50 Years Of Statistics Teaching In English Schools Some Milestones

 2003 Royal Statistical Society 0039–0526/03/52439
The Statistician (2003)
52, Part 4, pp. 439–474
50 years of statistics teaching in English schools:
some milestones
Peter Holmes
Nottingham Trent University, UK
[Read before The Royal Statistical Society on Wednesday, April 9th, 2003, the President,
Professor P. J. Green, in the Chair]
Summary. Over the past 50 years the amount of statistics in the English school curriculum
has grown from almost nothing to becoming both a major part of the mathematics taught to all
5–16-year-old children and also an integral part of other school subjects. It has also become
well established as a General Certificate of Education advanced level subject and as part of
mathematics and other subjects at this level.This paper traces the major events that have led to
this penetration of the English school curriculum over this period (generally these comments will
also be true for Wales and Northern Ireland, but not Scotland) and attempts to draw out some
lessons that can be learned to make effective future developments in statistical education.
Keywords: Aims of school statistics; Historical development; Lessons to be learned; Project
on Statistical Education; Royal Statistical Society reports on teaching; Teaching statistics in
schools
1. Background
Bibby (1986), pages 79–83, identified some moves in the first half of the 20th century to include
statistics in the school curriculum in England. He suggested that Wishart’s paper (Wishart,
1939) on some aspects of the teaching of statistics (largely at university level) may be seen as a
turning-point in the Royal Statistical Society’s (RSS’s) attitude to statistics and led to the sta-
tistical education boom. It is certainly true that following World War 2 in 1945 there was much
activity in the RSS. E. S. Pearson chaired a committee to report on the teaching of statistics in
universities and university colleges. This was published as a report of Council (Royal Statistical
Society, 1947). In it the committee quotes Darwin (1938) as expressing the hope that
‘generations will grow up which have a facility that few of us at present possess in thinking about the
world in the way which quantum theory has shown to be the true one. The inaccuracies and uncertain-
ties of the world will be recognised as one of its essential features. Inaccuracy in the world will not be
associated with inaccuracy of thought, and the result will be not only a more sensible view about the
things of ordinary life, but ultimately, as I hope, a fuller and better understanding of the basis of natural
philosophy.’
The committee goes on to say that they shared that hope and thought that it may ultimately be
realized through the teaching of statistics in schools.
In the meeting arranged for discussion of this report Wishart (1948) posed the question
‘Should an attempt be made to introduce an elementary course of instruction in statistics into the
normal curriculum of the secondary school?’
Address for correspondence: Peter Holmes, RSS Centre for Statistical Education, Nottingham Trent Univer-
sity, Nottingham, NG1 4BU, UK.
E-mail: Peter.Holmes@ntu.ac.uk

440 P. Holmes
Of three contributors on this point two were very much in favour; one dissented on the grounds
that the secondary school curriculum was overcrowded and, if any time could be spared, he
would rather it went to woodwork, metal-work and drawing. In his summing up of the discus-
sion, Wishart referred to the existence of a syllabus for statistics as a subsidiary subject for the
Higher School Certificate examination. I have not been able to trace this syllabus nor to find
out the number of students who took it.
It was at this time that the first steps were taken to include statistics in the school curriculum
for a wider range of pupils. The first syllabuses came in with General Certificate of Education
(GCE) ordinary (O-) and advanced (A-) level, which replaced the School Certificate and the
Higher School Certificate in 1951.
2. The 1952 report of the Royal Statistical Society
In 1952 the RSS published a report on the teaching of statistics in schools (Royal Statistical
Society, 1952). The committee was chaired by E. S. Pearson and the report followed closely on
the earlier report on teaching at universities (Royal Statistical Society, 1947).
The report was well ahead of its time in considering the teaching of statistics in schools from a
broad educational perspective of what was needed by pupils for their own personal development
(section 4). The arguments were summarized in a later paper (Yates, 1968) as follows.
(a) The most fundamental result of a statistical training is that it encourages a habit of
disciplined thinking about ordinary affairs in terms of quantities (section 7).
(b) The statistician is taught, and the citizen also should learn, to appraise figures critically,
to appreciate their fallibility and limitations, and, in particular, to consider the effects of
the errors with which such figures measure things (section 8).
(c) Students should develop a habit of examining critically and accepting with reserve con-
clusions from numerical data drawn by other people (section 10).
(d) Some of the more elementary statistical devices such as charts, averages and percentages
are widely used in the mass media, and the educated citizen should learn to understand
them. Familiarity with social and economic statistical information is a help towards an
understanding of public affairs (section 11).
(e) Some appreciation of sampling surveys is also needed, since the public is often asked to
accept some result obtained from a sample survey (section 12).
(f) Probability is an idea which has applications, not only in scientific work, but also in daily
life (section 14).
(g) The mathematical specialist will derive satisfaction in finding that statistical theory
applies concepts and methods that he has learnt in his general mathematics (section
25).
I would add to this summary that Royal Statistical Society (1952) also included the following
points:
(h) the argument that the development of a balanced and reflective outlook on figures is a
slow process, and if it is not begun at school, before the child’s mind begins to crystallize,
it may never take place (section 9);
(i) an ability to argue accurately from data is a fundamental need if the person is to be an
active member of society (section 10) and the citizen should learn to appraise figures
critically (section 8).

50 Years of Statistics Teaching 441
It was over 20 years before these ideas were taken seriously for changes in the school curriculum
and over 30 years before they received serious implementation.
To ensure that statistics at school was taught in practical contexts, the committee recom-
mended that the bulk of its teaching should be done in the contexts of other subjects such as
natural science, geography and history, though they also record that some teachers whom they
had consulted thought that statistics would only make headway as a separate subject in the
timetable. The committee also recommended that syllabuses be developed for the sixth form
(pupils aged 17 and 18 years) related to the GCE A-level that had recently been introduced.
In an appendix the committee recorded the way that statistics was included in some GCE
mathematics syllabuses. Of eight examining boards mentioned, four had no statistics at O- or
A-level. Three of the remaining four had some statistics in an alternative ordinary syllabus for
mathematics; three had some statistics in at least one variant of mathematics at A-level.
This makes the position look much more encouraging than it actually was. The following
facts are relevant.
(a) When it was first introduced, the GCE O-level was taken by 17% of the relevant school
population (currently 93% are entered for the General Certificate of Secondary Educa-
tion (GCSE) mathematics).
(b) The alternative syllabuses were taken by only a small minority of those taking O-level
and, typically, were those who had stayed at school after 16 years of age.
(c) In these alternative syllabuses the statistics is not the same as that described by the com-
mittee in the main body of its report; nor does it have the emphasis that they placed on
practical use.
(d) In all except one of the examples given at alternative O-level, full marks could be obtained
without doing any of the statistics questions; the same was the case for two of the three
A-level syllabuses.
2.1. Some lessons to learn
(a) There is a long way from a group of experts, such as an RSS committee, who decide that
something is a good idea to ensuring that it happens in practice.
(b) Good ideas may take a long time to penetrate the public consciousness and to come to
fruition.
(c) An overview of the general nature of statistics and its importance for all pupils is needed
if a balanced provision of statistics in the school curriculum is to be made.
3. The first introduction at General Certificate of Education advanced level
Following the introduction of some statistics into some A-level GCE mathematics syllabuses
described above, a qualification in pure mathematics and statistics was introduced. The first
examination board to do this was the Northern Universities Joint Matriculation Board. The
Assessment and Qualifications Alliance, which was the successor to the Joint Matriculation
Board, reports that the first examinations for this qualification were in 1961. The statistics pa-
per was set as an alternative to theoretical mechanics for students aged 16–19 years who were
specializing in mathematics. The aim was to provide a relevant application of mathematics to
those whose main subject interest was in fields such as geography, psychology and biology. The
other boards followed with their own versions. The Associated Examining Board produced an
A-level syllabus in statistics in 1963. The core content was similar to that of the statistics of the
pure mathematics with statistics syllabus but the students did not have to study mathematics as

