12. INSIGHTS INTO SIXTH YEAR STUDIES STATISTICS Les Dickson Strathclyde Department of Education Lenzie Academy, Myrtle Avenue, Lenzie, Glasgow.

12.1 Introduction

When I first sat down to write a few words on `Insights into Sixth Year Studies Statistics', (SYS statistics) I didn't take long to discover that I didn't have any! What I could do, however, was relate some personal experiences and views on the teaching of statistics at this level. I also thought that teachers might be interested in the comments of some of my students, so there is a contribution from them in this paper.

I've asked them to tell you how they enjoyed the course. They have been given a free hand in what they say. However, these students are quite bright and have more sense than to say anything that will annoy me!

School students are not daft. An important feature about any elective course is its attractiveness to the students, so I have asked them to comment on a particular point. Would they recommend the course to fellow pupils further down the school?

The main thrust of my paper is geared towards promoting the teaching of statistics in sixth year - or for that matter in any other year - as I feel it is a greatly undervalued subject. Any comment I make is of a purely personal nature and in fact I hope that my experiences will provide a platform for an exchange of views or ideas.

In section 2 I describe the background needed by the students. I reflect on the last 20 years in section 3 and enthusiastically describe the new course at Lenzie in section 4. The comments of some of the students are also recorded at the end of the paper.

12.2 Why Statistics?

Now WE all know what kids are like. You could strip naked in front of them, dance around, jump out of the window and they'd be bored before you hit the ground. However, statistics is different! It can catch their attention and stimulate their minds... I like it because of the rich variety of material that can be used in teaching. It is all around us. For example, in Scottish law there exist 2 distinctions relating to probability:

In the civil court - there are the balance of probabilities;

In the criminal court - beyond all reasonable doubt has to be established.

As another example, consider the following true story. A few years ago in America, a crime was committed and witnesses gave the following description of people leaving the scene of the crime. Black male, white woman, she was blond, they drove a particular make of car, it was convertible, colour was yellow, had the first two letters EE on the licence plate.

A few days later a couple answering their description was arrested and the case went to trial. The prosecution based their case on the evidence of an eminent statistician who analysed the rarity of combination of the description - it had to be them. It was 1 in umpteen million - until during the trial another couple were arrested matching the same description. So what happens to the prosecution case - it's now 1 or 2 - who's guilty? From being a near certainty it is suddenly a toss of a coin. This type of example gives students an insight into the judgment required and how to apply statistics sensibly.

Statistics is in very many university degree courses. Students undertaking a sixth year course in statistics will derive a great deal of benefit from that course. The sixth year should be used to make the transition between secondary and tertiary education easier.

Moreover good results can be achieved. In the past students who passed 'Higher' mathematics at C level have achieved success in SYS statistics. The course lends itself to a wider involvement of staff and the expertise of other teachers.

12.3 Credentials

I shall deal with this first because a major obstacle in getting staff involved in SYS is a lack of confidence in the subject. The cry of 'Oh I'm not a statistician!' can be heard when teachers are approached to take on the class. Well I'm not a graduate statistician - I've a degree in engineering. I'm a non-promoted, chalk-face teacher with 18 years experience and I've only got 22 more fun-filled years to go. I've been involved with the teaching of statistics for most of this time with the last 8 years at SYS level. As part of my degree course statistics was involved in the first two years and some quality control in the third.

There are very few graduate statisticians in teaching, in fact many maths teachers have degrees in a numerate discipline other than mathematics. If you are thinking about becoming involved in teaching statistics - don't hesitate - as long as you have reasonable confidence and competence at this level, you'll be fine. However, like anything new, it takes time, practice and a lot of hard work.

On the subject of hard work, anyone involved with SYS, either for the first time, or developing the new course, will be fully aware of the hours needed at home in the evening preparing lessons - you cannot stand up in front of a sixth year class and wing-it. So how many of you saw 'Question Time' recently and heard Edwina Currie inform the nation that a teacher's working day was too short and holidays too long? I almost erupted but I was instantly reassured of her competence to pontificate on the subject when she informed the audience that she gleaned much useful experience of life from having run a bed and breakfast establishment for several years.

Many teachers feel insecure at this level because this is the level which they themselves achieved and this is quite understandable but the new SYS course lends itself to a variety of strategies that enables greater participation in the subject by more teachers. I shall report on this later in the paper.

