Contents

1. Introduction
2. The place of Statistics
3. Mathematics
4. Science
5. Geography
6. History
7. Design & Technology
8. Information & Communications Technology (ICT)
9. Physical Education
10. Personal, Social and Health Education (PSHE) and Citizenship
11. English
12. Modern Foreign Language
13. Art and Design
14.Music

Appendix 1. Phrases in the Science. Programmes of Study that have implications for Statistics
Appendix 2. Phrases in the ICT Programmes of Study that have implications for Statistics.

1. Introduction

The National Curriculum for pupils in schools in England and Wales was first introduced between autumn 1989 and 1996. Since then it has been periodically revised and the latest revision comes into effect in September 2000. This latest revision was not designed to change the content substantially, but did change the programmes of study which describe how the material should be taught in the various Key Stages. The responsibility for revising the National Curriculum rests with the Qualifications and Curriculum Authority (QCA).

The National Curriculum is compulsory for all state schools. Independent schools do not have to teach the National Curriculum but many of them do follow most of it.

The teaching is programmed into four stages. Key Stage 1 and Key Stage 2 are at primary school; Key Stages 3 and 4 are at secondary school. For each Key Stage there is a Programme of Study which describes how the subject is to be taught. One major change on the previous order is that there are now separate programmes of study for Key Stages 3 and 4, where previously they were combined. Additionally, in mathematics, there are two separate programmes of study at Key Stage 4, designated foundation and higher. Table 1 gives an approximate breakdown of Key Stages (KS), year at school and age in years during that year

Table 1 Key Stages, Ages and Year at School

The core subjects, taken by all pupils throughout the whole of the 5 to 16 year-old age range, are English, mathematics and science. Foundation subjects (technology, history, geography, music, art, physical education are compulsory up to the end of Key Stage 3 and a modern foreign language must also be taken at Key Stage 3).

The subject content for the Key Stages is described in more detailed Attainment Targets which usually go from level 1 to level 8 and then a level called exceptional performance. Table 2 shows the relationship between the key stages and the attainment levels

 Table 2 Key Stages and Attainment Levels

All pupils taking the National Curriculum are tested in English and Mathematics at ages of seven, 11 and 14. These standard assessment tests (SATs) are intended to see whether pupils have met the National Curriculum learning targets. The tests are based on the programmes of study for the various key stages. General Certificate of Education (GCSE) examinations are taken at the end of Y11. The content of the new mathematics National Curriculum, starting in September 2000, is the content of the GCSE mathematics syllabus.
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2. The place of Statistics

Since its inception the National Curriculum in Mathematics has had a major component of statistics under the heading Data Handling. This is still the case for the newest version starting in September 2000. Although the content has been little changed the philosophy and approach outlined in the programmes of study have been substantially revised. Details are considered below.

Statistics has always been a multi-disciplinary study and so has also, for many years, been part of other subjects in the school curriculum. At the main school level statistical techniques have found a place in science (particularly biology), in geography and other subjects where there is quantification. In the official documents and programmes of study the exact role is not always clear. There are many places where statistics could be used with advantage as part of the topic. Although they may not be required, a good teacher would use them to give better insight.

The current revision of the National Curriculum was done subject by subject with no direct contact between the groups. This means that there is the possibility of a subject like statistics having the same items at different key stages in different subjects. To some extent this has happened as is shown in the detailed analysis below. It is also possible that teachers of a subject which uses statistics may not fully appreciate the difficulties of the concept or technique being used, and so introduce it earlier than a specialist statistics teacher would.
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3. Mathematics

The National Curriculum for mathematics is divided into four strands:

MA1 Using and Applying Mathematics
MA2 Number and Algebra
MA3 Shape, space and measures
MA4 Data Handling.

The content of these strands is described in detail in a series of level descriptions going from level 1 to level 8 and then exceptional performance to cover the whole age and ability range. These are also known as the attainment targets (ATs). The way of incorporating this content is described in the programmes of study (PoS) for each key stage (KS). In mathematics, uniquely, there are two programmes for Key Stage 4. They are KS4 (Foundation) and KS4 (Higher). Their content and purpose is described below.

There are no programmes of study for MA1. The official document says 'teachers should expect attainment at a given level in this attainment target to be demonstrated through activities in which the mathematics from the other attainment targets is at, or very close to, the same level'. In other words, you teach the process of mathematical thinking through the activities in number, algebra, shape, space, measure and data-handling.

Table 3 gives the approximate connection between attainment levels and the other variables in table 1 for mathematics.

