Teaching

• The planning stage in statistical reasoning

An important step in the statistical problem-solving process is the selection of the appropriate statistical procedure for the real-world situation under analysis. A decision-tree term project has been found to be an effective teaching device to help MBA students understand this step. The project requires the students to construct a decision-tree structure, which, through a series of questions and responses, will lead from the statement of a statistical question to the appropriate sampling distribution to use in addressing the question.

• Creating data to explain statistical concepts: Seeing is believing

Students from many disciplines take statistics as part of their degree requirement. Some of these students lack the mathematical background to follow theoretical proofs and/or the expertise to conceptualize abstract concepts. Concrete examples may provide the best means to aid these students in grasping statistical principles. This paper highlights the use of computers to create, analyze, and present data that models a wide range of statistical concepts. An illustration of the technique is presented for explaining the Central Limit Theorem, Type I error rates, and a host of other statistical concepts.

• Nonprobabilistic statistical inference: A set-theoretic approach

The familiar sampling procedures of statistical inference can be recast within a purely set-theoretic (ST) framework, without resorting to probabilistic prerequisites. This article is an introduction to the ST approach of statistical inference, with emphasis on its attractiveness for teaching. The main points treated are unsophisticated ST significance testing and ST inference for a relative frequency (proportion).

• Sample space: Practical experiments for teaching sampling

This paper presents a series of practical experiments that can be used to demonstrate the ideas of sampling at all levels, from introductory to advanced. The material presented consists of a brief introduction to sampling, the "Sample Space" star map, and two sampling experiments based on the map. It is presented in a form that can be used directly for teaching classes or for individual study. Further experiments can be found in Petocz (1990). Three of these were described in the original draft of this paper, as presented at the ICOTS Conference, and are available from the author on request.

• The case of the wayward data collector (How projects can be used in our statistics class)

Projects can be a good way for students to apply what they've learned in class. I have my students pick a topic of interest to them; they gather and collect the data; present it via a research report which is due at the end of the semester. It definitely helps their grades and provides some meaning and perspective to the semester's work. The students picked some very interesting subjects as well. All of this was explored in the workshop.

• Statistics in non-mathematics courses

This paper shows some of the opportunities in primary schools for integrated teaching where statistics (and other mathematics) can easily be taught within other subjects because one teacher has responsibility for all the areas of the curriculum.

• Statistics and mechanics

This paper illustrates some connections between a subject, in this case mechanics, and high school statistics. Other subjects such as geography or economics could have been chosen and would have shown similar links.

• Integrated real life themes and the teaching of probability and statistics at 11-16 level

This paper re-evaluates the basic notions of probability and statistics and discusses their introduction through integrated real-life themes, a method already successfully tested in schools for students aged 11-16. In effect, this approach provides a viable alternative to the great majority of school/university courses which teach probability and representational/parametric statistics virtually as an extension of pure mathematics.

• From cooperation to coordination - The school's statistics coordinator

This paper is based on a project which ran during 1988 and 1989 at the Center for Statistical Education, University of Sheffield. The purpose of the project was to produce materials both to train schools' statistics coordinators and for the coordinators themselves to use in school, for their work with pupils and other teachers. These materials are now available from the Center in loose-leaf folder (Holmes and Rouncefield, 1989). In this paper, I shall attempt to explain the rationale behind the project and to describe some of the project materials.

• Teaching statistics to students from a non-english speaking background

This paper suggests ways of teaching and adapting materials to help all students, not only those from a non-English speaking background. These techniques are well-known to teachers of English as a second language but not well-known to statistics teachers. Techniques canvassed in this paper include cloze, matching, composition, sequencing, and cooperative logic. The methods are in line with the trend in mathematics education toward small group activities, problem-solving and open-ended activities. For students studying in a second language, however, group work will need to be structured to encourage verbal interaction.