442 P. Holmes
such. These courses have their successors today, though their content and approach has changed
somewhat to become more practical and to take in more of the real needs of the user subjects
outside mathematics.
As far as I can ascertain, the courses were developed by mathematicians and some statisti-
cians from departments of mathematical statistics. No specialists from the user subjects were
involved with the development of the syllabus. The syllabuses had to be seen as mathematically
respectable since they carried a qualification in mathematics and they were under the authority
of the boards’ mathematics subject committees.
They were a brave introduction to elementary mathematical statistics, but they were soon the
subject of criticism. Some of these are referred to in Downton (1968). Holmes (1981a) listed the
weaknesses as follows.
(a) The questions tested mathematical principles rather than statistical insight (Barnett
(1982) gave a particularly good example).
(b) Little emphasis was given on the practical implications of the final mathematical conclu-
sions.
(c) Syllabuses were much less useful than they might be for the user subjects.
(d) Neither the syllabuses nor the examinations developed or considered the expertise that
is required in carrying out a long-term investigation.
(a) Involve practical as well as mathematical statisticians in the development of a syllabus.
(b) Take advice from the user subjects about the nature of the statistics that they need.
(c) There is more to statistics than mathematics—it is essentially a practical subject.
(d) Practical statistical skills need to be developed as well as theoretical ones.
4. Primary school developments in the 1960s
4.1. Edith Biggs HMI
During the 1960s, in the move towards introducing ‘modern’ mathematics into schools, there
was a growth of practical data collection, representation and intuitive inference in primary
schools (pupils aged 6–10 years). This was spearheaded by active promotion by Her Majesty’s
Inspectors, the most dynamic of whom was Edith Biggs. She wrote the Schools Council’s bul-
letin number 1: ‘Mathematics in primary schools’ (Schools Council, 1965), which sold 75000
copies in its first year (Fig. 1). There is a chapter on graphical representation in the learning of
mathematics, and most of these graphs are of statistical data. The children were also expected
to collect the data for themselves and to interpret their graphs in real terms. She and others
ran many in-service courses for primary school-teachers where there was the same emphasis
on collecting data for yourself, representing it graphically and drawing (elementary) inferences
from the data. Biggs (1971, 1972) give further details.
4.2. Nuffield primary mathematics
The major curriculum development for primary school mathematics at this time was funded by
the Nuffield Foundation and directed by Geoffrey (later Sir Geoffrey) Matthews. Their motto
was ‘I hear and I forget; I see and I remember; I do and I understand’. To ensure that teachers
were both aware of the philosophy behind their teaching and knew what they were teaching and
why, they set up a network of teachers’ centres throughout the country.

Fig. 1. Figure taken from Schools Council (1965), page 71 (Crown copyright: reproduced with the permis-
sion of the Controller of Her Majesty’s Stationery Office and the Queen’s printer in Scotland)
These centres became a resource for the teachers and a base from which they organized many
in-service courses. They produced many activities for teaching primary mathematics. Activities
in probability and statistics occurred in several of their books for teachers (Nuffield Mathemat-
ics Project, 1967). Among other things the book on pictorial representation included a list of
about 75 topics with indications of what might be appropriate for different ages of pupil. They
specifically refer to work connected with geography, science and social surveys. There was also
an individual book on probability and statistics which was based on practical work (Fig. 2)
(Nuffield Mathematics Project, 1969). The text-book for teachers in training by Williams and
Shuard (1970) gives a good feel for what was happening in primary schools at that time.
(a) Primary school children can learn and enjoy elementary probability and statistics.
(b) It is possible to begin to develop early ideas of probability and inference at this age.
(c) Pupils learn concepts better if they are introduced in a practical way and calculations are
deferred.
(d) Teachers need to be enthused and trained to teach new topics and this takes time and
money.
(e) Well-provided local teachers’ centres were a major factor in the success of the Nuffield
Mathematics Project.

444 P. Holmes
Fig. 2. Page 39 from Nuffield Mathematics Project (1969) (copyright of the Nuffield Foundation and repro-
duced with permission)
5. Secondary developments in the 1960s
During the 1960s there was a revolution in the teaching of mathematics in the secondary schools.
Many groups were active in developing a modern mathematics syllabus and producing text-
books for their syllabuses. Groups included the Midland Mathematics Group, the Kent Mathe-
matics Project, the Mathematics in Education and Industry Project and the Inner London
Project known as ‘SMILE’. The most active of these groups was the School Mathematics Pro-
ject (SMP). This was the creation of an enthusiastic group of teachers, mostly working in some
of the better-known public schools. The SMP books were the first mathematics texts to include
illustrations and cartoons, which made them more attractive to teachers and pupils (School
Mathematics Project, 1969). The SMP writers saw probability and statistics as an important
part of modern mathematics and were concerned to develop a proper understanding of the
basic concepts and techniques. Previously the only statistical technique in the standard mathe-
matics course was ‘averages’, which was treated from a very mathematical point of view. The
SMP, and others, introduced a probability and statistics strand into the mathematics courses
for secondary pupils (aged 11–16 years). The secondary strand tended to emphasize theoret-
ical probability and was weak on practical statistics but included many examples using real
data as well as fictitious data. Fig. 3 shows an example where pupils are asked to look at real

Fig. 3. Abstract from page 33 of book 2 of School Mathematics Project (1969) (copyright of the SMP and
reproduced with permission)
newspaper articles. It tended to be focused on statistical techniques; some references were made
to the practical uses made of statistics in everyday life but less on statistics in other school
subjects.
The syllabus included tables, tally charts, bar-charts, the mean, median, mode, range, use of
statistics in newspapers, trends in time series of data on things such as telephones, and pictorial
misrepresentations of data. Probability was introduced as experimental probability and theo-
retical probability and went as far as combinations of events by using tree diagrams. There was
a chapter on thinking statistically which looked at common statistical patterns and attempted
to introduce the normal distribution. Book 5 (School Mathematics Project, 1969) ventured on
an introduction to the idea of significance.
Fig. 4 shows the use of real data in terms of a breakdown of expenditure of tax revenue in
1962, from question 6, and the use of fictitious data from the ‘Richkwick Investment Company’,
in question 5. Even with its shortcomings, this first SMP publication was a major step towards
including some statistics in the main curriculum for a large number of secondary school pupils.
Although it started in public schools it quickly spread into selective state schools and, by the
end of the 1960s, books were being produced to cover the lower level Certificate of Secondary
Education and so the material became part of many secondary modern and comprehensive
schools’ mathematics programmes.
(a) When good enthusiastic teachers are given freedom to experiment, they can change the
curriculum for good and enthuse both their pupils and other teachers.
(b) Plenty of probability and statistics can be done by secondary school pupils.
(c) Statistics is more than a set of techniques; probability is more than coins and combinat-
orics.
(d) A school needs to decide what is an appropriate education in statistics for all, and how
it can be included.
(e) First attempts at introducing new topics into the school curriculum are almost bound to
be flawed. It is best if they can be tried out with small groups of pupils in a context where
quick revision is possible and without penalizing the pupils involved.
(f) Interesting activities are not enough; the topics must link together to form a coherent
whole.

446 P. Holmes
Fig. 4. Abstract from page 37 of book 2 of School Mathematics Project (1969) (copyright of the SMP and
reproduced with permission)
6. The 1968 Royal Statistical Society meeting on the ‘Teaching of statistics
in schools’
In 1964 there had been a symposium on the teaching of statistics (Royal Statistical Society,
1964) but this had concentrated on the teaching at universities and the training of statisticians
for government, economics and business, and medical work. It only had incidental implica-
tions for school teaching. More importantly for school work, in May 1968 there was an RSS
open meeting at which the RSS Committee on the Teaching of Statistics in Schools, chaired by
G. B. Wetherill, presented its interim report (Yates, 1968) and Downton (1968) presented his
response paper. Afterwards there was a wide-ranging discussion. The theme of the two papers
was essentially on what should be an appropriate A-level syllabus in statistics. Both the com-
mittee and Downton sought to define a course which required only O-level mathematics and
later discussants queried whether this was feasible.
The committee referred to a change of view since Royal Statistical Society (1952). Since,
they claimed, the incorporation of statistics teaching into scientific and other subjects was not
happening, it was feasible to introduce statistics as a subject in its own right. After a pass-
ing reference to the existence of an O-level in statistics, the rest of the report was on A-level.
They suggested that such a course should not have a heavy emphasis on theory; nor should it
emphasize computational methods but should
‘make basic concepts clear and . . . will show how these concepts are used in the interpretation of
experimental and observational data’.
They then gave a course outline for such a syllabus. Downton disagreed with their proposals and
considered their syllabus to be adding probabilistic experiments to a conventional syllabus. His
view was that statistical thinking requires high level skills and that an appropriate course could
be developed based on the different probability distributions as models for practical situations
spread over various fields of application.