Table 3 Key Stages and Attainment Levels in Mathematics

There is so much material here that it is difficult to summarise and readers are encouraged to see the whole order. It can be found at http://www.nc.uk.net/servlets/NCFrame?subject=Ma .

The following summary is based on a detailed consideration of the programme of study for KS3 and considering how KS2 leads up to it and the two KS4 programmes of study follow on.

At the heart of the KS3 and 4 programmes is the handling data cycle, which can be shown diagramatically.

This cycle occurs specifically (but not as a diagram) as item Problem solving (1a), in the section entitled Using and applying handling data. The individual items are then picked up later and given in more detail.

At KS3 pupils should be taught to carry out the four aspects of the handling data cycle to solve problems (1a) and identify what further information is required to pursue a particular line of enquiry (1b).

As part of Communicating they have to interpret, discuss and synthesise information presented in a variety of forms (1e), communicate mathematically, make use of diagrams and related explanatory text (1f), examine critically, and justify their choice of mathematical presentation of problems involving data (1g).

As part of Reasoning they have to recognise the limitations of any assumptions, and the effects that varying the assumptions could have on conclusions drawn from the data analysis (1j).

The four aspects of the data-handling cycle at this stage are given in more detail. They include the following.

Under Specifying the problem and planning pupils should be taught to see that random processes are unpredictable (2a), identify questions that can be addressed by statistical methods (2b), discuss how data relate to a problem, identify possible sources of bias and plan to minimise it (2c), identify which primary data they need to collect (2d) and design an experiment or survey; decide what secondary data to use (2e).

Under Collecting data pupils design and use data-collection sheets … using … observation, controlled experiment, data logging, questionnaires and surveys (3a), gather data from secondary sources (3b) and design and use two-way tables for discrete and grouped data.

Under Process and represent data pupils draw and produce … pie charts … diagrams for continuous data, including line graphs for time series, scatter graphs, frequency diagrams and stem-and-leaf diagrams (4a), calculate mean, range and median of small data sets…(4b), understand and use estimates or measures of probability from theoretical models (4d), find the median for large data sets…(4g) and draw lines of best fit by eye, understanding what these represent (4h).

Under Interpreting and discussing results pupils relate summarised data to initial questions (5a), interpret a wide range of graphs and diagrams and draw conclusions (5b), compare distributions and make inferences (5d), evaluate and check results, answer questions, and modify their approach if necessary (5e). have a basic understanding of correlation (5f), use lines of best fit (5g), use the vocabulary of probability in interpreting results involving uncertainty and prediction (5h) and compare experimental data and theoretical probabilities (5i).

The Breadth of study statement for KS3 says that pupils should do practical work in which they draw inferences from data and consider how statistics are used in real life to make informed decisions (f). They should also carry out a sequence of activities that address increasingly demanding statistical problems.

This is quite a substantial amount of statistics in both breadth and depth for school years 7 to 9. There is preparation for it in KS2 and it continues in two different ways at KS4 (Foundation) and KS4 (Higher)

The earlier work in KS2 requires only simpler ideas and techniques. The practical work is done in simpler contexts. The KS2 description is under two headings only: Using and applying handling data and Processing representing and interpreting data. Using and applying handling data has two subsections problem solving and communicating.

In general the requirements under using and applying … are simpler versions of those at KS3. There is an interesting reference, though, to pupils using handling data skills when solving problems in other areas of the curriculum, in particular science. This sort of reference does not occur at KS3 or KS4.

In the processing, representing and interpreting data the techniques required are simpler. They include pictograms, bar charts, line graphs, the mode, the range and words to describe early ideas in probability such as fair, equally likely, unfair and certain.

Pupils are expected to draw inferences from data in practical activities and recognise the difference between meaningful and misleading representations of data. (Breadth of study)

There are two different continuations of KS3 to KS4. KS4 (Foundation) and KS4 (Higher)

KS4 (Foundation) is for those pupils who have not attained a secure level 5 at the end of KS 3. In content it covers the same attainment levels as KS3 but is intended to be broader and require a more mature approach. Nearly all the programme of study is the same as KS3. The difference comes at the end of Interpreting and discussing results where pupils are expected to interpret social statistics including index numbers (for example, the General Index of Retail Prices); time series (for example, population growth); and survey data (for example, the National Census). (5k). This breadth of study is also reflected in the Breadth of study where pupils carry out practical work in which they draw inferences from data, consider how statistics is used in real life to make informed decisions and recognise the difference between meaningful and misleading data (f). They are also expected to be involved with activities focused on the major ideas of statistics, including using appropriate populations and representative samples, using different measurement scales, using probability as a measure of uncertainty, using randomness and variability, reducing bias in sampling and measuring, and using inference to make decisions (g).

