# Teaching

• ### EDA in the primary classroom- Graphing and concept formation combined

It is important to develop children's mental images of numbers parallel to their acquisition of counting and calculating skills. This is achieved by various kinds of activities which reveal, in one way or the other, the underlying structures. In school mathematics numbers are closely connected with calculations, which are, in my opinion, too much emphasized. The emphasis should be shifted towards handling of numbers without calculations. The introduction of stem-and-leaf displays is a step towards that end. Being based on the fundamental idea of place value stem-and-leaf displays also help developing the children's understanding of number.

• ### A statistics course for all students aged 11-16

In England and Wales all pupils take major examinations at the age of 16. Until recently these were either the General Certificate of Education (GCE) for the more-able pupils and the Certificate of Secondary Education (CSE) for those not taking the GCE. As from courses starting this year there will be only one set of examinations, the GCSE, which are aimed at pupils of all abilities. Whilst combining the two systems the opportunity has been taken to rethink all the syllabuses and the purposes for which they are devised. This rethinking shows in published national criteria. All syllabuses have to conform to general criteria, many individual syllabuses have their own extra subject specific criteria (but statistics is not one of these).

• ### Using simulation to model real world problems

The primary source of the material used in this presentation is The Art and Techniques of Simulation, a book from the Quantitative Literacy Series. These techniques are designed for use in middle school through senior high school. They feature statistical topics that are important to students, a wealth of hands-on activities, real data sets and active experiments which motivate student participation, and graphical methods instead of complicated formulas or abstract mathematical concepts. In particular, simulation is introduced as a technique for solving probability and statistics problems.

• ### A practical approach to the central limit theorem

The most important aspect of the Central Limit Theorem is that no stipulation is made concerning the population from which one is sampling. From a pedagogical point of view, a student needs to draw a random sample from a population with a known distribution and then to compare the sample mean with the population mean to see "how close", he or she comes. Any student who does this will know the difference between the two. Students will also be led to understand the difference between the population mean and the mean of the sample means. It is not enough for a teacher to talk about these ideas - concrete experience with sampling is necessary for success. It is hoped that these experiments go some way towards enabling students to observe the central limit phenomenon operating, as well as providing empirical evidence of the truth of the theorem.

• ### Mutually exclusive and independence: Unraveling basic misconceptions in probability theory

Two central concepts in probability theory are those of "independence" and of "mutually exclusive" events and their alternatives. In this article we provide for the instructor suggestions that an be used to equip students with an intuitive, comprehensive understanding of these basic concepts. Let us examine each of these concepts in turn along with common student misunderstandings.

• ### A way of teaching significance testing

Nowadays increasingly many people are admitting and increasingly many people are claiming to be Bayesians. We have heard a lot already at this conference about Bayesian statistics. Our pupils are going to read many texts by non-Bayesians and they need to learn how to interpret the various terms involved. The concepts and methods to which those terms refer are rooted in common-sense. This emerges, I believe, when they are exposed (rather than taught) in the way I adopt and that I want to share with you. I am asking you to participate in a speeded-up version of what would take several sessions with pupils.

• ### Using microcomputers in teaching time series analysis

Time Series Analysis is a particular area of Statistics that has seen remarkable progress in the last 20 years. There has been increased activity and interest in both the theory and practice of the subject that has led in some sense to a unification of methodologies that existed previously. It is clearly not pure coincidence that the growth in Time Series Analysis has occurred at the same time as the growth of computing availability. Software of suitable quality was a little slow in appearing at first. But recent years have seen the introduction of many new and re-vamped statistical packages, and most of these nowadays contain quite extensive Time Series routines.

• ### The role of the computer in the teaching of statistics

In this paper we consider the nature of a statistics course and discuss the role of the computer in it. In particular, we discuss the course for the first-year students at the university level.

• ### Teaching data analysis using interactive APL-based graphics packages

The present paper is essentially a preliminary report on the author's experience of teaching a course in Data Analysis to students at the Naval Postgraduate School, Monterey, California. The main emphasis in this paper is on the use of graphics packages as a teaching tool, and, in particular, on how these packages can assist the student (and the teacher) to achieve greater insight into both the data analytic and methodological aspects of our discipline.

• ### The challenge of computers in today's statistical education

This paper begins with a brief discussion of the role of the statistician and how this is changing, particularly in view of the microcomputer revolution. Historically the training of the professional statistician has been undertaken within academic institutions and has often incorporated little practical training. The advent of relatively cheap and accessible computer power has allowed more applied elements to be incorporated into statistical education, in particular larger and more realistic data sets may be used, models fitted (and compared) with greater ease, and so on. There are numerous ways in which this computing power may be exploited in the education of statisticians and this paper outlines a number of these and discusses their usefulness.