12.4 The Past Twenty Years

I've been involved in the teaching of statistics for quite a while and my introduction was in Albert Secondary School in Springburn - a somewhat different type of school to the one I teach in now. Rumour has it that at Glasgow High School or Hutchesons' Grammar School, if you walk into the sixth form class and say good morning, the students all stand up and reply 'Good morning Sir/Miss' - or whatever the case may be.

When I walk into my class in Lenzie, I'm ignored; when I say 'Good morning', the students write it down in their notebooks (those that can write of course), but when you walked into a class in Springburn and said 'Good morning' - the class would swear at you for wakening them up.

In those days the following groups were identified:

Those doing 'O' arithmetic with statistics were considered to be too good for arithmetic only but not good enough for Arithmetic and Maths.

The rationale was that statistics is an extension of arithmetic and the kids will be quite happy writing up columns of numbers, and multiplying and adding to their hearts content. To a certain extent the philosophy was quite correct because the kids did not have the maturity or ability to make sound value judgments nor did they have sufficiently developed analytical skills.

You may yourselves have heard the comment that SYS statistics is easy because 'it's only number crunching'. This is a legacy of 10 - 15 years ago. The new course should dispel this myth once and for all because the investigation and class assignments cannot be done without analytical skills, without reasoning, without hypotheses.

Let us put to rest the second division status that has embraced statistics in recent years.

12.5 The New Course at Lenzie

I'm a great enthusiast of the new course. The people involved in its development deserve a pat on the back. It's well structured and well thought out and pitched at the right level. It's also very similar to the courses completed by university students in their first two years.

Time Allocation

Syllabus

The course splits nicely into 3 parts:

For our prelims we complete the syllabus up to and including the normal distribution and approximations. This is usually completed before the Christmas break, leaving significance tests and the investigation to be completed between February and April.

I mentioned before that the new course provided a means to extend the participation of teaching staff. Allocating Stats 1 to someone new to the course is an ideal first step and as experience is gained so they can extend their participation.

When I was first approached to become involved, I was given the choice between a first year SMP course and the sixth year. Into my head came images of

'Please sir - I don't have a pencil!'

'Please sir - I don't have my jotter!'

'Please sir - I've forgotten my book!'

'Please sir - Can I go the toilet?'

Now why is it kids only need to go the toilet 5 minutes after their morning interval or 5 minutes after their lunch break?

'No! Sit down! But sir I'm bursting!' I have yet to see a wean actually burst! But nonetheless, that's the behaviour of the sixth year at Lenzie so you can imagine what the first year is like! I required very little encouragement.

Software

I've mentioned the breakdown of time and how it's distributed. One period per week for computing/class assignments and investigations. I regard this aspect of the course as very worthwhile.

Most colleges and universities use a Statistics package called MINITAB for many of their first and second year courses. The SEB recommended a package called MICROTAB - the little brother of MINITAB. However, it was not too user friendly. I thought it would be a good idea to issue every student with a MICROTAB disc so that they could access a computer at their convenience to complete the course package or perform computations for their assignments or investigations.

At this point SOD's law comes into effect. We have books, course guidelines and objectives, exemplar materials, assignments, and investigations. When we tried to buy MICROTAB we found that it was no longer being produced! At this point I must acknowledge the assistance given to me by a colleague at Napier University - including a full set of tutorials and MICROTAB.

Furthermore, on any occasion that I have approached any college or university for help it has been freely given - this is an additional resource that secondary teachers should be aware of. If you experience difficulty with your course, phone your local university for assistance. Well, Glasgow University Statistics Department are going to love me for that one as their phones will melt because of enquiries from teachers!

There is a problem with SYS development. In-service provision just doesn't seem to figure particularly high on an education authority's priority list. The percentage of students taking SYS is small in relative terms, but I would still like to see more assistance for teachers from the authority.

I now believe that Computer Illustrated Texts by Robinson and Bowman (see the references in paper 9 in this book) is the new package recommended by the SEB - it has to be better than MICROTAB!

Resources

We have kept the best of the old and introduced the best of the new, so at Lenzie the following texts are used.

Weiss & Hassett is a very good publication, as it is well written, clear, has plenty of worked examples and plenty of exercises. It is also widely used in tertiary education. However, being an old-fashioned person who dictates notes, I refer to Hodge & Seed for exercises as I feel the ones in Weiss & Hassett are a bit light-weight at SYS level. I also commend to you the old statistics book from the Glasgow Stats Panel. It will be well out of print, but search a cupboard in your school and you'll probably find one - it is especially good for Stats 1.

