13. STATISTICS: A ROUTE TO THE REAL WORLD Ralph Riddiough Kyle Academy, Ayr, Scotland

13.1 Introduction

Recent changes in the curriculum from S1 to S6 have emphasised investigative approaches to learning, stressed the value of real life contexts, and highlighted the role of information technology. Teaching statistics within the mathematics syllabus provides the classroom teacher with superb opportunities to incorporate these strategies in their lessons.

It could be argued that there is not a great deal of statistics in the mathematics curriculum. Information handling in stages 5 - 14 is a noteworthy exception. Standard Grade does not advance the pupils' knowledge of statistics very far beyond this. Not all schools offer the SEB Short Course, or the SCOTVEC Modules in statistics. The Revised Higher contains no statistics. CSYS Paper 3 does not reach a large audience! There is a growing concern in certain quarters, to raise an awareness of the need to be statistically literate, as evidenced by a number of the Royal Statistical Society's initiatives.

At Kyle Academy we have found it relatively easy to attract pupils to CSYS Paper 3 Statistics. It has a good syllabus, and fills a need. Many jobs and post secondary courses require a knowledge of the subject, and we hear regularly from former pupils who took Paper 3, that it proved to be extremely worth-while. We have also found that pupils who would never dream of doing SYS Maths can derive great pleasure and achieve success. Paper 3 may be their only SYS level course!

13.2 Computer Needs

High speed, colour graphics, a minimum of 2Mb RAM, a hard disc, and a friendly operating system are the desirable features. We use Acorn Archimedes with a Hewlett Packard DeskJet printer, but the faster colour Apples and the higher specification PC's offer similar facilities. For software we use content free packages such as industry standard spreadsheets and databases, each with graphics capabilities (in our case, PipeDream 4 from Colton Software, and Pinpoint from Longman Logotron). I realise that there are a number of specialised statistical packages but one advantage of a spreadsheet for teaching and learning is that pupils must know how to set out the calculation, rather than have it all done automatically at the press of a button. Each of the activities I will outline here assumes there is one such computer system available in the classroom.

13.3 Attracting Students to Statistics

To attract interest in statistics, don't leave it until S6. Although not an original idea, a class survey in S1 is a good choice. Statisticians young or old are, I suspect, never happier than when they are poking their noses into other people's business, so what better time than right at the start of S1, when pupils meet for the first time in a new school. What would they like to know about their new friends? A list of questions is prepared. PinPoint is ideally suited to this type of activity.

Creating the database using PinPoint involves producing a copy of the questionnaire on screen. This task is similar to desk top publishing and although not onerous, is best done by the teacher, using the pupils' questions. Each question has to be designated as requiring a certain type of answer: character, numeric, Yes/No, multiple choice, ordered choice, or date. A questionnaire one page in length is adequate at this level, and over the period of a week or so, the pupils can take it in turns to type their answers into the computer. This may be done while the regular work of the class continues. Once all the data is entered, various bar charts, pie charts, or line graphs may be produced as appropriate, and form the basis of a number of exercises in interpretation. The database may be interrogated and reports produced summarising qualitative data (pet, favourite fast food, make of car, etc) or quantitative data (number of brothers and sisters, hours of television watched each day, number of cars per family, etc). This provides the data necessary for many more activities, such as drawing bar charts, calculating averages, and so on. Pupils are greatly motivated because the data pertains to them, and for the teacher, there are often valuable insights into the sociology of the class. It can be quite a surprise to learn just how many hours of TV the pupils we teach are in the habit of watching!

Using a spreadsheet to track personal performance is great fun and an activity that pupils enjoy. The old idea of noting marks for homework on the back page of the homework jotter can be enhanced by using a spreadsheet to tabulate each pupil's record and drawing a line graph to try to spot any trend. If the teacher sets up the spreadsheet ahead of time it is an easy matter for pupils to type in their own marks and ask the computer to print their graph. This is especially exciting in colour!

For Standard Grade classes, quality newspapers can be a great source of data. By applying some of the ideas and techniques described in the SEB short course on statistics to such data as share prices, unemployment figures, temperatures, tables showing government grants, etc. (the list is long), and by harnessing the power of the computer to manipulate these figures, many valuable lessons on number work take on a new vitality. The actual syllabus requirement in statistics is quite minimal at this level, but there is no need to interpret the syllabus in a limiting way. Number work that is in context and the interpretation of graphs and tables of information is very much part of Standard Grade mathematics, and can be a statistically worthwhile activity.

