What are the problems we can expect to meet when project work
forms a significant part of a C.S.E. examination course in statistics?
Mrs Dolan desribes her experiences.
Timing
Pupil
Choice
Which
Topics?
Organising
a Project
The
Results
At Upbury Manor School in Gillingham, a large secondary school of approximately 1700 pupils, we have devised a Mode 3 syllabus which includes two projects to be done by pupils either individually or in small groups and which are internally assessed as part of the final C.S.E. grade. The weighting for the final assessment is made up of 3 for the written examination, 2 for the practical work and 3 for course work. The syllabus is similar to many others at this level but it does start with the following two paragraphs.
1 . The use and misuse of statistical common-sense interpretation of
trends indicated in graphical representation.
2. Collection of statistical data; census and sampling methods of enquiry;
general treatment of basis of statistical survey including questionnaires,
postal or interviewing techniques; simple ideas on the design of questionnaires
and avoidance of bias; the use of tables of random numbers; the use of
electronic computers in data analysis.
The first set of pupils who completed this course during the summer of 1977 received above-average results; I attribute much of their success to the practical nature of the course.
The first 21/2 terms of the course were spent on
introducing statistical ideas and measures as laid down in the syllabus;
this was done by practical experiments where possible. For example,
the use of a tally chart, frequency table and histogram was demonstrated
with the aid of drinking straws, which can be purchased very cheaply.
Each straw was cut into two pieces and straws were then selected at random
and measured to provide data for the frequency distribution of a continuous
variable. These experiments were popular with the pupils; however,
I found that some examples drawn from real life situations had the disadvantage
of producing quite difficult calculations, as in measures for calculating
the standard deviation of a sample. When this happened, I allowed
the use of calculators for the more difficult or lengthy calculations and
supplemented the work with examples in which the data was pre-selected.
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Timing
One of the first problems to be resolved was that of the timing of
the project work. It is necessary for pupils to have had experience
of a number of statistical techniques if they are to be able to make decisions
on which ones are suitable for their particular project; on the other hand,
if there are to be any real comparisons made, it is often desirable to
do so over a period of weeks or months. I therefore decided that the most
suitable time to start would be during the second half of the summer term
of the first year of the two-year course.
I allowed pupils to be out of school during one or two lesson periods,
in groups of two or three, in order to collect the data; they were given
complete freedom to collect the data how and where they wished, provided
that I was informed beforehand where and how they would be collecting it.
This privilege was not abused by any of the pupils. The remainder
of the data had to be collected in the pupils' own time, at weekends or
after school. I had hoped that much of the collection of data could
be carried out during the summer holidays but, in fact, few of the pupils
lived near enough to other members of their group to be able to co-operate
successfully out of school time. This was not helped by the fact
that during term time a long absence by one pupil could hold up work for
several others. However, despite these difficulties, and in spite
of a heavy work-load for fifth-year pupils in other subjects, the projects
did get completed in time.
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Pupil Choice
Having decided when to start on the projects, I gave the class a choice
of either following suggested investigations or choosing ones which related
to their particular interests. I soon became concerned when I found that
a large proportion of the class had selected the same topic-that of price
variation in shops and supermarkets, but my fears proved to be unfounded
as different groups approached the subject from different angles.
Some compared prices between a large supermarket, a small supermarket and
a corner-shop, some compared three supermarkets to find the cheapest one
and others looked at price rises over a period of two or three months,
arriving at a price index which in fact agreed with one from official sources.
Two girls were interested in why people buy particular brands of soap powders
and two more found that shops' own brands of goods were invariably cheaper
than the same goods produced by well-known brand names. The group
that compared shop prices in different areas of the borough of Gillingham
concluded that although one area was cheaper to shop in, this advantage
could be offset by the cost of bus fares if housewives travelled into that
area solely for shopping purposes.
In addition to this popular choice, many other topics were chosen, some
relating to the pupils' own interests. For example, one girl linked
her project with her biology work in which she was comparing the growth
of cultivated with uncultivated plants of the same type. This was
a particularly interesting piece of work in which a number of problems
arose. One was the difficulty of measurement; she started by measuring
the height of the plants in millimetres but then found that the variation
in the soil level made such accuracy impossible and she therefore decided
to use centimetres as her unit of measurement. Some of the plants
then died, thus reducing the number of types of plants for comparison.
She also found that to use the same scale for comparing the heights of
two different types of plants meant that they could not be shown on the
same graph, so she decided to compare the increase in height rather than
the height itself. Finally, she expressed surprise that the graphs
approximated to a normal curve, whereas she would have expected to see
a progressively larger increase in height as the plants grew taller.
One of these graphs is shown in Fig. 1; the lack of growth between
weeks 2 and 3 was apparently due to a particularly hot and dry spell of
weather.
