Peter Petocz

Students' conceptions of statistics: a phenomenographic study

This paper reports on the results of an empirical study of students conceptions and understanding of statistics. Six qualitatively different conceptions are described, ranging from fragmented to inclusive views. Students expressing the more inclusive and holistic conceptions approach their study of statistics through a focus on ‘higher-order’ statistical thinking. Students expressing limited and fragmented views may not be able to understand the complexity or applications of the discipline. This paper describes the use of a qualitative methodology – phenomenography – that aims to explore the qualitatively different ways in which a group of people experience a specific phenomenon, in this case statistics. It also describes an overarching framework, the “Professional Entity,” that relates students understanding of statistics and their perceptions of working as a statistician. Investigating and describing the ways in which students learn statistics, how they understand statistics, and how they perceive their own work will enable teachers to develop curricula that focus on enhancing the student learning environment and guiding student conceptions of statistics.

Learning domains and the process of creativity

Creativity is viewed in different ways in different disciplines: in education it is called ‘innovation’, in business it is ‘entrepreneurship’, in mathematics it is often equated with ‘problem solving’, and in music it is ‘performance’ or ‘composition’. A creative product in different domains is measured against the norms of that domain, with its own rules, approaches and conceptions of creativity.However, learning in any discipline area consists of both product and process. While the product may be quite different in different domains, there are general principles of pedagogy that encourage creativity of process. ‘Creative teaching’ could be said to consist of setting up a learning environment that encourages students to see the essence as well as the detail of the subject, to formulate and solve problems, to see the connectedness between diverse areas, to take in and react to new ideas, and to include the element of surprise in their work. Such a learning environment involves not only appropriate materials and assessment techniques, but also methods of learning that address the important affective dimensions of creativity.

From expert student to novice professional

Students entering higher education expect that their studies should lead them towards some form of professional career. They come to university wilh a range of ecpectations for their learning as well as for the outcomes of their learning. In this age. when complex internationalised professions are the main soure of work for graduales, sludents need to prepare themselves for a future that can be volatile, changeable and challenging. Our overall aim in this book is to show how students navigate their way through learning and become effective students and how they shift the focus of their learning away from the formalism associated with the university situation towards the exigencies of working life. In this sense. we explore how poople move from being expert sludents tio novice professionals starting to establish themslves in a profession. When a person is an expert at somelhing they are usually able to demonstrate an excellent skill or understanding. whilst a novice is usually a relative newcomer to an arca who will undertake some sort of probation (articulated or not) before he or she can be fully embraced by the particular area. We look at how students become pre-professional experts. in the sense that they hold and demonstrate professional knowledge and disposilion, and reel a personal interest and engagement with a specific discipline area that leads them into professional practice. However. when these expert students finally make the transition to working life their profcssional expertise is subsumed as they take en a novice role in the work place. So. we consider how students make this transition from e xpert to novice and perhaps back again.To support the ideas presented in this book. We will utilise a decade of research undertaken in countries halfa world away from each other - Sweden and Australiaand use the combined outcomes to present a model ofprofessional leaming. Rather than building our theory out of our own common experience. we use empirical research gnthered from students and leachers to show how student, negotiate the forms of professional knowledge they encounter as part of their studies and how they integrate their understandings of a future professional world with professional knowledge and learning. As students move from seeing themselves as learners, they take on more of a novice professional identity. which, in turn, provides a stronger motivation for their fonnal studies.

Statistics Education Research

This chapter sketches in broad strokes and critically examines several aspects of the world of research that pertain to the teaching, learning, understanding, and using of statistics and probability in diverse contexts, both formal and informal. It reflects on the methods and conceptual schemes that underlie the research activity in this field (the how), the topics being researched (the what), and the people carrying out the research (the who). The chapter examines purposes and motivations for different types of studies in statistics education, distinguishing between large-R research that often aims for academic reporting and generalizability versus small-r types of research whose motivation is more on local problems set in a particular context. We illustrate some trends in the field by presenting empirical results from an exploratory qualitative analysis of the text of a body of papers and publications in the field. The chapter points out that the range of what qualifies as research in (or of relevance to) statistics education is much broader than what gets published in leading journals and conferences in our field. It highlights the multiplicity of philosophical foundations and methodologies in use. Some directions for future development and research are outlined, including aspects of statistical literacy, cultural dimensions of statistics education research, the role of practitioner inquiry, and the importance of broad interdisciplinary research in statistics education.