KS4(Higher) builds on KS3 to require the use of more difficult techniques and to solve more difficult problems. This shows in several places.

Pupils are expected to select the problem-solving strategies to use in statistical work and monitor their effectiveness (1b) and identify exceptional or unexpected cases when solving statistical problems (1e). They have to justify a sampling scheme and a method to investigate a population, including random and stratified sampling (2d) and deal with practical problems such as non-response or missing data (3d).

The diagrams used now include box plots and histograms, measures include medians, quartiles, interquartile range and means (including a moving average). There is also a greater emphasis on probability and calculating the probability of combined events (not just mutually exclusive or independent) using tree diagrams where appropriate. They are expected to understand frequency density and have a greater understanding of correlation and regression. There is nothing in the KS4 (Higher) equivalent to the references to index numbers etc. or to the major ideas of statistics described in KS4 (Foundation). This last omission seems strange and the KS4 (Higher) pupils could well gain from having it included.

The above summary has concentrated on the description in the programmes of study. The attainment levels in Attainment Target 4 give more details of the specific techniques as they develop. Collection starts at level 1 with classifying objects. Representation begins at level 2 with simple lists, tables and block graphs. Summarising data begins at level 5 with the mode and median of discrete data. Probability also begins at level 5 with an understanding and use of the probability scale from 0 to 1. Bivariate data and their representation begins at level 6 with scatter diagrams and a basic understanding of correlation. At level 8 there are cumulative frequency tables and diagrams; use of the median and interquartile range to compare distributions and make inferences. Probability includes calculating the probability of a compound event and using this in solving problems.

Assessment

At Key Stage 4 the content of the mathematics order becomes the content for a GCSE in mathematics. It is up to the various GCSE Boards to carry out the assessment under the criteria laid down by the Qualifications and Curriculum Authority (QCA). These criteria state that 20% of the overall marks are to be allocated to data-handling. Half of these marks are to be awarded to a practical project in statistics with marks allocated under the three headings Specify the problem and plan, Collect, process and represent data and Interpret and discuss results. This is in line with the four-stage process described above as part of the key stages and should encourage a practical approach to the teaching of statistics.

The assessment procedure is different for the other key stages. This is linked to the SATs. Since 1996 these have officially been linked to the programmes of study. In fact, because their aim is to assess pupils' levels of attainment on the Attainment Targets, the questions have been more closely linked to the specific statements in these targets. They tend to test individual techniques and do not test the holistic approach described in the new programmes of study. The philosophy of the current questions is more atomistic and encourages an emphasis on teaching and learning individual techniques in isolation and not necessarily in a practical context. If the style of the SATs is not changed to match the new programmes of study then there is a real possibility that the teaching of data-handling up to key stage 3 will continue to be based on techniques rather than seeing statistics as a four-stage process of solving problems in which these techniques are embedded.
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4. Science

The programmes of study in Science are similarly laid out for all Key Stages. There are two separate programmes of study for Key Stage 4 - for single and for double science. Since the content is described from a scientific point of view there are times when phrases could imply statistical ideas and techniques, but may not. There are other places where it is unambiguously statistical ideas that are being used. There are several instances of the same words being used at different key stages so they clearly need to be interpreted in the light of the age and ability of the pupils.

Appendix 1 gives a summary of the phrases in the science programmes of study that have statistical implications.

Unlike data-handling in mathematics, science starts at Key Stage 1 and clearly implies some elementary statistical representation of data. The major references to the use of statistics occur in the sections designated introduction, scientific enquiry (Sc1) and breadth of study. There are a few references under the variation section of Life processes and living things(Sc2 section 4) and a few other areas where statistics could be used.

The idea of an investigation is a common theme in the introductions. Beginning with systematic investigations at KS2 these are expanded to be quantitative, involving teamwork and using appropriate reference sources at KS 3 and 4. Evaluating evidence is part of KS3 and 4. Presenting results begins at KS1 with charts and tables and moves to using conventional diagrams, charts and graphs at KS2. This is rather earlier than similar items occur in mathematics.