The discussion that followed showed a wide range of views from a large number of partic-
ipants. Many of the school-teachers were disappointed that so little had been said about the
teaching of statistics before A-level.
This meeting raised greatly the profile of teaching statistics in schools among RSS Fellows.
The following comment by Downton was repeated by Wetherill in his reply to the discussion:
‘A substantial project is called for to investigate the whole question of teaching statistics in schools’.
This was to have major repercussions in the next few years.
7. The Schools Council Project on Statistical Education, 1975–1980
7.1. The Committee on Statistical Education
Late in 1967, Toby Lewis and Vic Barnett, both Fellows of the RSS who had been working
over the years to help teachers of A-level statistics, gathered a group of people concerned with
the teaching of statistics at school level and formed themselves into an action group called the
Committee on Statistical Education. Most of them were Fellows of the RSS and the group in-
cluded not only Vic Barnett and Toby Lewis but also Frank Downton, Dennis Lindley, Arthur
Owen HMI and Alan Stephenson of the University of London Schools Examination Board.
The group had the encouragement of the RSS and the Institute of Statisticians but was not a
formal committee of either body. They looked at the current position of probability and sta-
tistics in schools and were not convinced that what was being taught was appropriate. Their
aim was to obtain funding for a major development programme that would consider the role
of probability and statistics in school courses for pupils from the age of 6 to 18 years. In the
event they were successful in obtaining a major grant from a quasi-governmental body called
the Schools Council to investigate and develop materials for the main secondary school (pupils
aged 11–16 years). This project, the Schools Council Project on Statistical Education (POSE),
ran for 5 years, from 1975 to 1980, and had an overall budget of about £220000. It was based
in the Department of Probability and Statistics at the University of Sheffield and directed by
Peter Holmes.
7.2. Brief of the Project on Statistical Education
The aims of the project, as defined by the Schools Council, were the following:
(a) to assess the present situation in statistical education, regarding content, level, motivation
and teachers’ attitudes, and to relate these to the position of statistics outside schools;
(b) to survey the needs of teachers, whether they are teaching statistics as a specialist subject
or working in a related field, and the implications for both initial and in-service needs;
(c) to devise detailed proposals for implementation of the teaching ideas;
(d) to produce teaching materials such as notes for teachers, descriptions of experiments,
work sheets and sets of examples.
The results of the research carried out to cover the first two points of this brief are summarized
in Holmes et al. (1981). The project team found that only between 7% and 10% of all second-
ary schools were entering candidates for GCE O-level or Certificate of Secondary Education
syllabuses in statistics. Of these schools an average of 12.5% and 22% respectively of 16-year-
old pupils were entered for these examinations, so statistics as such was taken by only a small
percentage of the school population.
On the positive side the project team found that a growing amount of statistics was being
taught in mathematics lessons and that also much statistics was being taught in other subjects

448 P. Holmes
across the school curriculum. But when the content was considered more carefully the position
was not as encouraging. Holmes (1981b) noted that the statistics included in mathematics was
there because it was seen as an element of modern day mathematics, so it was the mathematical
techniques that were emphasized; there was very little real data or application to real problems.
The statistics was included in the other subjects across the curriculum because it was seen as
useful for those subjects and so the difficulties of the concepts being used were not always appre-
ciated, and the order in which the statistical ideas were introduced was often not appropriate.
For example the team found the use of Spearman’s rank correlation coefficient, together with
the formula
1 −
6

d2
n3 − n
,
in a geography lesson for 13-year-old pupils.
7.3. Philosophy of the Project on Statistical Education
In developing their teaching material, the team summarized the aims of school statistics in two
global aims.
(a) Children should become aware of and appreciate the role of statistics in society, i.e. they
should know about the many and varied fields in which statistical ideas are used, including
the place of statistical thinking in other academic subjects.
(b) Children should become aware of, and appreciate, the scope of statistics, i.e. they should
know the sort of questions that an intelligent use of statistics can answer, and understand
the power and limitations of statistical thought (Schools Council Project on Statistical
Education, 1980a).
To put this philosophy into practice the project team developed a large amount of teaching
material, which was widely tested in a variety of schools, and published under the title Sta-
tistics in Your World (Schools Council Project on Statistical Education, 1980b). The material
covered a wide range of applications of statistics in society, including, for example, equal pay,
smoking and health, quality control, the national census, Premium Bonds and the retail price
index. Each unit developed statistical techniques in a practical context. Fig. 5 shows a page
from ‘Choice or chance’, a unit on probability. Fig. 6 shows a page from ‘Multiplying people’,
a unit on population growth. It was the first teaching material in the world aimed at developing
a statistical awareness and ability among secondary school pupils through a practical approach
using examples of statistics from everyday life.
7.4. What is statistics?
At the time of the project, the prevailing perception of statistics in school mathematics cour-
ses, as shown by text-books and syllabuses, was that statistics was a set of techniques such as
bar-charts, pie charts, scatter diagrams, the mean, median, mode and interquartile range. To
the project team this seemed like defining human biology as only the study of the skeleton.
As such, these techniques had no life in them and school courses did not give a flavour of the
importance and the ubiquity of statistics in all aspects of life. The project team considered it
important to have a broad view of statistics so that pupils could gain an insight into the nature
of the subject.
One way of looking for a definition of statistics is to look in breadth at what statisticians
do. Any definition of statistics must be sufficiently broad to encompass the work of academic

Fig. 5. Abstract from page 12 of Schools Council Project on Statistical Education (1980b) (copyright of QCA
Enterprises Ltd and reproduced with permission)
statisticians, applied statisticians in all fields and governmental and official statisticians. The
team took the following as a working definition.
‘Statistics is a practical subject devoted to obtaining and processing data with a view to making state-
ments which often extend beyond the data. These statements are called inferences and take the form
of estimates, confidence intervals, significance tests etc. Statistics is concerned with the production of
good data, and this involves consideration of experimental designs and sample surveys. It has its origin
in real data and is concerned with the processing of data in the widest of contexts and with a wide
variety of applications such as social, administrative, medical, the physical sciences and the biological
sciences’ (Schools Council Project on Statistical Education, 1980a).
7.5. Why teach statistics to everyone?
The POSE team thought it better to consider general educational reasons for incorporating
statistics into the school curriculum and then to see the implications for what sort of statistics
should be included and where and how they may best be implemented.
Why should we teach statistics to all? Here are the reasons of the Schools Council Project.
(a) Statistics is an integral part of our culture.
(b) Statistical thinking is an essential part of numeracy.
(c) Exposure to real data can aid personal development and decision-making.

450 P. Holmes
Fig. 6. Abstract from page 15 of Schools Council Project on Statistical Education (1980b) (copyright of QCA
Enterprises Ltd and reproduced with permission)
(d) Statistical ideas are widely used at work after school.
(e) Early exposure can give sound intuition which can later be formalized.
In this they were in line with the reasons given in Royal Statistical Society (1952).
7.6. Trying to influence the curriculum
The material that was produced by the Schools Council was highly innovative and was well test-
ed in a wide variety of schools with a wide variety of teachers. It was well received by those who
used it. It was not, however, part of the curriculum examined; it did not lead to a qualification
at the end and it did not easily fit into mathematics lessons geared to the existing syllabuses, so
it was not widely taken up. At that time there was no national curriculum so the material had
to be marketed and sold on its own merits.
(a) Producing innovative material is very costly in time and people. New ideas must be
developed and properly tested to ensure their appropriateness and validity.
(b) If philosophy is to be put into practice, teachers need teaching material which embodies
the philosophy.
(c) To change the teaching in schools requires more than good material; you need to find
the levers in the system and to use them. (At the time the major levers were the exter-
nal examinations taken at 16 years of age. Although such examinations in statistics did
exist they were not widely taken; nor were they sympathetic to the philosophy behind

the POSE. A syllabus that was more in line with the POSE philosophy was developed
shortly afterwards by the Northern Examining Authority (1988) working with the project
director as chairman of examiners.)
(d) Major changes of philosophy may take a considerable time to be accepted; a long-term
strategy for acceptance is needed.
8. Changes at advanced level in 1970s and 1980s
8.1. Introduction of project work
Following the criticisms of the earlier material for 18-year-old pupils, the University of London
Schools Examination Board introduced an element of practical or project work into its A-level
syllabus for mathematics and statistics in the mid-1970s. Since this practical and project work
was not assessed directly, it was not taken as seriously as the theoretical aspects of the course.
In 1978 the Joint Matriculation Board introduced an A-level in statistics that was designed to
have students work practically through the whole process of doing a statistical investigation and
to develop the global skills that are associated with this process. To emphasize the importance
of this practical approach, and to encourage teachers to put the theoretical work in practical
contexts, the course required a compulsory project which was directly assessable. Although this
faced some opposition from examiners in mathematics, on the grounds of decreased reliabil-
ity of marking, the counter-argument that the assessment was more valid was accepted. This
particular syllabus was not like either of the two possibilities suggested by either the RSS 1968
report (Yates, 1968) or Downton’s alternative view. It did not, though, require candidates to be
studying mathematics at A-level at the same time. It did not attract large numbers of entries.
Teachers coped well with the teaching, but many were put off from trying—the other route of
pure mathematics with statistics, and no project, remained more popular with schools.
8.2. Introduction of advanced supplementary levels
In 1989 advanced supplementary (AS-) syllabuses in statistics were introduced by most of the
GCE boards as part of a move to try to broaden A-level studies. These syllabuses were intend-
ed to have half the content of an A-level but to require the same depth of thinking. Many of
these played down the mathematics side of the subject and increased the emphasis on the design
of questionnaires, sample surveys and designed experiments to collect good data. In this they
took more account of the needs of user subjects. The syllabus from Joint Matriculation Board
(1989) included an assessable project that was similar to that required for its A-level syllabus in
statistics.
(a) If you want project work to be taken seriously you must assess it.
(b) If you want project work to be done it must not be an option.
(c) It is not easy to set syllabuses that meet the needs of all user subjects—different subjects
require different approaches and different topics.
9. ‘Mathematics counts’: the Cockcroft report
9.1. Influence of the Project on Statistical Education and the Royal Statistical Society
In 1978 the Government set up an enquiry into the teaching of mathematics in schools under

