Memorandum submitted by Doug French, University of Hull



This response relates primarily to mathematics, because that is the writer's area of expertise, but some of the remarks certainly have wider application. Although it is clear that the detailed issues differ between subjects and phases of education, concerns about the effectiveness of the current system are widespread.


I have written this response in a personal capacity. I have been a mathematics teacher in comprehensive schools and a teacher trainer in a university over the past forty years. Since my recent retirement I have continued to work with teachers on a free-lance basis. I have written extensively about mathematics education in books and journals and I am an active member of the Mathematical Association. I have recently completed a year's term of office as President of the Association and continue to serve on its Council and as Chair of its Teaching Committee.


General Issues

1.1 Why do we have a centrally run system of testing and assessment?


A centrally run system is needed:


to provide certification for individuals so that society can select people for employment and further and higher education on the basis of some objective evidence;


to provide a means of monitoring changes in performance at national and local level over time.


The first of these needs is best met by a modified and significantly reduced system of the current type, but the second is best achieved independently of the qualifications system through sampling in the way that was done in the past very effectively by the Assessment of Performance Unit (APU).

1.2 What other systems of assessment are in place both internationally and across the UK?

There are many assessment systems run by organisations which are usually vocationally oriented, but the qualifications they generate are not necessarily transferable to other spheres of activity. It is significant that no other country in the world has an assessment system which is so dominant and all-pervasive at every level as that in England. In many countries the only national examinations take place in the final year of schooling at the age of 18 and few have national testing at any stage before the age of 16. It is also significant that, following devolution, Wales abandoned Key Stage testing with no apparent ill effects. Scotland has never had any equivalent of Key Stage testing.


1.3 Does a focus on national testing and assessment reduce the scope for creativity in the curriculum?

Some form of national testing and assessment is necessary, but currently there is far too much testing. Its dominance is greatly increased by a variety of accountability measures - targets, league tables, performance measures for teachers and Ofsted inspections. This has created a situation which has seriously narrowed what is taught, particularly in the key subjects of English, mathematics and science, which are at the centre of this focus on testing. Moreover, it has led to the relative neglect of aspects of education that are not tested such as music, the arts, sport and citizenship. These two aspects of the narrowing effect of too much testing have undoubtedly reduced 'the scope for creativity in the curriculum'.


This is observed particularly in year 6 in primary schools and years 9 and 11 in secondary schools when national tests are taken. In year 6 far too little time is spent on subjects other than those being tested and too much teaching time is devoted to a narrow focus on practising test questions. In secondary schools each subject has its own time allocation, but a narrow test-oriented focus within each subject is commonplace. At sixth form level, the situation, if anything, is even worse with module assessments twice a year leading to AS level after one year followed by A level in the second year.


Although there is no evidence that good results can only be achieved by focusing narrowly on teaching to the test, the pressure on teachers from school leaders, parents and pupils to do so is very intense. In mathematics this leads to constant practice of routine skills and standard types of question. This fails to develop a deep understanding of simple ideas so that they can be applied to novel situations and reduces enjoyment of the subject so that further study at higher levels is discouraged. These concerns are expressed well as one of the factors influencing 'achievement, motivation and participation' that Ofsted highlight in the findings of their recent report Evaluating Mathematics Provision for 14-19 Year Olds[1]:


'A narrow focus on meeting examination requirements by 'teaching to the test', so that, although students are able to pass the examinations, they are not able to apply their knowledge independently to new contexts, and they are not well prepared for further study.'


Education should be concerned with 'long lasting learning': what matters is the learning that remains six months or five years after the last test has been taken. Both employers and higher education are interested in the skills, strategies and attitudes which have 'stuck', so that they can be relied upon in employees and students.


The counter-productive nature of the focus on testing is linked to the closely related issue of giving students marks and grades, not just for their final assessment, but for regular class and homework tasks. There is plenty of evidence from many countries which shows that giving students marks or grades causes them to focus their attention on the marks rather than any advice that is given on how to improve the quality of the work (see Black and Wiliam[2] and the Assessment Reform Group[3]). Without the marks they are more likely to take notice of advice about how to improve. How to provide helpful advice lies at the heart of what is referred to as assessment for learning or formative assessment. The constant focus on results which accompanies an over-emphasis on tests and marks detracts from the effectiveness of good advice that is aimed ultimately at improving those results.