The ideas of central location and analysis of data figured prominently in 'O' grade arithmetic. Looking up a set of Standard Grade papers I could not find one question on the mean - so although students in S3/4 are required to know mean and average, by the time they get to S6 you could be starting with a clean slate.

Using measures of dispersion and central location to describe data is really quite a difficult concept for some students. We as teachers take it for granted but my students do find it difficult.

12.6 Conclusion

I have to state that I'm not overjoyed at the policies governing sixth year courses. This is no criticism of the people who have obviously worked very hard to get them off the ground and update sixth year education in Scotland, but unless opinion is expressed we trundle along in the same old vein thinking everything is hunky-dory. As I've said before these are personal opinions formulated from experience.

There are 47 presenting centres for SYS statistics in Scotland, and I believe we should have at least three times that number! Last year I had a class of 22 students and in the past 10 years classes of 15 - 20 were usual. This year there has been a disappointing drop to 10.

There are 2 reasons for this:

1. The SEB recommend SYS Paper 1 General plus 1 other.

In the past many students have worked hard and passed at B or C and have gone on to SYS maths; they may not have excelled but they derived some benefit from it, for it made university a bit easier. Today I feel we are losing these students.

I now list another criticism of the general paper. How many teachers have sufficient expertise to breeze in and teach all the topics in the General paper - the algebra, the calculus, stats, mechanics - I don't mean throw a book at them and let them get on with it - I mean actually teach all topics. There may only be four or five in a department and any aspirations they may have to develop the maths provision to sixth year is made more difficult because of this emphasis on paper 1.

To those teachers who are already teaching paper 3, I hope my observations have been useful.

To those teachers who are not yet involved in paper 3, here are a few points to think about:

There are a set of course notes available from me which can be photocopied;

The comments from three of Les Dickson's students are reproduced 'as delivered verbatim' in the following paragraphs.

Ms Laura Caldwell

'Ladies and gentlemen, Mr. Dickson said that I was to tell you the truth about how I found the sixth year course. Well here goes! Parts of it were alright, parts of it were terrible and some of it was utterly boring. However, I find that most of my school topics fall into very similar categories. I have no doubt that I will find the course to have been of value. Next year I'm coming to Glasgow University to study law and I'm sure that I will find some of the statistics course relevant to my future studies.

I particularly enjoyed the probability part of the course. I found many of the questions demanding but some quite stimulating. On the other hand I loathed MICROTAB. This was an absolute waste of time. It was difficult to use and the questions we did were extremely tedious. I would hope never to do this again.

Well he did say - tell the truth!'

Mr. Andrew Fryhad

'The best thing about the course has been the teacher. Mr. Dickson has been absolutely brilliant - he is such a talented guy, great in class, a brilliant communicator, a fantastic teacher and he has not paid me a penny to say that!

I enjoyed the statistics course. I'm coming to Glasgow to study medicine and I don't know if there's any statistics in the degree course but just the way you look at problems I'm sure has developed my judgment and the way I look at things. A lot of emphasis was put on treating statistics properly. Mr. Dickson was always going on about how statistics can be massaged and things are not always the way they seem.

I will eventually have to weigh up evidence in clinical diagnosis. I'm sure that the training I got in statistics will really be of benefit to me. I also agree with Laura - the MICROTAB part of the course was dreadful. I simply couldn't understand it.

However, I would recommend the statistics course to anyone taking a sixth year.'

Miss Alison O'Brien

'I found the course quite difficult, but then again I could have worked a lot harder. I really enjoyed being in the class. I got on well with Mr. Dickson who even made probability interesting. I found this part of the course difficult especially when we got into combinations and permutations.

I have been accepted to do Forensic Sciences 'down South' and they recommended sixth year statistics. I will have to do a course in statistics as part of my degree so I'm in absolutely no doubt that the time I've spent in sixth year will stand me in very good stead.

As far as recommending the course, yes I would. Although I found parts of the course difficult and the MICROTAB classes a waste of time, I enjoyed doing the class assignments and the investigation was very interesting. I enjoyed the team-work and the need to organise oneself when going round classes collecting data for the investigation. Yes, I found the course beneficial and I would recommend it.'

This paper makes many references to methods in the Scottish system of education and there may be items and jargon that are unfamiliar to teachers south of the Scottish border.

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