Figure 1
Figure 2 shows a comparison between the total growth of different
plants in which any difference between cultivated and uncultivated plants
appears to be no more than might be expected by chance. Of course,
the pupil realised that much larger samples are needed to provide accurate
results but she learnt enough about the problems of making statistical
comparisons to make the project worthwhile.
Figure 2
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Which Topics?
The following investigations were carried out by the group of 24 pupils:
Price variation in shops and supermarkets.
Investigation of short-term memory.
Favourite sports of school pupils.
Experiments with dice; different distributions obtained from various numbers of dice and from biased dice.
Investigation of eye colouring of parents and their children.
Comparison of the growth of herbs in cultivated and uncultivated conditions.
Telephone numbers-are they random?
The predictability of football team results.
Comparison of the performances of various makes and types of motorcycles.
Which magazines give the best value for money?
Investigation into the wearing of spectacles by school pupils.
The distribution of boys and girls in 4-children families.
The popularity of various newspapers and their value for money.
Investigation into the age and makes of cars in present use.
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Organising a Project
It is important that emphasis should be placed on the written work
which accompanies the project work, as this is an area which secondary
school pupils often find difficult. I therefore asked for the written summary
to contain four sections:
1 . Statement of aims (about 50 words).
2. Data. Tables and diagrams should be fully labelled.
Written work should explain how it was collected, what precautions were
taken in collection, what difficulties were encountered and any other relevant
details.
3. Analysis of results.
4. Conclusions. This should contain implications and critical
comments and should be about 100 words in length.
One problem which arises when the first project is about to be started
is that most secondary school pupils find difficulty in formulating their
aims. It is important that each pupil limits himself to one aim and
that he keeps it as simple as possible in the
first instance. In order to help them to think clearly about
their aims, I first of all gave
them the following four questions to answer about their chosen topic:
1 . What sort of data should I collect?
2. Why am I collecting it?
3. What am I going to do with it?
4. How am I going to collect it?
Having answered these, they set about collecting data or writing questionnaires.
The class of 24 pupils split up naturally into groups of two or three with
similar interests, which lightened the task of data collection considerably,
with the added advantage that data could be collected from different areas
of the borough by the two or members of a group.
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The Results
The experience of pupils who are collecting data or distributing questionnaires
leads to an awareness of bias it is so much easier to ask questions of
people who are not in a hurry or who are in sympathy with the topic being
pursued. One girl commented on the rudeness she met from a shopkeeper
and also on her embarrassment when collecting prices in a supermarket,
caused by stares from the assistants. Another store only allowed
prices to be collected in the presence of the manager. As a result
the pupils became very much aware of problems which arise in the course
of the collection of data and which can sometimes affect their choice of
sample. This was especially true of the projects on price variation;
some goods selected for comparison were out of stock in subsequent weeks.
One group made an unfortunate decision to compare prices of salad cream, but the heat wave which occurred at this time caused all of the shops selected to run out of salad cream completely and it had to be taken off their list of goods. Despite these setbacks pupils completed their work by making sure that they were comparing the same size of product or by making an allowance for size in their calculations. Figure 3 shows one of the graphs produced; this gave me an opportunity to ask the pupil whether she felt that the scale chosen was in fact a suitable one. This topic gave pupils an excellent opportunity to experiment on suitable ways of putting a large amount of information on to one graph in a way that is clear and easy to follow.
Figure 3
Figure 4 is an illustration of how one girl set out a table
to calculate the price index from a selection of goods. The group
decided on the weighting after asking their parents how much of each item
they would buy in the course of one month.
Evidently the family included a dog and a cat! This table provides
a good discussion point as to the possible different results that would
be obtained with a different weighting.
One problem that arose amongst groups using questionnaires was in estimating how many would be needed to provide a reasonable sample. In the investigation of 4 children families it was found that out of 200 questionnaires which were completed only 47 were by families with 4 children. However, the group who issued questionnaires to 12-year old children on the wearing of spectacles found that the large majority were answered by non-users of spectacles. The findings from this survey were that most children only start to wear glasses after having their eyes tested at school, a justification for the school medical service.
It is often difficult to decide how much help should be given to pupils
who are pursuing projects as part of an examination course. I resolved
this problem by first of all giving as much practice as possible beforehand
on the main statistical techniques within the syllabus, and secondly, by
giving help on project work in the form of open-ended questions whenever
possible. This encouraged the pupils to think about what they were
doing and to ask themselves questions about their findings. The result
was that by the time they were ready to start their second project they
needed far less help. They were encouraged to make comparisons and
by the end of the course were acquiring the habit of looking for reasons
to explain their results. One girl summed it up succinctly when she
said, "When we are doing statistics projects, we have to think!"
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