The section Scientific Enquiry begins with ideas and evidence in science. KS1 starts with making observations and measurements; KS2 moves on to cause and effect (the example given is a statistical one from Jenner's vaccination work). At KS 3 pupils consider the interplay between evidence and scientific explanations with a clear implication for inference from data.

The second strand of Scientific Enquiry is headed Investigative skills. For KS2, 3 and 4 the subsections of this are Planning, obtaining and presenting evidence, and considering evidence and evaluating. Philosophically and in many practical details this is the same as the four point programme used in KS3 and 4 in the data-handling section of the mathematics programme

Even at KS2 in the planning stage pupils are to be taught to ask questions that can be investigated scientifically, consider sources of information including first-hand experience and other sources, think about what kind of evidence to collect and make a fair test or comparison by changing one factor and observing or measuring the effect whilst keeping other factors the same. In KS3 they have to see if evidence matches predictions. By KS4 they have to turn ideas into a form that can be investigated, plan an appropriate strategy, consider key factors to take into account in collecting evidence, decide the extent and range of data to be collected and the techniques to use. This planning includes both data from planned experiments and from surveys such as observations on biology field trips

Statistical work plays an explicit part in the obtaining and presenting evidence stage. Making observations begins at KS2, extends to time series at KS3 and to several variables at KS4. Pupils present evidence with tables, block graphs and pictograms at KS1, bar charts and line graphs at KS2, charts and graphs at KS3. This more or less parallels the use of the same techniques in mathematics but starts earlier.

The first entries in the considering evidence and evaluating do show a progression. At KS1 pupils make simple comparisons, at KS2 they make comparisons and identify simple patterns or associations in their data, at KS3 they use diagrams and lines of best fit to identify and describe patterns and at KS4 they explain patterns or relationships in data. The example given at KS1 is not clear. It gives hand span and shoe size as example of simple comparisons. If this is comparing hands with hands and feet with feet then there is no real problem. If it is comparing hand span with foot length then this bivariate example is more in line with KS3.There are many places in the strand where the same words are used at KS2, 3 and 4. Presumably the same ideas are used in more difficult contexts and with more difficult examples. Pupils have to use observations, measurements or other data to draw conclusions. They have to decide whether (or to what extent in KS3 & 4) these conclusions agree with any prediction made and have to use scientific knowledge to explain observations, measurements or other data or conclusions. At KS4 they have to consider anomalous data and, in double science, consider the reliability of data in terms of uncertainty of measurements and observations. This last clearly requires a good level of statistical sophistication. The content of this strand matches well with the data-handling in mathematics.

In Sc2 Life processes and living things the section on variation includes classification of data at KS1 and 2 and monohybrid inheritance with dominant and recessive alleles at KS4 double science. Other examples where statistics could be used are in Sc3 Materials and their properties.

The Breadth of Study section uses statistics at all Key Stages. KS2 requires pupils to use a range of information and data, using first hand and secondary data; KS2 goes on to include ICT and use them to carry out a range of scientific investigations with complete investigations at KS3.

Since the publication of the National Curriculum the QCA has introduced suggested schemes of work for key stage 3. In these there are many explicit references to the use of data sets.

Breadth of study also includes a reference to assessing risks in the context of hazards in scientific experimentation.

There is clearly a lot of scope for co-operation between the teaching of data-handling and mathematics and in science.
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5. Geography

From the statisticians point of view the geography order is both exciting and frustrating. There are a many references to topics which could clearly benefit from some statistical input to clarify the concepts and to harden up the results, but it is not at all clear from the descriptions whether this is expected.

The geography order only has programmes of study up to and including KS3 but there are the usual attainment target levels 1 to 8 and exceptional performance.

The programmes of study have a few specific references to statistical techniques and skills. At KS2 pupils have to:

Geographical enquiry and skills

1c … draw conclusions (for example by comparing population data for two localities)
1d identify and explain different views of people - which seems to imply some sort of questionnaire survey, or analysis of someone else's survey.
2f … create a data file to analyse fieldwork data - which assumes that they have collected some data doing fieldwork, and presumably some of this is numeric data.

At KS3 pupils have to:

Introduction

… identify geographical questions, collect and analyse written and statistical evidence - which implies they have to look for some of the statistical ways of looking at a geographical question

Geographical enquiry and skills

1b … gather views and factual evidence about a local issue and use them to reach a conclusion
1c collect, record and present evidence (for example, statistical information about countries, data about river channel characteristics)
1d analyse and evaluate evidence and draw and justify conclusions (for example, analysing statistical data …)
2b mentions datalogging
2e … select and use appropriate graphical techniques …(for example, pie charts, choropleth maps) …

Together these imply carrying out a survey, collecting categoric and numeric data, tabulating and charting in some way and may be some basic summary data and then drawing some inferences in a specific geographic context. This looks like a simplified version of the cycle in KS3 and 4 of the data-handling strand in mathematics.