452 P. Holmes
the chairmanship of Sir Wilfred Cockcroft (Cockcroft, 1982). The terms of reference for the
committee were
‘to consider the teaching of mathematics in primary and secondary schools in England and Wales, with
particular regard to the mathematics required in further and higher education, employment and adult
life generally, and to make recommendations’.
The committee included probability and statistics as part of their consideration of math-
ematics. Their findings on probability and statistics were strongly influenced by the Schools
Council’s POSE and the RSS Education Committee from whom they received evidence (Royal
Statistical Society, 1979). Paragraphs 774–781 dealt specifically with the teaching of probability
and statistics, though there are other references throughout the report.
Two paragraphs in particular reflect the POSE–RSS influence.
‘§775 Statistics is not just a set of techniques, it is an attitude of mind in approaching data. In particular
it acknowledges the fact of uncertainty and variability in data collection. It enables people to make
decisions in the face of this uncertainty.’
‘§781 Statistical numeracy requires a feel for numbers, an appreciation of levels of accuracy, the making
of sensible estimates, a common-sense approach to data in supporting an argument, the awareness of
the variety of interpretation of figures and a judicious understanding of widely used concepts such as
mean and percentages. All these are part of everyday living.’
The committee also suggested that each school should have a statistical co-ordinator. The
recently set up Centre for Statistical Education at the University of Sheffield obtained a grant
to produce a handbook for such co-ordinators (Holmes and Rouncefield, 1989), but very few
schools took up this idea.
9.2. Influence on Government decisions
In its turn this report influenced the Government who decided, for the first time in British
history, that there should be a national curriculum. The mathematics content reflected the
recommendations of the Cockcroft report.
10. Further developments at Sheffield
Following the success of the POSE and the international reputation that was coming to Shef-
field because of this work, several other initiatives to provide resources for school teachers were
funded and based in Sheffield.
10.1. The journal Teaching Statistics
In 1978 the Teaching Statistics Trust was set up with Joe Gani, Vic Barnett, Peter Holmes and
the treasurers of the RSS and the Institute of Statisticians as Trustees. The aim of the trust was
to promote the teaching of statistics at the school level, particularly by publishing a journal
called Teaching Statistics. Financial backing came from the RSS, the Institute of Statisticians,
the Applied Probability Trust and the International Statistical Institute. The first issue of the
journal was published in January 1979 with Peter Holmes as the first Editor (Fig. 7).
It has continued to publish articles of wide applicability with an emphasis on practical help
to pre-university teachers of statistics in all disciplines ever since. It is difficult to quantify the
effect that it has had on teaching, but there is no doubt that Teaching Statistics has raised the
profile of statistics in the school curriculum and encouraged continued thinking on the ways
that it can best be taught.

Fig. 7. Contents page of volume 1, number 1, of Teaching Statistics (reproduced by permission of the
Trustees of the Teaching Statistics Trust)
10.2. The first International Conference on Teaching Statistics
In 1978 the International Statistical Institute’s Education Committee set up a task-force, under
the chairmanship of Lennart Råde, to organize international conferences on teaching statistics.
Because of the reputation of the University of Sheffield in this area, and because of the expertise
that the Department of Probability and Statistics had in running conferences, the task-force
decided to hold the first International Conference on Teaching Statistics in Sheffield in August
1982. This conference attracted many teachers and lecturers from the UK, as well as from more
than 60 other countries, and so raised the profile of teaching statistics and generated even more
interest in teaching statistics in the UK (Grey et al., 1982). Successive International Conferences
on Teaching Statistics have been held around the world every 4 years.
10.3. The Centre for Statistical Education
The activities developing from the POSE at the University of Sheffield were carried out under
the umbrella heading of the Centre for Statistical Education. This Centre came into formal
existence as a joint Centre of the University of Sheffield and Sheffield Hallam University in
September 1983. The co-chairmen were Vic Barnett of the University of Sheffield and Warren
Gilchrist of Sheffield Hallam University. The director was Peter Holmes.
Although the Centre was interested in statistical education for all ages, the focus of its activ-
ities was at the school level. It ran several projects aimed at producing material to help teachers
to make their teaching more interesting and stimulating.
The Statistical Education Project 16–19, funded by the Leverhulme Trust, ran from 1981 to
1984. It conducted a survey of the statistics being used in industry, commerce and Govern-
ment by employees starting work at 19 years of age without specialist statistical qualifications
(Holmes, 1985) and then set up working parties to produce teaching material for statistics in
economics (Holmes, 1987), geography, science, business and psychology (Leverhulme Project
on Statistical Education 16–19, 1987).
The Department of Education and Science funded a 2-year project to encourage practical
work in teaching A-level statistics. The project officer was Mary Rouncefield and the material
was published as a text-book Practical Statistics (Rouncefield and Holmes, 1989a) with a teach-
ers’ guide (Rouncefield and Holmes, 1989b). Mary followed this project with a study into the
role of the statistics co-ordinator as envisaged by the report of the Cockcroft committee. This
led to a handbook for use by teachers entitled From Cooperation to Coordination (Holmes and
Rouncefield, 1989).
The Nuffield Foundation funded a project on using databases and spreadsheets to teach
statistics across the curriculum. Mike Hammond was the project officer and the material was

454 P. Holmes
Fig. 8. Activity 18 from Hammond (1990a)
extensively tested in schools and published as a series of worksheets in book form under the title
Fifty Things to do with Databases and Spreadsheets (Hammond, 1990a) together with a series
of handbooks for in-service courses in different subjects (Hammond, 1990b,c,d, e). Fig. 8 gives
an example.
With the advent of the national curriculum there was a call for practical activities that could
be used to teach the probability and data handling strands. The Universities Funding Coun-
cil financed a 1-year project to produce books to meet this need. The project officer was Glyn
Davies who wrote the two books Practical Data Handling, book A, and Practical Data Handling,
book B (Davies, 1993a, b) (Fig. 9).
When the University of Sheffield indicated that they would be closing down the Centre for Sta-
tistical Education at the end of 1995, the RSS decided that this work should continue and estab-
lished the RSS Centre for Statistical Education at the University of Nottingham. The two centres
overlapped for one term and then the resources of the Sheffield centre were moved to Notting-
ham. In 1999 this moved to Nottingham Trent University where it currently operates and as part
of its portfolio of activities is continuing the Sheffield tradition of being proactive at school level.
In the context of school statistics, a national Centre for Statistical Education is an important
resource since it can
(a) be the focus for curriculum development and research into statistical education,
(b) respond quickly to immediate needs,
(c) keep high the profile of statistics teaching both nationally and internationally,
(d) give authoritative advice on teaching, curricula and examinations in statistics, and
(e) consider developments, such as those in information technology, that have implications
for teaching statistics and make appropriate provision.
11. The first national curriculum in England and Wales
11.1. Background
In July 1987 the Department of Education and Science and the Welsh Office published a con-
sultation document for a national curriculum for pupils aged 5–16 years (Department of Edu-

Fig. 9. Activity 62 from Davies (1993a) (reproduced by permission of Hodder Arnold)
cation and Science, 1987). Mathematics was to be one of the foundation subjects and a working
group was set up to develop proposals for attainment targets (content) and programmes of
study (approach to teaching). The Department of Education and Science and the Welsh Office
(Department of Education and Science, 1988) published their proposals for mathematics, based
on the working group’s recommendations, in August 1988 and the revised proposals came into
force on August 1st, 1989.
11.2. Content and approach
The design of the national curriculum in mathematics reflected both the process of mathemati-
cal thinking and the technical content of a mathematical syllabus. Initially the programme was
described under 14 strands—one of which was probability and three were statistics (called data
handling) spanning all ages from 5 to 16 years. In a major revision (Department of Education
and Science, 1991) these 14 attainment targets were reduced to five:
(a) using and applying mathematics;
(b) number;
(c) algebra;
(d) shape and space;
(e) data handling;
but the content was essentially unchanged.
The technical content was described in great detail under attainment targets with levels 1–8
and exceptional. The programmes of study made little reference to the real life applications of
statistics or to the use of real data. Non-statutory guidelines for teaching the course were pro-
duced (National Curriculum Council, 1989) which included some excellent ideas such as relating
school policy across the school curriculum and giving examples of cross-curricular approaches

