention for their learning is to understand the subject Statistics.

(D) Linking: learning in statistics is linking statistical theory and practice in order to understand statistics. This conception focuses on linking theory with practice. Students intend to find out how the practical exercises and investigations can inform their understanding of statistical theory, and vice versa. Students describe an intention to use statistics in 'real life' situations and they enjoy trying out their ideas on 'real' data.

(E) Expanding: learning in statistics is using statistical concepts in order to understand areas beyond Statistics. Here, students intend to connect statistical concepts with other areas. They aim to understand what they are doing, the meaning of data summaries, the broad subject area, and the real-world meaning of what they are doing with numbers. They can see how statistics can be used outside the subject area or even outside the university context.

(F) Changing: learning in statistics is about using statistical concepts in order to change your views. This is the most expansive and inclusive conception. Students focus on the changing quality of their own understanding of the broad idea of statistics and of the world. They see statistics as an intellectual tool that can be used to inform their understanding of many other areas, or to solve problems in other areas. They believe that their study of statistics pushes them to change the way they view the world.

In one sense, knowing this range of variation in the experience of learning statistics would provide ample material for the development of learning environments and materials that would support the more inclusive levels and provide a way for students at the 'less' inclusive levels to become aware of differences in learning and ways in which they can broaden their conceptions. In another sense, it is not enough to focus on this alone, as the students' understanding of the subject - the focus of their learning - is also important.

These categories were first described in Reid and Petocz (2002). As in the previous section, we summarise the students' conceptions of the subject statistics in summary form without quotations.

(1) Statistics is individual numerical activities. In this conception, students' understanding of statistics is limited and fragmented. They see statistics as a sort of mathematics which involves using 'boring calculations', 'numbers' or 'probability'.

(2) Statistics is using individual statistical techniques. In this conception, students see statistics as individual techniques that can be used to look at data; for instance, graphing, line-of-best fit, collecting data, regression. This conception is like Conception 1, as students focus on fragments, but is unlike Conception 1 in that students describe the fragments in statistical rather than solely mathematical terms.

(3) Statistics is a collection of statistical techniques. In this conception students describe statistics as a collection or set or 'stockpile' of different techniques that can be used at some time to deal with data. This conception is similar to Conception 2, with the difference that students accumulate and are aware of a range of techniques, rather than relying only on one. They often describe statistics by listing these techniques.

(4) Statistics is the analysis and interpretation of data. In this conception, students describe statistics to be about understanding, interpreting and making sense of data. Students explore different relationships found in the data and use these relationships to draw conclusions about the data. Students describe statistics using the techniques characteristic of conceptions 1-3, but consider these techniques to be part of a coherent whole, and aim to be able to analyse and interpret a complete set of data.

(5) Statistics is a way of understanding real-life using different statistical models. In this conception, students view statistics as a way of understanding real-life situations using a variety of statistical models. This conception is like Conception 4, as students aim to interpret a set of data and obtain the information they can from it. But in Conception 5, students focus on looking at a variety of models to compare their data with reality, and to test the appropriateness of their conclusions.

(6) Statistics is an inclusive tool used to make sense of the world and develop personal meanings. In this conception, students focus on understanding and making sense of reality using statistical methods. However, this is only one aspect of the statistical analysis: beyond this, students use statistical methods to develop their own thinking, to create new interpretations of data and life. Such students actively relate their statistical understanding to the data, the interpretive models, to wider aspects of reality and to their own creative and critical thinking. This conception is quite unlike the other conceptions as it focuses on the importance of meaning. As this is the most inclusive, integrated and expansive conception, students expressing this view may use any or all of the characteristics of the previous conceptions, if their perception of the situation demands it.

As with the categories describing variation in students' experience of learning statistics, it is not enough for teachers to know that students think differently about the subject. The students' understanding of the subject, and their conception of learning (incorporating their learning intention and approach to learning) are important for the overall development of the learning environment. We consider that these two components are only part of the possible variation, as students' perceptions of professional work may also be related to their understanding of the subject and their learning in the subject.

Previously, we have explored the similarities and differences between student musicians' and student statisticians' perceptions of work (Petocz and Reid, 2002). Our previous research has shown that that there is a relation between students' perceptions of their future work and the way they go about learning, and that this perception of work may be generic across disciplines. This relation - the Professional Entity - comprises three levels of understanding of the nature of professional work, Extrinsic Technical, Extrinsic Meaning and Intrinsic Meaning.