13.4 Working with the Local Hospital

And so to SYS statistics. In April 1991, the new Ayr Hospital, providing about 300 acute care beds, replaced 3 old hospitals, and was one of the first trust hospitals in Scotland. As part of their application for trust status, the new hospital emphasised amongst other things:

Quality assurance means work for statisticians. Our school is less than a mile from the new hospital and clearly part of the community it serves. With these points in mind, I approached the Director of Quality and Standards for the new Trust in August 1992, and explored with him the possibility of forging a link between the mathematics department and the hospital. Could some of our S6 pupils gain valuable experience handling real life data while assisting his department with their analysis workload? He was very receptive to the idea.

Meetings were arranged between hospital personnel and myself, to choose a suitable topic, and to establish guidelines for the conduct of this joint venture. A number of possible projects were considered:

We settled on the latter for the following reasons:

This last point should not be overlooked. It has to be remembered that when working with data from outside organisations, they own the data.

The plan was to seek the opinions of about 300 parents whose children were patients in the Paediatric Unit, over a period of a couple of months. It was decided to make use of a four page questionnaire prepared for this purpose by the charity 'Action for Sick Children' (National Association for the Welfare of Children in Hospital Ltd.). As this was our first venture, we were quite happy to use a questionnaire prepared by others. However, in the light of our experience, we might not be so shy a second time! The questionnaires would be distributed by nursing staff. Our job was to analyse the returns, and prepare a report for senior nurse managers.

13.5 Getting the Students Involved

I broke the news to the class, and asked for volunteers. This opportunity would, I told them:

Four pupils came forward, and this turned out to be a most satisfactory number.

By mid November a box containing 140 completed questionnaires arrived at the school, and the hard work began. For the period of about a month, every study period on these senior pupils' timetable, and a bit more besides, was devoted to the task. About 100 hours of work altogether, shared equitably. The pupils had to plan their approach and decide the best way to do the job. We used an Acorn A5000 computer, and again the PinPoint package was invaluable. We also made use of other packages to extend the range of presentation graphics and to facilitate calculations. It is quite easy to transfer data between applications in the RISCOS environment.

13.6 The Questionnaire

I don't propose to go through all the questions in the questionnaire here. Suffice it to say that the main topics investigated included:

Essentially we wanted to know if parents were satisfied with all the many aspects of the service provided, but leaving out any reference to specific medical matters. The questionnaires received at the school had however been coded to indicate which medical speciality had been involved (ENT, Plastic Surgery, Ophthalmology, ... etc.).

The first question was 'How old is your child in hospital?' This very innocent looking question turned out to present us with our first problem. A selection of the responses illustrates this point:

2 years 9 months

41/2 years

15 months

5 weeks

21 days

4 days

not answered

Clearly the responses are of the numeric type, but which units should be used? Factors such as, speed of data entry, avoiding loss of detail, and facilitating the calculation of mean and standard deviation, all had to be considered before the database structure could be finalized. In the end we decided on years before, and months after the 'point'. All ages were correct to the nearest month, and those few who were very young (viz 4 days) were assigned the age of 1 month to distinguish them from no response which appears as zero. The first age listed above, 2 years 9 months, appeared as 2.09 This approach had the advantage of permitting very fast data entry, but some conversion was required before attempting calculations (not a daunting task when the ages are easily exported to a spreadsheet).

13.7 Analysis

The type of analysis undertaken was mostly of a descriptive nature. Some very interesting facts can be uncovered through interrogation of the database. For example:

These and many other questions were investigated, and the results were presented in the form of a 26 page report, prepared using a DTP package, and printed complete with full colour graphics on a HP DeskJet 500C. Just before Christmas the pupils were invited to visit the hospital, tour the Paediatric Ward, have lunch with the Chairman of the Trust, and present their findings to an audience of consultants and senior managers.

13.8 Conclusions

Did the pupils feel it had been a worthwhile exercise? Their comments indicated that all had experienced a sense of purpose and achievement, knowing that their work was not a text book exercise, but that the results of their labours would be of immediate use to professional people. They had a feeling of responsibility, because they realised that the correct answers were not at the back of the book! The onus was on them to decide if their work was valid. There was also a realisation that statistics and mathematics is a human endeavour. To a greater extent than they had thought possible at the outset, mathematics had deeply involved them with people. Not only had they made contact with hospital personnel; they had been moved by some of the data they had analysed because it pertained to real people.

I think the experience sharpened their ability to analyse data critically, and they seemed to have grown in confidence when discussing issues and tackling problems. Certainly their communication skills improved. There had also been an opportunity to explore certain professional issues, such as the confidentiality and security of data, and the need on occasion to keep personal opinions at bay. Because of the wide use of statistics in industry, commerce, and the service sector, and because managers need well organised information, often involving quite simple calculations, I suspect that there are many opportunities for links between schools and the outside world of the type I have described. From time to time various schemes are organised to promote this. However, I believe it is possible to complement these on occasion by making use of personal contacts.

Did the hospital appreciate our efforts? Very much so. We hope to do another project next year.

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