456 P. Holmes
and activities. Since they were not part of the assessment, they were not taken as seriously as
the main document.
11.3. Assessment and its effects
To check its effectiveness, the national curriculum included very detailed assessment tests so
that each pupil could be identified as having reached a particular level. Over a couple of years
or so, the assessment tests so dominated the teaching that the non-statutory guidelines were
effectively ignored. The emphasis of the assessment was whether the pupils could answer very
clearly defined questions relating to very specifically detailed statements in the attainment tar-
gets. Teachers had to make sure that their pupils could answer the test questions, so they taught
to the test. This meant that, in statistics, there was great emphasis on teaching the techniques; any
global views of the importance of statistics and the nature of statistical thought were relegated
to secondary importance.
(a) It is possible to include a substantial amount of probability and statistics as part of the
main school mathematics curriculum.
(b) If you have statutory and non-statutory parts of a curriculum, the statutory ones will
eventually dominate.
(c) External assessment moulds the teaching; if you assess atomistically you will obtain
atomistic teaching.
(d) If you do not assess global skills and understanding they will not be taught.
(e) Integration of statistics teaching across the curriculum requires a whole school strategy.
Statistics must not be seen solely as part of the work of the mathematics department.
12. The current position in the national curriculum
12.1. Changes in the programmes of study
The current national curriculum in mathematics (Department for Education and Employment,
1999) has rationalized the original structure. There is one strand in data handling, which in-
cludes probability, another in number and algebra, another in shape and one on mathemat-
ical thinking. As well as the technical content, which is still listed under attainment levels,
there is a statutory programme of study which indicates how the material is to be taught.
The assessment process is meant to be based on these ‘Programmes of study’ which are set at
four key stages. Stages 1 and 2 are for primary schools; 3 and 4 are for secondary school pupils.
The RSS Education Committee offered to help with the revision of the programmes of study
for this version of the national curriculum. As a result of this co-operative attitude, two Fel-
lows were part of the team that carried out this revision for the Qualifications and Curriculum
Authority (Qualifications and Curriculum Authority, 1999). At key stages 3 and 4 the pro-
gramme of study for data handling is clearly written round the statistical process described in
the cycle
Specify the problem
Collect the data
Process and represent
Interpret and discuss

The instructions are that pupils should be taught to carry out every aspect of the handling
data cycle by using the techniques that are appropriate to the relevant key stage. Pupils are
to be taught to communicate mathematically by using diagrams linked to related explanatory
text. They also must make decisions about problem solving strategies to use in their statistical
work.
12.2. Technical content
The headings for the detailed syllabus for key stage 3 (pupils aged 11–14 years) are
(a) using and applying handling data,
(b) problem solving (includes a description of the cycle), communicating and reasoning,
(c) specify the problem and planning,
(d) collecting data,
(e) processing and representing data, and
(f) interpreting and processing results.
A section entitled ‘Breadth of study’ at the end of each key stage is included for all mathemat-
ical strands. For key stage 3 it includes the statement that pupils should be taught knowledge,
skills and understanding through practical work in which they draw inferences from data and
consider how statistics are used in real life to make informed decisions and that address increas-
ingly demanding statistical problems.
This is emphasized even further at key stage 4 for the foundation strand (those who may
not be expected to do any more mathematics). These pupils, it says, should be taught about
the major ideas of statistics, including the identification of appropriate populations, obtaining
a representative sample to draw inferences about populations, different measurement scales,
probability as a measure of uncertainty, randomness and variability, an awareness of bias in
sampling and measuring, and inference and its use in making decisions.
Suitably interpreted, this can be considered as a reasonable summary of the major ideas in
statistics and statistical thinking that are appropriate for pupils of this age.
In addition there is a section emphasizing the strong links to be made to the use of statistics
in society. Three points made here are that
(a) through problems and investigations pupils should gain insight into how statistics are
used in real life to make informed decisions,
(b) pupils should be introduced to important uses of statistics in society and
(c) pupils should interpret statistics from society, including index numbers (general index of
retail prices), time series (population growth) and survey data (national census).
12.3. Statistics across the curriculum
It is not only in mathematics that statistics appears in the national curriculum. Holmes (2001a)
gave details of the amount of statistical thinking that is required in subjects such as science,
geography and history, and across most of the school curriculum. Since these syllabuses were
all developed independently there are discrepancies between the level of statistical competence
that is required in different subjects at the same age. We still have the problems of integrating
all this teaching so that the statistics is well taught and the pupils gain an integrated view of
statistics.
12.4. The present position
Statistics (called data handling, a serious understatement of the ideas that are to be developed) is

458 P. Holmes
now well established as a part of the national curriculum in mathematics. How well it is taught
and learned will depend on the teachers and their resources. The national numeracy strategy,
which started in primary schools in 1998 but is now effective in secondary schools, is making
help and guidance available (Department for Education and Skills, 2001). Text-books need to
incorporate the ideas that are described in the various programmes of study. Crucially the teach-
ing will reflect the way that the material is assessed. Officially the assessment should be based on
the programmes of study, and it remains to be seen how much those responsible can abandon
the mentality of assessing individual techniques of the attainment levels and move towards the
broader skills described in the key stages.
13. The present and the future
13.1. The present position at General Certificate of Secondary Education and General
Certificate of Education advanced level
The national curriculum is now the syllabus for GCSE mathematics and, as part of the as-
sessment, from 2003 all candidates must carry out a practical project in data handling. These
mathematics syllabuses are administered in England by the Assessment and Qualifications Al-
liance (Assessment and Qualifications Alliance, 2001), Edexcel (Edexcel, 2001) and Oxford,
Cambridge and RSA Examinations (Oxford, Cambridge and RSA Examinations, 2001). The
data handling project carries half the marks that are allocated to the data handling part of
the syllabus. The general instructions from the Qualifications and Curriculum Authority to the
examining boards require centres to be given the option of choosing their own topics for these
projects. In fact, all the boards are giving board options, and it is clear that they are applying
pressure on schools to use these options. One of the boards is reported to be constructing a
large, fictitious, database which candidates are expected to use in their projects. This is alien to
the spirit behind using projects, that they should allow candidates to make real inferences in
real contexts. The desire to make assessment manageable is understandable, but there is a real
danger that these projects will become overformalized and so will not encourage or assess the
overall statistical skills that are part of being a statistician. The teaching of data handling in
mathematics will depend on the provision of good teaching material for teachers to use. As was
found in the Schools Council Project, material that covers the ideas described in the programmes
of study is not easy to write. It may be necessary to find resources to provide such material.
The Assessment and Qualifications Alliance has made available a GCSE in statistics (Assess-
ment and Qualifications Alliance, 2000a). The syllabus for this is broad and puts the techniques
in contexts. There are, as should be expected, more techniques than are in the data handling part
of the national curriculum in mathematics and there is explicit reference to the use of statistics
in real life circumstances. Unfortunately, at the moment, the specimen questions (Assessment
and Qualifications Alliance, 2000b) do not reflect the breadth of the syllabus. They are limited
and unimaginative and do not encourage a discussion of the issues that the statistics raise. Yet
it is these practical issues and contexts that make statistics interesting. Most of the questions
concentrate on techniques and the opportunity has not been taken to widen the type of ques-
tion from the fairly narrow sort of question that is asked in mathematics. For example consider
specimen question 5 from the higher paper illustrated in Fig. 10.
It is not so much what it does ask as what it does not ask that is at issue. The scenario men-
tions a managing director wanting to assess the effect on sales. This is never referred to again
in the question. There is nothing on where the weights for the retail price index have come
from, whether they are the relevant weights for people buying his product, whether the items
that he has chosen are the relevant items and so on. It is not just that these questions are not

5. The managing director of a company is keen to assess the impact that retail prices may
have on sales. He therefore obtains, in a summarised form, the following information
from the Monthly Digest of Statistics.
Item Group Single Item
Index 1995
Single Item
Index 1998
Weights
Food 250 291 208
Alcoholic Drink 305 310 77
Tobacco 358 364 38
Housing 308 320 149
Fuel and Light 391 402 67
(a) Show that the total weighted index of retail prices for 1995 is 299 (3 marks)
(b) Work out the equivalent weighted index of retail prices for 1998. (3 marks)
(c) Hence calculate the all item (aggregate) weighted index of retail prices for 1998 using 1995 as
the base year. (2 marks)
(d) Using your earlier results, if the food group were excluded from the calculations in part (c) what
effect would this have had on the resultant index? (2 marks)
Fig. 10. Specimen question from Assessment and Qualifications Alliance (2000b) (reproduced by permis-
sion of the Assessment and Qualifications Alliance)
asked here—they never seem to be asked. The statistical and contextual issues, in contrast to
the narrow arithmetical issues, take a distinctly second place. du Feu (2002) analysed the 11
questions set on the higher level Assessment and Qualifications Alliance GCSE statistics paper
for summer 2001. He states that, although there were 11 different contexts only one contained
real data (though, arguably, there are three). He found nothing in the paper for the biologists,
the geographers, the scientists or the environmentalists.
At A- and AS-level we have many modules in statistics but, apart from an AS-level on the
use of mathematics and the Mathematics in Education and Industry Project’s AS-level on com-
mercial and industrial statistics, they are all part of a mathematics qualification. More of them
do include some practical and project work, but it is still possible to do a substantial part of
statistics in a mathematics course without doing any practical work. No AS-level in statistics is
specifically designed for user subjects; nor is there one designed for general understanding of
the nature and role of statistics such as is available in some US colleges for liberal arts students
(Moore, 2001). Some of the emphasis in earlier AS-level syllabuses on the collection of data,
surveys and design of experiments has been discarded. There is nothing on a deeper reading of
tables of data as described in Abramson (1988).
13.2. Have the lessons been learned?
Throughout this paper I have tried to draw out lessons to encourage continuing improvement
in statistical education. In this section I try to identify which of the lessons have been learned
and to raise points for discussion so that we might see more clearly where to go in the future.
Clearly many things have changed for the better over the past 50 years. To a large extent many
of the things that were envisaged in Royal Statistical Society (1952) have been taken on board
and are in place. Statistics is explicitly recognized as a practical and important subject and it is
important to develop practical as well as theoretical skills. It is firmly part of the primary school
curriculum and can be enjoyed there.
There are still some worries. Now that we have a national curriculum, how will things change?
The flowering of ideas in the 1960s and the eventual selection of what was good and the discard-
ing of that which did not work required two things. These were an environment where teachers