In Breadth of study pupils have to be taught through the study of 10 themes. These include:

6f population distribution and change, including the global distribution of population and the causes and effects of changes in the population of regions and countries, including migration. 

At KS1 most of the observations seem to be qualitative but these become more formal at KS2 and 3 so become more quantitative. Here are some of the topics that could benefit from some statistical input, and this may be expected but it is not specific in the order.

Key Stage 2

Geographical enquiry and skills

1b collect and record evidence (for example carry out a survey of shop functions … )
1c analyse evidence and draw conclusions (see above)
2d use secondary sources of information
2g decision making skills

Knowledge and understanding of places

3e identify how and why places change
3f describe and explain how and why places are similar to and different from other places
3g … the supply of goods, movements of people

Knowledge and understanding of patterns and processes

4a recognise and explain patterns

Knowledge and understanding of environmental change and sustainable development

5a recognise how people can improve the environment

All these KS2 items continue and are extended in KS3 to give even more scope for useful statistics.

Key Stage 3

Geographical enquiry and skills

1b,c and d were quoted above

1e appreciate how people's values and attitudes … affect contemporary … issues
1f communicate in ways appropriate to the task
2b and e were quoted above
2d select and use secondary sources of evidence

Knowledge and understanding of environmental change and sustainable development

5a describe and explain environmental change

But it is in the breadth of study section where the pupils are to be taught through the study of two countries and 10 themes that the scope for a good use of statistics becomes apparent.

Countries

a two countries in significantly different states of economic development

Themes

d how and why weather and climate vary
e ecosystems - how physical and human processes influence vegetation
f population distribution and change
g the changing characteristics of settlements
h changing distribution of economic activity and its impact
i development
j environmental issues
k resource issues

Work done at KS3 is vital to enable pupils to use statistical data in the equivalent of KS, especially in coursework assignments.

There is clearly a statistical strand of thinking that pupils are encouraged to develop in the geographical way of looking at things. This means that many of the other topics that are part of the order can expect to have statistical thinking at an appropriate level incorporated in to them. A statistically aware teacher could make a lot of cross links with data handling in mathematics and in science. The level of statistical technique in the geographical application needs to be matched to the degree of difficulty of the concept or technique as shown by its position in the mathematics data-handling order.
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6. History

Like geography, the history order has Key Stages 1, 2 and 3 with Attainment levels 1 to 8 and exceptional performance. Also like geography there are places where it appears that statistical insights and techniques would be useful, but here none are specified as such.

There is a strand through the attainment levels, starting at level 2, about handling sources of information. The progression is from handling sources of information to answer questions about the past (AT level 2) through selecting and combining information from different sources (AT level 4). This continues through identifying and evaluating sources of information which they use critically to reach and support inclusions; selecting , organising and deploying relevant information to produce structured work (AT level 6). This is continually refined so that by the exceptional performance level pupils are expected to … use sources of information critically, carry out historical enquiries, develop, maintain and support an argument and reach and sustain substantiated and balanced conclusions independently. They are expected to select, organise and deploy a wide range of relevant information to produce consistently well-structured narratives, descriptions and explanations

Presumably somewhere along the line this information will include quantitative information and the use of tables of data and other statistical sources. It would be relatively easy to incorporate such quantitative information into the teaching to parallel the use being made of statistics in other subjects, particularly mathematics.

At KS2 the pupils begin to look at history in a variety of ways. These include looking at history from economic, scientific and social perspectives. It is difficult to see how this could be done without some use of data and statistics.

At KS2 history has to be taught through a local history study, three British history studies, a European history study and a world history study. The programme of study gives several examples in these studies which, at an appropriate level, would benefit from the use of data as part of the study. These include the following:

• Local history of the area could include education, population movement, houses and housing, religious practices, treatment of the poor and care of the sick, law and order and sport and leisure. Data on the changes over time are clearly an important part of the evidence. So some elementary reading of tables and interpreting of time series is implied. Many of the data would come from censuses carried out over the period.
• One example of Britain in the wider world in Tudor times is everyday life, life for the rich and poor, differences between town and country. Data could help here
• An example of life in Victorian Britain is Florence Nightingale as a significant individual. This presumably includes her collection and use of statistics to influence changes in the countries laws. This same section gives examples of changes to work and transport; the growth of industrial towns etc. Again data make the study more quantitative.
• Examples of Britain since 1930 include code breaking; impact of social and technological changes; immigration and emigration. These all have links with probability and statistics.

