# Teaching

• ### The results of a performance test: A multilevel analysis.

The aim of the paper is to analyse the results of a performance test, created to evaluate how well a group of middle school pupils learned statistics, using multilevel analysis. The results show the importance of the classroom/teacher and the school on the learning process.

• ### An item response analysis of statistics use in the workplace.

Training in statistics at university should be informed at least in part by what graduates will have to do with acquired statistical knowledge after graduation. A sample of 977 employed graduates with PhD and Masters degrees in seven specialties with statistics pre-requisites at university identifies which of 46 statistics based techniques (the items) they use in their work. A two parameter item response model uses 32 of the 46 items to build a scale measuring the extent of statistics use in the workplace and creates a value for each graduate which is used to summarize differences between the use of statistics in the seven specialties. Implications for syllabus construction to better prepare graduates for the workplace are discussed.

• ### New paths in the teaching of statistics - with the help of spreadsheets.

Situations, in which data form the basis of decisions, are abundant. The paper illustrates some concepts involved like "the correlation coefficient" and how it measures the degree of connections between several variables, or "remaining risk" and how it is possible to draw general statements from restricted data. To embed such notions in concrete manipulations of data and easily accessible diagrams facilitates understanding of statistics. The ideas may be worked out with the help of any spreadsheet, here EXCEL is used.

• ### A post-calculus introduction to statistics for future secondary teachers.

We describe our experiences with developing and teaching a new introductory statistics course for prospective teachers of secondary mathematics. The course emphasizes statistical concepts through their applications in the context of recent scientific studies, and it uses an interactive technology-enhanced pedagogical approach that models recommended practice for teachers. A concurrent seminar course introduces students to seminal articles and research findings in statistics education, and encourages them to reflect on their learning experiences in the course as a way to prepare for their own teaching of statistics. Feedback and evaluation from students will be discussed.

• ### Student teachers interpreting media graphs.

The official inclusion of the teaching of graphing in school curricula has motivated increasing research and innovative pedagogical strategies such as the use of media graphs in school contexts. However, only a few studies have investigated knowledge about graphing among those who will teach this curricular content. We discuss aspects of the interpretation of media graphs among primary school student teachers from Brazil and England. We focus on data which came from questionnaires which gives evidence of elements of "Critical Sense," which involves the mobilisation of several kinds of knowledge and experiences, in the interpretation of statistical graphs.

• ### Letting students understand why statistics is worth studying.

Whether they are studying statistics as a disciplinary major or through service courses, students will be more motivated towards what they are learning, and will retain a richer recall of it, if they feel they are doing something worthwhile. I have previously argued that three elements in teaching are salient in giving a sense of worthwhileness: showing that statistics is interesting, useful, and substantial. The first two of these elements are already well discussed. But letting statistics be seen as a substantial discipline, in the sense of being resilient to challenging questioning prompted by students' own curiosity, has not been previously addressed in the statistics education literature. Here I show the kinds of challenging questions which serve this goal. The answers given need not be overly-detailed: what matters is that they satisfy students' curiosity. In this way they strengthen the students' sense that statistics is worth the effort of study.

• ### Creating statistical resources from real datasets: The STARS project.

The aims of the STARS (Statistical Resources from Real Datasets) project are to make available real datasets and associated scenarios applicable to a range of disciplines and to develop learning and assessment materials to accompany these datasets for use with various packages. The project team, based in 4 universities in England, have developed worksheets in Psychology, Health and Business, using mainly Excel, MINITAB, SPSS in both pdf format and Word. The worksheets are designed to be used in introductory statistics courses in service teaching and cater for a range of student abilities, backgrounds and needs. Further, resources for individualised datasets and assignments with solutions to be generated from the datasets have been produced. The materials developed and the concepts behind them have a far greater potential and use throughout the statistics teaching community.

• ### Teaching students and staff consultancy skills.

Consultants are well aware of the skills we must impart. These include: an appreciation for the role of the work one does in the context of the research effort; an understanding of what we can and cannot do as statisticians; a general appreciation for modeling and visualization; and an understanding of the nuclear elements of modeling tools. All of these skills contribute to one's ability to communicate ideas to a client and, ultimately, to the reader of any findings. Changes in the toolkit for statisticians require that we continually learn. In this talk I describe a process that creates a continual improvement cycle for the mastery of these skills. By mastery, I mean that the student has demonstrated understanding through the application of a principle and taught what they have done to others, including non-professionals. The principles, based on modeling and visualization efforts, give rise to the nuclear elements that are the simple and communicable features of the tool.

• ### Analysing data from a class taught with clickers.

During the fall 2005 the author taught a large introductory Statistics class at the University of Connecticut with the aid of a student personal response system (also known as "clickers"). Apart from its pedagogical value, the system has the secondary advantage of building vast day to day data on students' performance. This article presents an analysis of the data gathered from the course, together with conclusions and suggestions on how to collect and organize data for further educational studies.

• ### Practice improves presentation.

Practice in doing consultancy, and in teaching consultancy skills to statisticians, improves that teaching, regardless of the teaching method used. Teaching consultancy skills involves emphasis on communication skills, making statisticians aware of the range of problems they might meet, and showing them ways of dealing with non-standard problems. Examples based on actual consultancy sessions are discussed in this paper, and suggestions are made as to how to integrate these into a course intended to equip students for work as a practical statistician.