460 P. Holmes
could experiment with different ideas and a climate where they were empowered so to do. With
the current emphasis on school assessment and adherence to the national curriculum, teachers
have been disempowered and demotivated from experimenting. There needs to be a mechanism
wherebyexperimentscanbemadeonchangesintheschoolcurriculumwhichencourageteachers
to be active participants and do not penalize the students who are part of the process. This would
allow continual change and improvement of the national curriculum on the basis of evidence.
The lesson that statistics is an interdisciplinary subject has not been learned. The various
subject revisions in the recent review of the national curriculum all took place on the basis of
what was important in that subject. So we still have discrepancies across subjects about what
techniques should be included at what level and there is still the danger that there is no proper
overview in a school of the received curriculum in statistics.
It has been a feature over the years of the RSS reports on the teaching of statistics that teach-
ers need training. In the 1960s and 1970s this was addressed by the growth in practical in-service
courses and the wide provision through teachers’ centres and support through local authority
subject advisors. In the 1980s and 1990s funds for these were cut and this support network is not
as strong. We still have problems of teachers who are undertrained in statistics and its teaching.
The importance of a national Centre for Statistical Education has been accepted by the RSS
and other sponsors, shown by their continuing funding of the Centre at Nottingham Trent
University, and this facilitates all the points made in Section 10.4.
13.3. The future
The place of statistics in the structure of English schools is still not satisfactory. Royal Statistical
Society (1952) suggested that the place for statistics was with the user subjects. At the time of
the 1968 report (Yates, 1968) the position had changed to suggesting that statistics should be
a subject in its own right in the curriculum. This has not happened in schools. I do not know
of any departments of statistics as such. The de facto position in most schools is that it is the
mathematics department that takes first responsibility for the teaching of statistics. This has be-
come even more the case since the national curriculum in mathematics has included the major
strand of data handling. Linking across the curriculum is still a problem, and the mathema-
ticians’ approach to statistics has its weaknesses as well as strengths. Statistics co-ordinators,
as envisaged by Cockcroft, do not exist. How do we link theory with applications and breadth
of knowledge about the work of statisticians? How do we best achieve a balanced and relevant
statistical education for all, as envisaged by Royal Statistical Society (1952) and by the POSE?
Part of the answer may lie with in-service training.
For many years it has been said that the future of school statistics will be influenced by
the growing availability of computers and software. There is no doubt that these facilities are
becoming more available and it is relatively much easier to obtain real data from the Internet.
Developments such as the RSS Centre’s project CensusAtSchool (Royal Statistical Society Cen-
tre for Statistical Education, 2000) with its large database of pupil responses and wide range of
work sheets and teachers’ notes have made it much easier for teachers to find good material.
The Internet also makes it easier to link across to other subjects in the school curriculum. It
is largely the external assessment that is slowing down this process; examining bodies have not
solved the continuing problem of not being able to assume that all candidates have access to
particular software.
It is to be expected that the statistics that is part of the national curriculum in mathematics
should have a mathematical bias. Even so, the programmes of study show a well-founded attitude
to the subject. This raises the question of the relationship between GCSE mathematics (with a

data handling strand and a data handling project) and a GCSE in statistics, which presumably
should be more rounded and holistic and include much more than mathematical considerations.
At the moment there is a danger that this will be seen as trivial and the whole subject will not be
seen as worthwhile by students at a crucial decision time in their lives. The difficulty here appears
to be, not the specification as such, but the assessment. Examiners are largely drawn from a
background in mathematics with its strong emphasis on the reliability of marking. There is a
move towards having assessed project work, but this increased validity needs to be extended to
the examinations as well. There is a need for much more holistic assessment with things such as
open-ended questions, discussions of issues, short essays, questions requiring more than simple
or technical answers and items relating the data to a real issue in a context. Only in these ways
will we get the assessment encouraging good statistics teaching. These types of assessment are
done in other subjects; why not in statistics?
The price of good statistics teaching is eternal vigilance. If we can encourage teachers, de-
velopers and examiners to incorporate the best of what has been developing over the last 50
years then there is some hope. The major need is to maintain a broad vision of the nature of
our subject and its applicability, and continually to apply this vision to the detail of our school
courses and their assessment.
Acknowledgements
The idea for this paper came from a short talk given by the author at the Golden Jubilee
Celebrations of the International Statistical Education Centre in India, and published in the
proceedings (Holmes, 2001b). This paper is a very much expanded version of the talk and in
writing it I have had much help from many colleagues, particularly those at the RSS Centre
for Statistical Education. Comments from two referees have helped me to improve the paper. I
am aware that in trying to summarize in one paper all that has happened in school statistical
education over 50 years I have had to leave out much detail, and not everyone will agree with
my emphasis on what has happened or be content with some of the omissions. I can only accept
responsibility for the paper and plead fallibility to those who disagree.
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Discussion on the paper by Holmes
F. R. Jolliffe .University of Kent, Canterbury/
It is no mean feat to describe 50 years of statistics teaching in English schools in such detail in one paper,
and there is probably no-one more qualified than the author to have done so. As can be seen from the
many references to Holmes in the paper, he himself has helped to shape statistics teaching in English
schools over the more recent decades of the last 50 years. In fact he has made, and continues to make,
many contributions to statistical education at all levels and in many countries around the world.
As this Ordinary Meeting is the first and last to be organized through the Society’s Education Section,
I feel that it is appropriate to mention some of its history and the contributions that it made to statistics
teaching in schools. In February 1996 the Society’s Council approved the Education Committee’s proposal
to form the Section. It was hoped that the Section would appeal to teachers from the Associate Schools
and Colleges, and the Section’s regulations stated that two Committee members were to be appointed from
those teachers. Recognizing the need to provide meetings for this part of the Society’s membership, the
Education Committee had previously arranged a meeting that took place on June 30th, 1994. About 60
people, mainly school-teachers, attended. The first of the two talks at this prenatal meeting of the Section
was given by Peter Holmes on ‘Reflecting the statistics in society by the statistics we teach in schools’. The
other talk was given by Jim Garbutt, then teaching at a school in York, and was on ‘Motivating secondary
school pupils in statistics’. The Section’s first meeting was held on June 4th, 1996.
The Section arranged a programme of meetings on statistical education issues at all levels and was also
responsible for organizing workshops for school-teachers (previously these had been organized by the
Education Committee). In June 1997 it started to organize workshops for pupils also, with the first a sixth
form day in Belfast. Many of these workshops involved practical work and/or information technology.
In December 1999 the Executive Committee established a team to review the Society’s educational pol-
icy, and in April 2001 Council accepted the team’s recommendations, including one that the Section should
be discontinued. The Section’s last meeting was held on May 1st, 2002. This was a discussion meeting on
recent developments in statistical education in schools and higher education and was held jointly with the
RSS Centre for Statistical Education. The meeting started with a presentation on ‘Enhancing statistical
numeracy in schools for teaching, learning, and assessment’ by Peter Holmes and his colleague Doreen
Connor. They considered how an active approach to teaching statistics, using meaningful data collected
from and by school-children, can enhance statistical skills to produce a deeper understanding of important
principles, and they suggested some methods for evaluating the knowledge gained. The rest of the meeting
was concerned with statistical education at higher levels than school. Thus Peter Holmes was in at both
the start and the end of the Section.
There are important messages under the headings of ‘Some lessons to learn’ in this paper, and many of
these, sometimes with slight modification of wording, apply to statistics teaching at other levels. I particu-
larly like the emphasis that statistics is a practical subject made in Section 3.1 such as ‘involve practical as
well as mathematical statisticians in the development of a syllabus’ and ‘take advice from the user subjects
about the nature of the statistics that they need’. Sadly, some of the lessons have not yet been learnt, as is
noted in the author’s conclusion.
The place of statistics in English universities is not satisfactory either. In recent years some statistics
departments, or even combined mathematics and statistics departments, have closed. Is this partly because