At KS 3 pupils continue to look at history in a variety of ways and these include those highlighted above for KS2. The use of data gives an idea of the magnitude of the effect in such cases as the Black Death, dissolution of the monasteries, industrial expansion and deaths in two world wars. The teaching is done through three British studies, a European study and two world studies. The description of the British study for 1750 to 1900 includes expansion of trade and industrialisation. In general the specific examples for all the studies at KS3 have fewer obvious uses of data as part of the sources of information than those given for KS2, but they do exist.
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7. Design and Technology

Design and Technology has the full set of Attainment levels 1 to 8 and exceptional performance; the programmes of study cover key Stages 1 to 4.

There are two strands where some statistics is implied. The first of these is indicated at KS3 by stating that pupils take into account how products will be used, who will use them, how much they cost and their appearance. This implies some sort of data from a survey or market research. The second strand concerns the making of quality products in quantity. Eventually at KS4 pupils are taught to apply quality assurance techniques - which clearly has a statistical component.

In more detail these strands develop as follows.

At KS2 pupils are asked to think about who will use products and what they will be used for using information from a number of sources. At KS3 they are also asked to consider their cost (and presumably what would be an acceptable cost). At KS4 they are also asked to consider the needs and values of a range of users. This strand of thinking could usefully link with the design of questionnaires and the carrying out of a sample survey in data handling.

The 'quality in quantity' strand starts at KS2 with pupils being taught to recognise that the quality of a product depends on … how well it meets its intended purpose (for example, how well products meet social, economic and environmental considerations). In itself this need not require statistical input. At KS3 pupils are taught to make … products in quantity using a range of techniques … to ensure consistency and accuracy. Consistency will be measured statistically by some measure of variability and accuracy by some measure of location. At KS4 pupils are introduced to more quality ideas such as taking account of critical dimensions and tolerances (1e), manufacturing products in quantity applying quality assurance techniques (2c), simulating production and assembly lines (2e), devising and applying tests to check the quality of their work at critical points during development (3b) and the importance of feedback in controlling systems (5a).
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8. Information and Communications Technology (ICT)

The order for ICT covers Key Stages 1 to 4 and has the usual Attainment levels 1 to 8 and exceptional performance. From the statisticians point of view the word 'information' includes numeric information and so there will always be a strand that related directly to the use of statistics and statistical techniques. This numeric strand may not necessarily be all the sort of information that is implied, nor need it even be the most important part, but it will be there in most cases.

This paper considers the use of statistics in the various subjects of the school curriculum; in this case how ICT uses statistics. ICT is itself also a cross-curricular subject so there are also ways in which statistics uses ICT. This cross-curricular service aspect of ICT is recognised in a special section of the order. Here it states:

1. Pupils should be given opportunities to apply and develop their ICT capability through use of ICT tools to support their learning in all subjects. (It then goes on to give some qualifiers to this statement, but data-handling will be one such area as will all the statistical components of other subjects in the curriculum).
2. Pupils should be given opportunities to support their work by being taught to:

1. find things out from a wide variety of sources, selecting and synthesising the information to meet their needs and developing an ability to question its accuracy, bias and plausibility
2. develop their ideas … to amend and refine their work and enhance its quality and accuracy
3. exchange and share information (with the implication for data presentation in statistics)
4. review, modify and evaluate their work, reflecting critically on its quality as it progresses

Because the word 'information' occurs many times in the order, the references to where statistics might be used are summarised in the table in Appendix 2.

There are several areas where statistical skills will be involved in ICT. There is the strand which requires selecting sources and checking accuracy (KS2) and questioning the plausibility and value of the information (KS3). Very specifically the requirements to collect analyse and evaluate quantitative information (KS3) links with the ideas being described at the same key stage in data-handling. Indeed the two examples given (carrying out a survey of local traffic and analysing the data collected in fieldwork) could easily be the same projects carried out in mathematics.

