# Teaching

• ### Students' project work and the UK applied statistics competition

From the statistical education point of view, each discipline teacher needs to fond that discipline's relationship to statistics before statistics can provide a meeting ground, a common "language", with other disciplines. A basic idea of its principles and a certain baseline awareness and appreciation of its possibilities (with respect to "my" discipline) are needed fist of all. Statistics Prize entries show that this kind of cross-curriculum project is usually better handled in primary schools. There, the teachers are general in their orientation, so they already have an elective view of research activities. At secondary level, however, this perspective has often disappeared and has to be encouraged in the teachers first before their students will get a taste of real cross-curricular work.

• ### Projects and practical work in an external examination

To overcome of the difficulties that external examinations present for the teaching of statistics, a number of countries have introduced course work into their assessment. This paper looks at how this is done in New Zealand.

• ### Classroom practicals using the binomial distribution

In this paper, practical experiments are used not only to illustrate the binomial distribution, but to make it relevant and important to the pupils. The aim is to take statistics and probability out of the textbook and into the pupils' direct experience.

• ### Simulations in the classroom

At Southland Boys' High School simulations are included in the course work for Sixth Form Certificate Applied Mathematics and elsewhere in the curriculum from Form 3 to Form 7, that is, with students aged from 13 to 18 years old. The reasons for their inclusion are: 1) their wide-ranging applications; 2) the simplicity of the methodology; 3) the experience they give students in elementary experimental design; 4) the opportunity they provide for the study of situations that are not readily explored by other methods. It is also important that simulations are included which analyse phenomena or deal with problems that can be solved by other methods to give an idea of the reliability of simulation techniques.

• ### Using real applications in the teaching of probability theory

Students should gain an insight into the usefulness of what they have learned in class such as the applicability of formulae, ideas, and methods. They should also have the opportunity of developing hypotheses and proving theorems. Probability theory and statistics provide many suitable ways for learning about these concepts. Students will be motivated to learn mathematics by using it to solve real problems. Consider, for example, a discussion of the risks associated with nuclear reactors - we should all be able to critically evaluate official statements and the arguments of so-called experts which are based on apparently legitimate mathematical methods. Looking at real applications in mathematics lessons, students get an insight into the part mathematical sciences play in the real world. We shall give three examples to illustrate our ideas.

• ### A practical approach to statistics

The first part provides a perspective showing how the influence of the subject has grown. From this the main aims are advocated and a specimen syllabus linked to applications is outlined. Suitable teaching strategies are described, illustrated by a specific example. References to suitable teaching materials are also given. Throughout, the international context is borne in mind, for statistics is an essential part in any education system.

• ### On the teaching of order statistics

To deal with order statistics is very fruitful from several aspects. Besides getting the pupils acquainted with different statistical notions (median, range, etc.) we have an opportunity to show how to distinguish between independence and dependence and the different levels of dependence (correlation). The variety of combinatorial methods used in connection with order statistics is also an argument in favour of teaching this topic. The program to be presented is for pupils of 13-15 years who learned some stochastics (relative frequency, probability, mean etc.) within the new mathematical curriculum.

• ### Amount and kind of statistics to be taught to 16+ year olds

I will describe some personal experiences and ideas about teaching statistics and will propose a few methodological details and sources of applications useful at schools. The nature of statistical reasoning and selection of statistical school topics are also addressed.

• ### We must preach what is practiced

In teaching non-specialists, we need to cover the procedures they will come across in their other studies and subsequent work. Since many courses and introductory texts do not do so, students are often disillusioned with them and regard such courses as irrelevant. I now describe some topics which we often teach unnecessarily (or with the wrong emphasis) and some which we mostly do not teach at all even though they are often needed. They range from deep matters like statistical inference or causation to more hum-drum ( but important) ones like means, medians and modes.

• ### Teaching statistics to non-statisticians- An application oriented approach

The method of teaching statistics to non-statisticians must be application-oriented. They should be trained as to how to present interpretative results. Examples must be given to demonstrate what can be inferred and what cannot be inferred from real data. The teaching method can be the same in each specialised area except in areas as collection of agricultural statistics where the contents are purely descriptive. A course in computer programming is a must for most types of non-statisticians. Field work involving independent designing of data collection and analysis is also a must for most non-statisticians.