464 Discussion on the Paper by Holmes
courses given by statistics departments to user departments did not develop syllabuses which took account
of their needs? Were courses too mathematical or taught as a set of techniques with little attention paid
to real applications? Is it better if statistics is taught from within the user departments by people who are
knowledgeable in statistics instead of by members of a statistics department? It is easy to say that courses
were lost because user departments did not want to give away full time student equivalents for service
teaching, but would this be so if they had received an excellent service adding value to their graduates? It
would be interesting to have a paper on 50 years of statistics teaching in English universities.
I should like to end on a more optimistic note. The Society’s Careers Promotion Committee is producing
material that is designed to tell school pupils (and others) how useful and exciting statistics is. Look at
http://www.rss.org.uk for details. Perhaps this will help to ensure that our subject has a future for
another 50 years.
I have great pleasure in proposing the vote of thanks.
John Bibby .MatheMagic and University of York/
On being offered this onerous task, I was advised that, as Watson to Peter’s Holmes, I may venture to
take a critical viewpoint and could even stray from the subject as long as not too many people noticed.
For this reason, if for no other, it gives me very great pleasure to second the vote of thanks on this
thought-provoking paper.
The Royal Statistical Society can be justly proud at the role that we have played in enhancing statistical
education in the UK (or, more correctly perhaps, England), and via the International Conferences on
Teaching Statistics and other endeavours in the wider world. However, as Peter points out, much remains
to be done, some lessons have yet to be learned and pride must not breed complacency.
Peter and I first met in the mid-1970s on an interview bench during the halcyon days of the Schools
Council. We were both short listed in connection with the newly funded Project on Statistical Education.
Even then Peter displayed maturity of outlook and a clear focus, whereas I was still in the wishy-washy
days of new enthusiasm at the Open University. Needless to say, Peter was appointed, although I was glad
to be able to work with him on the project in a very small measure.
Peter has outlined the successes of the project and many other subsequent endeavours which he and his
colleagues have been involved in. Among these must be counted the dramatically improved position of
statistics in the school curriculum, and the panoply of publications and projects that are associated with
Holmes, Barnett and colleagues.
I am of course delighted that statistics is now firmly rooted in the school curriculum (even if it is often
called ‘data handling’) and I acknowledge the role of Peter and his colleagues in achieving this.
However, as we are discussing history, it behoves us to ask to what extent these dramatic changes resulted
from the Schools Council and subsequent projects, and to what extent they were due to exogenous or soci-
etal factors.
Undoubtedly the most correct answer is ‘a mixture’. The time was ripe for change; otherwise the Schools
Council and other sources of funding would not have been forthcoming, whatever Vic Barnett’s persuasive
abilities.
But what were the contemporary changes outside these projects—and indeed outside the educational
system more generally—that led to statistics’s heightened role?
One thinks of economic supply and demand and the evolving professions, as well as technological and
other factors. Also, there was a changing consciousness of the need for numeracy and statistical literacy
and for science generally—culminating perhaps in today’s mania where the rule is ‘if it moves, count it’
(and the converse, ‘if it is difficult to measure, ignore it’).
Perhaps in his response, Peter could address these environmental issues in somewhat more detail.
Peter noticeably does not use the word ‘history’ in his title. Indeed, it is used sparingly throughout the
paper. Thus perhaps he is giving ‘an account’, rather than ‘a history’. (Or perhaps it is indeed ‘his story’,
as he personally plays such a prominent role.)
I also note two further restrictions that are implicit in Peter’s title.
First, he refers to ‘English schools’—thereby excluding even Scotland, with its distinctly different sta-
tistical and education tradition, from his gaze. This is a lack, for in history as in statistics we often learn
more by shrewd comparisons than we can by examining just a single case. (Another interesting area would
be to compare the British colonial tradition with perhaps the French or even the American or Russian.)
Second, by focusing on schools alone, the vast bulk of even the English population is excluded. For,
though some of us may have attended school, for many of us learning did not stop there. (Nor indeed did
it start there—preschool statistical oracy is an interesting issue to explore.)

Discussion on the Paper by Holmes 465
However, we should not complain about Peter’s narrow focus, for his account provides depth and detail
where it might lack in breadth.
A more crucial restriction may be the title’s use of the word ‘teaching’. For teaching is not learning. I
need not elaborate on the many uncharitable things that have been said about the teaching process and its
practitioners, for many of these are untrue—apart from being unsympathetic. However, I would like to
present two basic axioms:
(a) teaching does not necessarily lead to learning;
(b) most learning takes place outside the classroom.
In a sense, we are all autodidacts. We learn what we want to learn—motivation and content are everything,
as every good teacher knows. Arguably, this applies especially to elements of literacy, including ‘statistical
literacy’.
These axioms are not new. The importance of informal learning has long been recognized. However, it
is often vastly underrated. This is especially so in the research community, which provides a ton of data
on schooling for every ounce of ideas on informal learning.
The successes of statistics education have been mentioned, and we certainly should celebrate these.
However, we may paradoxically be able to learn more by asking ‘What are the failures?’.
For Darwinian evolution teaches us, as do the Taguchi and total quality management approaches to
industrial engineering, that failures may point us to the biggest challenges. By examining ‘failures’ of the
past we may escape Whiggist triumphalism and see more clearly and in a comparative light the historical
factors which are conducive—and those that are not conducive—to the development of our subject.
I would therefore like to present briefly for your consideration ‘Two great British failures’ in statistics
teaching in England.
The Statistical Society of London’s ‘Statistics in Schools Committee’ (1870)
In its pre-Charter days, this Society established a Committee to ‘promote the teaching of statistics in
schools’ (Council minutes, July 14th, 1870). This Committee met twice, on July 14th and July 22nd, 1870.
William Newmarch and Leoni Levi were its leading personalities. The Royal Geographical Society seems
to have provided the impetus via one of its medal schemes—possibly under the influence of Francis Galton.
However, after its second meeting, the Committee disappeared from view after a lifetime of only 8
days—is this a record? The Society’s annual report for that year makes no mention of the Committee’s
existence, and it seems genuinely to have disappeared without trace—‘a veritable Marie Celeste of the
statistical world’ (Bibby (1986), page 79).
2 years later came the second great British failure to which I wish to refer. This was the so-called
‘Nightingale Chair’, proposed initially for the University of Oxford, and later (in the 1890s) for the Royal
Institution. Apart from Florence Nightingale, prime players here included William Farr, Benjamin Jowett
and Francis Galton, with Adolphe Quetelet in a brief role. (For further discussion and original documents,
see Pearson (1924) and Bibby (1986), pages 30–43 and 112–147.)
The Professorship’s aim was
‘for promoting by means of lectures or otherwise the cultivation and improvement of statistical science,
and especially its practical applications to social problems’
(Bibby (1986), page 41, Pearson (1924), page 423, and Pearson (1914, 1930)).
This was a long-lived proposal, lasting from 1872 until a few weeks before Nightingale’s death. The
coup de grace seems to have been administered by Francis Galton, who suggested that the post should
be transferred from Oxford to London and also started to investigate a statistical research programme
which would spend what was in effect Nightingale’s money. She eventually despaired and withdrew her
endowment because she felt that it would ‘only end in endowing some bacillus or microbe, and I do not
wish that’ (Cook (1913), volume 2, page 400, and Bibby (1986), page 41).
Commentators have ascribed the fall-out between Galton and Nightingale to the latter’s failure to
endorse the newfangled germ theory of disease, preferring the old miasmic theory. However, Kendall
(1972), page 141, may be closer to the mark in ascribing its failure to the fact that ‘our senior universities
were still whispering from their towers the last enhancements of the middle ages’.
In these two great British failures I perceive the following causative factors:
(a) discussions were in terms of structure rather than syllabus;
(b) both ventures were ‘supplier led’ (in the case of Nightingale, ‘funder led’).

Client-need was not established nor even considered (although Nightingale argued convincingly that
Oxford had a need, because this was where ‘most of our statesmen, and those who later become Members
of Parliament, legislators, administrators and holders of executive power carry out their studies’):
(c) in the Nightingale Chair at least, there was a tension between the research function and the peda-
gogic function of the professoriate.
If this sounds too contemporary or even Whiggist, let me simply reiterate that history is one step for-
wards, several steps back. Learning like epidemics often depends on a ‘tipping point’—or on which side of
the zero line the infinitesimal falls. It is often extraordinarily difficult to know what makes one innovation
‘stick’ whereas another fails.
What then do we see for the future? ‘Back to the future’ is where all good histories should start—to
see the future, one must ‘close one’s eyes and wish’. Rewriting history may be frowned on, but can we at
least indulge ourselves a little by creatively considering a range of imaginative histories for what might
tentatively be called ‘statistics 2020’?
Futurology often ascribes undue prominence to technological factors. How will the World Wide Web
affect teaching and learning? What about new computer packages? Will the dynamic visualization tech-
niques of DataDesk and Fathom presage new learning methodologies?
However, the future is far more than technology. We must also ask questions about changes in political
structure, financial climate, new theories of learning, attitudes to assessment and ownership of learning,
etc. At the risk of overdramatizing, will schools still exist in 2020? If so, will we still have teachers? And what
will be their role relative to non-teaching staff, parents, the pupils themselves and indeed new technology?
What about universities?: will they still be there in 2020? Will there be independent statistics departments?
These are questions which must be asked, however much they may make us shudder. They shout into
the tunnel far beyond the realm of statistics, and our colleague and friend Professor Adrian Smith will no
doubt come up with some good echoes when his inquiry on post-14-years education reports soon.
My personal worry is that statistics and perhaps mathematics more generally may have developed or be
developing to the stage where they no longer require evidential justification—they form part of canonical
‘commonsense’ necessity—to paraphrase Huxley, like all truths they ‘began life as heresy, and will end it
as superstition’.
To return to Holmes’s paper, in referring to current national curriculum developments and the key
stages 3 and 4 strategy (Section 12.1), he uses a Popperian or Tukeyite diagram which he refers to as the
‘handling data cycle’. This predates the references given and goes back at least as far as Open University
course DE304, Bibby and Evans (1978) and Bibby (1982) and multiple works of Alan Graham at the Open
University.
Of the four stages in this cycle, only one is mathematical in nature—the one that Peter calls ‘Process
and represent’, but which earlier Open University versions called ‘Analyse the data’. The other three stages
are substantive in nature. Thus it is no surprise that the iterative data cycle is especially useful in service
teaching.
Peter notes (Section 13.2) that ‘The lesson that statistics is an interdisciplinary subject has not been
learned’.
If we are looking for failures, this surely is one that we can learn from—for it is not for want of trying
that the lesson of interdisciplinarity remains unlearned in Britain.
Others learned early. In the 1860s, discussions of statistics teaching at the International Statistical
Congress were dominated by the requirements of geographers and other applied areas (Bibby, 1986).
A century later, the West African Examinations Council had a surprising innovation in terms of a com-
pulsory ‘statistical interpretation’ question which all A-level candidates had to answer. This question was
a compulsory part of the compulsory ‘General studies’ paper, without which one could not gain admission
to a university in any subject. The rationale for this was based largely on a concept of ‘statistics for citi-
zenship’ not unlike the rationale adumbrated by this Society in its submission to the ‘Post-14 mathematics
inquiry’ (Royal Statistical Society (2003), paragraph 9.1).
In the mid-1960s I went to Ghana and with my colleague Andy Miller, an economics teacher, was
commandeered to teach statistics to all sixth formers at Accra Academy. They did so well that I was
persuaded by Longman publishers to turn my class notes into a book—and Bibby (1972) was the
result.
Statistics also featured highly on the new ‘Joint schools project’, which I was honoured to co-author.
One lesson that stuck with me from these early endeavours was the advantage and joys of team teaching
and of using original sources. If you can persuade somebody from the ‘applied’ department to teach a