Putting information into tables (KS2), deriving new information from their tables (KS3) and interpreting the data in the context of solving problems will also use statistical skills. The requirements to reorganise, present and interpret information (KS3 and 4) will use some statistical displays and pupils will need to be aware of misrepresentation - some of which is inherent in widely available commercial packages. The requirement to reflect critically on social, economic, practical and moral issues will also often involve the use of data in the arguments. Some of these data may come from opinion surveys.
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9. Physical Education

The order for physical education covers all four key stages and attainment levels 1 to 8 and exceptional performance. The emphasis is on performance, planning and improving. There are no specific references to statistics, but the strands on evaluating and improving could benefit from some input from experimental data. Such data could be used, for example, to measure the effect of particular training measures or to identify which among several possible ways of improving performance may be the most useful to begin with.

Although KS2 says pupils should identify what makes a performance effective and suggest improvements based on this information (3a, 3b) this is probably meant to be a qualitative judgement. Quantitative measures may become part of the evaluating and improving performance strand at later key stages. At KS3 pupils should be taught to analyse their own and others' work using this information to improve its quality (3b). At KS4 the continuation of this strand is that they should judge how good a performance is and decide how to improve it. Knowledge and understanding of fitness and health would also benefit from experimental data at KS4. Here pupils are to be taught (4a) how preparation, training and fitness relate to and affect performance and (4d) how to monitor and develop their own training, exercise and activity programs. Some data recording and analysis would clearly be useful here.
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10. Personal, Social and Health Education (PSHE) and Citizenship

These two orders are combined and non-statutory for key stages 1 and 2. There are no attainment targets. For key stages 3 and 4 they become separate orders and become statutory. PSHE has no attainment targets; Citizenship has end of key stage descriptions rather than attainment levels.

In the common order for key stages 1 and 2 there are no specific references to statistics and it appears that the general discussion of issues will be qualitative. Nevertheless there are some areas where the introduction of data would be appropriate as part of the discussion at key stage 2. These become more necessary and explicit at later key stages as described below.

The most obvious reference to ideas of probability and statistics at KS2 is in the strand entitled Developing a healthy, safer life style. Pupils are to be taught about the effects and risks of commonly available substances and drugs (legal and illegal) (3d) and to recognise different risks in different situations (such as road use) (3e). The idea of risk is illuminated by the use of data and the ideas of probability.

There are several areas in the strand entitled Preparing to play an active role as citizens where data and ideas from statistics would be useful. 'How to take part in making and changing rules' (2b) could include the idea of petitions and how representative they are. 'What democracy is' (2g) could include polls and the national census. 'Appreciate the range of national, regional, religious and ethnic identities in the United Kingdom' (2i) would benefit from data on the size and distribution of the different groupings. 'How the media present information' (2k) would include some aspects of graphical representation and how the media interpret data.

At KS3 and KS4 the two orders for PSHE and Citizenship become separated.

PSHE would continue to benefit from real data in helping to make decisions and give informed discussion. At KS3 pupils are to be taught the basic facts about alcohol and tobacco and the risks of misusing prescribed drugs (2d), about HIV and high risk behaviour (2e) and how to recognise and manage risk (2g). These same topics continue at KS4 and include additionally the requirement to think about long- and short-term consequences when making decisions about personal health (2a).

In Citizenship there is one very specific reference to statistics at KS4. In Developing skills of enquiry and communication pupils 'research a topical political, spiritual, moral, social or cultural issue, problem or event by analysing information from different sources, including ICT-based sources, showing an awareness of the use and abuse of statistics.' This could easily tie in with practical and project work in data-handling. A similar description appears at KS3. Although the specific reference to statistics is not there, such information would usually form a natural part of the evidence.

One strand of Citizenship is entitled Knowledge and understanding about becoming informed citizens. In most cases part of the information would be numeric.

Examples are:

• the diversity of national, regional, religious and ethnic identities in the United Kingdom (KS3 & 4 1b)
• central and local government, the public services they offer (KS3 1c)
• how the economy functions (KS4 1e)
• the significance of the media in society (KS3 1k) including the internet in providing information and affecting opinion (KS4 1g)
• the world as a global community and the political, economic, environmental and social implications (KS3 1i).
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11. English

English is seen as the most important subject of the school curriculum. It is compulsory for all pupils. There are programmes of study for all four key stages, though key stages 3 and 4 are grouped together. There are Attainment Targets in three areas: Speaking and listening (EN1), Reading (EN2) and Writing (EN3). In each of these the attainment levels are from 1 to 8 and exceptional performance.