The Extrinsic Technical level describes a perception that professional work is constituted as a group of technical components that can be used when the work situation demands it - instrumental techniques and musical elements in music, biblical commands and custom in theology, a palette of spatial and visual techniques in design, a set of rules and regulations in law, and a collection of numerical or statistical techniques in statistics. Students who perceive professional work at this level are likely to focus their learning on the technical components of their subject and consider that the subject itself is a collection of various techniques.

The Extrinsic Meaning level describes a perception that professional work is about developing the meaning inherent in discipline objects - the historical and stylistic meaning in written music, the overall meaning of a religious text in theology, the inherent meaning found in the created artefact in design, the dynamic system that constitutes the law, and the meaning discovered in a set of data by appropriate statistical analysis. Students with this view of professional life are likely to try and find out what is meaningful about the subject they are studying and focus their learning on applying this understanding in some way.

The broadest level of the Professional Entity is the Intrinsic Meaning level. In this view, students and teachers perceive that their professional work is related to their own personal and professional being - musicians use the instrument, manuscript or performance to communicate their feelings or tell their story, theologians integrate Biblical truth with their own interpretations to help members of their community, designers communicate personal meaning by planning and constructing a visual artefact, legal professionals consider law as an extension of their ethical and moral selves, and statisticians create and develop their understanding of the world using statistical evidence in the form of data. Students who consider that the profession is an extension of their own being are likely to look for ways of integrating their learning situations and the subject with their own understanding of the world, and are willing to acknowledge that this integration may also change the way they look at the world.

In this paper, we describe the results of a further extension of the phenomenographic outcomes outlined above. We have used the categories that have emerged from the transcripts to reanalyse each transcript with the notion of exploring the categories' salience with the Professional Entity. In this sense, we are using the original outcome spaces to illuminate the richness of individual experience. (This is a change, as quotes from the transcripts were originally used to illustrate the meaning of each category and provide evidence for the qualitative differences and relations between the categories: here, instead, we use the phenomenographically derived categories as a way of analysing the depth contained within each transcript.) We hypothesised that this re-analysis would allow us to 'put' each transcript within a descriptive grid (see Table 1) that showed how limiting conceptions of learning statistics and statistics also show evidence of a perception of work that is Extrinsic Technical, that more inclusive conceptions may be related to the Extrinsic Meaning dimension, and that the most integrated and expansive conceptions may be related to the Intrinsic Meaning dimension. We expected to find an evident relation down the 'diagonal' of the diagram. The discussion that follows shows that most transcripts were classified on the diagonal, but that a few transcripts showed evidence of different combinations of ways of thinking. These specific cases are discussed as they come up.

As we have indicated earlier, our aim with the re-analysis of student transcripts is to identify the range of variation in two dimensions of the conceptions of statistics and the conceptions of learning statistics. We illustrate this two-dimensional range with brief quotations from the transcripts, although the assignation of a particular transcript to a cell in the diagram is only possible on the basis of the whole transcript. It is very important, however, to recognise that these transcripts - and our decisions about them - only represent students' responses at the time of interview, and may not now represent the current state (and certainly not the permanent state) of any individual student's understanding of learning, statistics or work (if it did, we will have failed as teachers!).

Here, Kim sees statistics as individual numerical activities, and learning in statistics as reading and reviewing, picking up techniques. These ideas about statistics and learning can be 1B. These views of the subject and learning in the subject are consistent with the Extrinsic Technical.

Tran sees statistics as individual statistical techniques and identifies the names of subjects. For Tran learning is described as doing required activities, memorising formulas, studying the basics: we classify this as 2A.

Emma sees statistics as a collection of techniques that can be used in a variety of situations, and learning in statistics as collecting and experiencing these techniques: we classify this as 3B. This transcript shows the extent of the range within the Extrinsic Technical dimension. Emma alludes to the 'people out there', who are obviously statistical professionals, who are sometimes not careful enough with statistical techniques to get the 'right result'.

The next three transcript selections illustrate the Extrinsic Meaning dimension.

Anne sees statistics as manipulating, analysing or interpreting data, and learning as consisting of carrying out analyses to get an idea of how statistics is actually used in practice: this seems to be an example of 4C.

Chris sees statistics as a practical subject, building models to solve applied problems, and learning as using the concepts of statistics to understand other areas: we classify this as 5E.