Discussion on the Paper by Holmes 467
service course with you, then this is politically very shrewd (it spreads ownership to parts that other statis-
tics courses fail to reach) and can also provide effective ‘idiot proofing’ as well as a good range of applied
perspectives.
This method developed in Ghana followed me to St Andrews. As a result, instead of three first-year
social science courses in statistics, there was soon a single course taught jointly by a geographer, a psy-
chologist and an economist or statistician (me). Previously, students who studied all three subjects (a
common occurrence in Scotland) had three different methods courses—along with considerable overlap
and inconsistencies.
Team teaching is a formidable learning experience for staff as much as for students. Nowhere was this
more apparent for me than at the Open University, where our interfaculty course ‘Statistics in society’
involved many people, provoked computer overflow problems since up to then no more than three faculties
had ever collaborated on a course (we had six, but the computerized acronym had to be reduced from
‘DEMAST’ to ‘MDST’, pronounced ‘maddest’) and also led to what are best described as ‘interesting’
political problems—within the Mathematics Faculty and university wide.
Much to everyone’s surprise, ‘Statistics in society’ appeared on time in 1983. Still more surprising
perhaps, it is running still, 20 years and 15 000 students later.
I think that the key to its success is another aspect of didactic philosophy which must be learned by
experience. This is the maxim ‘Start from your students’—use real life and real perception—as perceived
by the student. Customer-led philosophy beats curriculum led every time.
In the Open University course three main blocks focused on areas of particular interest to mature stu-
dents—economics (Labour Force Survey and the retail price index), education (‘How is my child doing?’)
and child development. These were reinforced by four television programmes on ‘energy’ (the statistics of
fuel, cavity wall insulation and renewable power). For other student types, one would choose other focus
areas (sport, music, travel—these all have interesting and real statistical questions).
You will notice that I am a great fan of ‘real statistics’—not artificial examples which often stultify a
vivacious subject and overwhelm it with whimsy. It is time perhaps for a ‘Salters statistics’ course to run
parallel to the problem-based Salters chemistry A-level course that was developed at the University of
York.
However, interdisciplinary teaching does not happen of its own accord. It requires conscious and con-
scientious planning. This should include
(a) a base-line assessment of where non-specialist teachers are, in terms of their statistical readiness,
(b) training of statistics co-ordinators, who would ideally be specialists in non-mathematical subjects
and
(c) structures so that teachers of different disciplines talk to be each other—a rare event in today’s over-
pressed staffrooms.
I am delighted to see that the Education Strategy Group under the leadership of Harvey Goldstein has
recently taken up some of these issues (mutatis mutandis) with the ‘Post-14 mathematics inquiry’ chaired
by Adrian Smith (Royal Statistical Society (2003), paragraphs 3.7 and 5.3). I am particularly pleased that
they have focused on ‘citizenship’ aspects of statistics and mathematics (paragraph 9.1)—an area that the
inquiry’s ‘key questions’ seriously underplays.
In conclusion, I congratulate the speaker, not just on an interesting and useful paper, but also on a
stunning career of contribution to the subject. In many ways, Peter Holmes’s work has changed lives and
has changed the way that we look at things. I salute him.
The vote of thanks was passed by acclamation.
Toby Lewis .University of East Anglia, Norwich/
May I join in congratulating Peter on his important paper?
He asks (Section 7.5) ‘Why teach statistics to everyone?’ Among the answers we read
(a) ‘Statistical thinking is an essential part of numeracy’ (Section 7.5),
(b) ‘children should . . . understand . . . the power and limitations of statistical thought’ (Section 7.3)
and
(c) ‘statistical ideas are widely used at work after school’ (Section 7.5).
But what are statistical thinking, statistical ideas and statistical thought? There are many views in the
literature. I myself think that the essential idea motivating statistical science is simply that repeats of the

same action or situation may give different results—i.e. uncertainty and randomness. This contrasts with
the deterministic approach which some of the students will be learning in their applied mathematics or
physics. In the paper it eventually appears in Section 9.1, the Cockcroft report:
‘Statistics . . . is an attitude of mind in approaching data. In particular it acknowledges the fact of
uncertainty and variability in data collection.’
In the same spirit I welcome, among the myriad published definitions of statistics, the recent one by Fisher
(2001), which is short and to the point:
‘Statistics is the science of managing uncertainty’.
So let students generate their own data and get direct experience of uncertainty and random variation!
This would be much more educative for them than having to use in their projects ‘a large fictitious data-
base’ (Section 13.1). In my teaching experience I have found simulation an invaluable tool, whether used
by teacher or student.
Finally, I welcome the important Section 4 on teaching at primary level. How right Peter is when he
says that
(a) ‘Primary school children can learn and enjoy elementary probability and statistics’ (Section 4.3,
lesson (a)) and
(b) ‘It is possible to begin to develop early ideas of probability and inference at this age’ (Section 4.3,
lesson (b)).
I have seen for myself what can be achieved by a gifted teacher. I shall mention only one of her data col-
lection, discussion and reporting exercises, the ‘Pedestrian graph’. For this, 9-year-old children observed
from the pavement and counted the numbers of people crossing the road in a 10-minute period. I recall
two pleasing entries from their subsequent written reports:
‘Some children went out to do the pedestrians’ (Ian);
‘When we whent it was the 18th of March and we all had something to do. The first day we whent out
we got a lot of children put down’ (Tracey).
Vic Barnett .Nottingham Trent University/
I should like to join others in thanking the author for an interesting and informative paper.
One thing which his natural modesty prevents him from telling us is how important was his own teach-
ing style and rapport with pupils for persuading them to accept the newer approaches of the ‘Statistics
in your world’ modules in the Project on Statistical Education—indeed sometimes almost hanging on his
words. I recall the day in the late 1970s when he puzzled a class of 12-year-old children by telling them that
statistics could reveal which of them smoked behind the bicycle sheds at lunchtimes. A judicious use of
the (Greenberg) sampling ‘principle of the irrelevant question’, some sampling luck and a few appropriate
blushes delivered on his claim and the class was ‘hooked’ on statistics and could not get enough of it.
The author has given us a wide-ranging bibliography. I would just like to extend this a little. In the
late 1970s (again) the International Statistical Institute (ISI) based in the Hague supported several educa-
tional task-forces. One, after many years of lobbying through the ISI Education Committee, was charged
with starting the important series of International Conferences on Teaching Statistics held every 4 years.
Another, which I chaired, was concerned with secondary level education, and on its behalf I produced
the wide-ranging review Barnett (1982). This described the situation in many countries but in particular an
opening chapter gave a detailed analysis of the prevailing position in England and Wales (with a supple-
ment on Scotland). A similar international résumé on university level education was produced by Loynes
(1987) on behalf of the ISI Taskforce on Tertiary Level Education.
Harvey Goldstein .Institute of Education, London/
I also welcome this important paper and congratulate Peter Holmes not only for an interesting and wide-
ranging account but also for all the effort that he personally has contributed to statistical education.
One important distinction between the pre-1990 and post-1990 period has been the move from a largely
decentralized school curriculum and assessment system to one controlled by central Government. This

50 Years Of Statistics Teaching In English Schools Some Milestones

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