Pupils doing work in statistics require many skills in the use of their native language. They need to be able to find sources of data, the sort of skills that come with using a library (and now the internet). They need to be able to read and interpret tables of data; in particular they need to be able to understand the context of these tables, the circumstances under which the data were collected, the meanings of the words used - including technical words. They need to be able to read reports of statistical work and evaluate critically whether the reports are a fair representation of the data and to identify bias. They may need to listen to others presenting the results of their work orally, and engage in discussion. In their own work they need to be able to summarise their results in their native language. They will have to communicate their results in different ways to different audiences. They need to be able to communicate the results orally and in writing, informally and formally. If they are using the data as part of a decision process they need to present a fair case persuasively. They may need to be part of a team working together to produce a report or come up with recommendations so require skills in listening and discussion. Many of these are part of generic skills that might be expected in the study of English. It is interesting to see how much they are included. .

The order for English does include these skills in general terms. Below is just a selection of relevant references.

KS2 EN1. Listening . pupils identify the gist of an account or key points in a discussion and evaluate what they hear.(2a)

KS 3/4 EN1 Listening pupils recognise when a speaker is being ambiguous or deliberately vague … uses and abuses evidence and makes unsubstantiated statements.

KS2 EN1 Group discussion and interaction pupils make contributions to the topic and take turns in discussion (3a) vary contributions to suit the activity and purpose …(3b)

KS3/4 EN1 Group discussion and interaction pupils help the group to complete its tasks by varying contributions appropriately, clarifying and synthesising others' ideas, taking them forward and building on them to reach conclusions … (3e)

KS2 EN1 Language variation pupils should be taught how language varies according to context and purpose (6a)

KS3 EN1 Breadth of Study the range of purposes [of speaking] should include presentations to different audiences (8b)

KS1 EN2 Reading for information use the organisational features of non-fictional texts, including captions, illustrations, contents … (2a)

KS2 EN2 Reading for information obtain specific information through detailed reading (3c), distinguish between fact and opinion (3f) and consider and argument critically (3g).

KS2 EN2 Non-fiction and non-literary texts evaluate different formats, layouts and presentational devices (for example tables ... ) (5g)

KS 3/4 Print and ICT-based information texts evaluate how information is presented (4b) and sift the relevant from the irrelevant, and distinguish between fact and opinion, bias and objectivity (4c).

KS2 EN3 Breadth of Study to persuade, focusing on how arguments and evidence are built up and language used to convince the reader (9c), the range of forms of writing should include … reports (12)

KS 3/4 Composition develop logical arguments and cite evidence (1i), form their own view, taking into account a range of evidence and opinions (1m) and organise their ideas and information, distinguishing between analysis and comment (1n).

KS3/4 Breadth of Study one of the purposes is to inform, explain and describe, focusing on conveying information and ideas clearly.

This all seems very encouraging until you realise that the only specific reference to these skills in a quantitative context is the reference given above to evaluating tables. The English teacher may be excused for overlooking this and it may be up to the teacher of statistics to point out the relevance of statistical work as part of the teaching of English.
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12. Modern Foreign Language (MFL)

There are several attainment targets, each going from level 1 to 8 and exceptional performance. Programmes of study only exist for Key Stage 3/4 not separated.

There is only one place where statistical work may genuinely arise in MFL. There is a strand entitled Developing cultural awareness. In this pupils have to work with authentic materials in the target language (4a) and consider their own culture, comparing it with the cultures of the countries and communities where the target language is spoken. These authentic sources could include data, and the comparison of the two cultures could include quantitative comparisons. So any of the appropriate statistical techniques being developed in other parts of the curriculum may well be used here.
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13. Art and Design

It is unlikely that the authors of this order had any statistical applications in mind but there is one place where it may be important. Attainment level 7 says pupils select, organise and present information in visual and other ways, taking account of purpose and audience. Statisticians who have experienced the distortions of visual presentation of statistical data will see here an opportunity to make sure that creative flair does not distort the overall message of the data.
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14. Music

There are no applications of statistics in this order,

Acknowledgements.

I would like to thank my colleagues at the RSS centre, members of staff at Chilwell Comprehensive School and at Queen Elizabeth's High School, Gainsborough for comments on an earlier draft of this article.

References

The National Curriculum for England (2000) Department for Education and Emplyment, and Qualifications and Curriculum Authority. (All subjects) available on http://www.nc.uk.net/

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Appendix 1 Phrases in the Science Programmes of Study that have implications for Statistics

Notes:

1. Items in italics are in double science only

2. A ? denotes an item where statistics could be used, but may not be.
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Appendix 2. Phrases in the ICT Programmes of Study that have implications for Statistics

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