Danny sees statistics as understanding data and making sense of real life using models, and learning as the process of using statistical concepts to understand other areas: we would classify this as 5E.

The next two selections show students who are probably "off the diagonal", maybe due to a change that is occurring in their views, or maybe due to our classification.

Here, Lily views statistics as the analysis and interpretation of data in various situations. Learning is looking at practical problems logically - which would be C - but then she makes the final statement, leading us to classify her transcript as 4F.

Jessica sees statistics as making sense of the world by developing personal meanings, and learning in statistics as understanding statistical concepts by connecting them to other areas: we have classified this as 6E.

Finally, here is a transcript illustrating Intrinsic Meaning, where both conception of learning and of statistics are at the most integrated and holistic level, according to our original categorisations.

Helen sees statistics as a tool for making sense of the world and developing personal meanings, and learning in statistics as using statistical ideas to change the way that you view the world: we classify this as 6F.

There are several points that emerged through our re-analysis of the transcripts. Initially, we targeted first and third-year students in an attempt to find the full range of variation possible. Although we have carried out no formal analysis comparing the two groups, our re-analysis has shown that students in each group - first year and third year of study - express the full range from the most limiting to the most holistic conceptions and perceptions of work. This provides us with compelling evidence that we should focus our teaching towards conceptual change, emphasising the more integrated and holistic conceptions right from the start. The results also show that students at all levels of their undergraduate study in statistics need to become aware of the range of ways that statistics can be seen as part of a work environment. Although these findings are obvious in the context of this paper, statistics teachers generally consider the first year to be the time to 'bombard' students with statistical techniques and methods in order to 'prepare' them for interpretation and inference later on. Then, by the time students get to third year, it is assumed that they should be able to think in more critical ways simply because they have been at university for some time. This analysis of qualitative data suggests that at least some third-year students have not yet begun to think about their future professional work in any meaningful way.

The re-analysis has also shown that our initial hypothesis regarding the possible diagonal relation between conceptions of learning, statistics and perception of work has actually been validated in this situation, although there are a few students who don't fit in neatly for some reason. It has also shown us that of the students involved in this research project, most had views of the statistical profession consistent with Extrinsic Technical or Extrinsic Meaning conceptions, and only a few expressed the personal connection to statistics implied by the Intrinsic Meaning conception.

The research outcomes afforded by a phenomenographic approach, and the consequent changes in teaching and learning environments, have profoundly affected the way in which we have come to consider teaching, learning and research in higher education. The identification of students' understandings of the subject of statistics, learning in statistics and their perceptions of work as professional statisticians has paved the way for educational developments that target specific student needs. In our case, it has resulted in an enhancement of the statistical learning environment at UTS: activities involved in the traditional lecture time are focused on helping students understand the meaning of statistical techniques and results, as a tool for understanding the world and the students' role within the world. This is quite a change for statistics education, which traditionally focuses educational development on individual statistical techniques and sequencing of statistical topics, with the assumption that the 'correct' sequence will enable students to learn better (for example, Ho Yu et al, 2002). Understanding the variation in students' expectations and approaches to statistics and learning has also enabled us to alter the assessment and tutorial components of our courses to emphasise interpretation, investigation and inference, rather than the acquisition of statistical methodologies and techniques. These research outcomes are critically important for the development of learning materials, for example, the laboratory exercises in Petocz (1998) and the book 'Reading Statistics' (Wood and Petocz, 2002) which encourages students to 'read' statistical papers, newspaper articles and research in a variety of areas of application, with the aim of looking beyond the data to the 'real life' meanings.

The insights gained from this research, however, have not been limited to our work with potential statistics professionals. The notion of the Professional Entity as an overarching framework for understanding the relations between institutional learning and perceptions of work has generated further research in the areas of music, law, mathematics, theology and design. These diverse areas have the commonality that they are all focusing on the development of individuals for professional practice. We have also started to explore the ways in which students in 'servicing' courses use specific subjects to support their understanding of their home discipline and their perception of work. In this sense, our research in specific disciplines has expanded into research throughout higher education. Involvement in teaching, research in learning, and application of the research outcomes has changed our own academic perspective from simply 'good' teaching practice (Ellington, 2000) to 'scholarly' and 'reflective' teaching (Howitt, 2000; Cross and Harris Steadman, 1996; Brookfield, 1995). Our research on student learning in statistics has resulted in our own learning about learning and informed our future research and teaching agendas.