In a broad sense it is certainly true that the current system of testing and assessment greatly reduces the scope for creativity in the curriculum, because the more creative elements of any subject are squeezed out by the pressures to 'teach to the test'. In the case of mathematics the creative element comes through stimulating students' curiosity with the challenges of solving interesting problems, explaining surprising results and seeing how ideas can be applied to a wide variety of situations. Whilst the quality and form of tests can and should be improved, they cannot test all the desirable attributes of a good education and must not be so dominant as to exclude the fulfilment of broader aims.

1.4 Who is the QCA accountable to and is this accountability effective?


QCA should be accountable to the wider public with a brief to ensure that the assessment system is fit for purpose and commands the confidence of users, both those involved in implementing it and those who rely on the information provided by the qualifications generated by the system. Clearly QCA has to work within a framework of decisions made by the DfES, but it is sometimes difficult to see which body is the source of particular policy decisions. It is nonetheless true that QCA has considerable power as the body charged with implementing decisions.


In practice QCA is not a body that commands great respect in the world of mathematics education, because it fails to consult those with wide experience and expertise at the stage where policies are being formulated. The result is that significant decisions are often taken before adequate consultation and any consultation that does take place is restricted to the details that follow from those decisions. Moreover the time scale within which changes take place is commonly far too short and too many changes are happening concurrently.


The decisions that led to the dramatic fall in uptake for A level mathematics following Curriculum 2000 are a stark reminder of this failure to consult beforehand with those who could see the serious implications of the proposed policies. Little seems to have been learnt from the mistakes made at that time, because similar concerns are being expressed about recent decisions concerning the move from three to two tiers in GCSE mathematics, the introduction of a second GCSE in mathematics, the introduction of assessment for Functional Skills in mathematics and aspects of AS and A level structures. Consultation about these and other changes is widely regarded as inadequate.

1.5 What role should exam boards have in testing and assessment?


All the best curriculum developments in mathematics over the past 50 years have arisen as a result of work done by good teachers often working with bodies that have been independent of government finance or control. At secondary level the work of both the School Mathematics Project (SMP) and Mathematics in Education and Industry (MEI) have been outstanding, because they have been enthusiastically adopted by teachers and have been successful in stimulating greater interest among students. Recently the Further Mathematics Network, which is run by MEI with financial backing from the DfES but with minimal central involvement in the nature and implementation of the project's aims, has made a very significant impact on the number of students taking AS and A level further mathematics.


Developments such as these have always worked with awarding bodies to ensure that the assessment matches the aims of the projects as closely as possible and does not distort the intentions behind those aims. The increasingly commercial and competitive nature of the awarding bodies, together with frequent changes to structures as a consequence of national policies, is making such valuable partnerships much more difficult to sustain. An excessive amount of energy on the part of those representing teachers and other mathematical interests, which could be used much more creatively, is diverted towards trying to ensure that QCA and the awarding bodies adopt coherent and manageable policies, which sustain and enhance the quality of students' learning in mathematics. There is a need for much careful thought about the right way forward for awarding bodies and the regulatory role of QCA.

National Key Stage Tests

The current situation

2.1 How effective are the current Key Stage tests?


When they were first introduced the tests had a beneficial effect in mathematics because they were in many respects better tests than GCSE and certainly better than the tests that many schools devised for themselves. However, as soon as they became 'high stakes' rather than a source of evidence for use internally by schools, there was an increasing pressure to 'teach to the test' and much of this original benefit has been lost, even though the form of the tests has not changed. The use to which the tests have been put has greatly detracted from the value that they might otherwise have.

2.2 Do they adequately reflect levels of performance of children and schools, and changes in performance over time?


Like most tests they put students in a crude rank order and provide a rough measure of performance of a cohort over time, but they are not adequate as a detailed measure of the precise skills that a student has mastered.

2.3 Do they provide assessment for learning (enabling teachers to concentrate on areas of a pupil's performance that needs improvement)?


Assessment for learning involves classroom strategies that are largely independent of formal testing, so it is not the role of national tests to provide such information.

2.3 Does testing help to improve levels of attainment?


Testing often only leads to short term gains in performance on test items. It does not necessarily contribute to longer term aims and long lasting learning.

2.4 Are they effective in holding schools accountable for their performance?

They have some value in this respect, but they currently distort the priorities of schools and will continue to do so unless considerable care is taken to take into account the multitude of factors, often outside a school's control, which influence test performance.

2.5 How effective are performance measures such as value-added scores for schools?


The same provisos as above apply to value added measures.

2.6 Are league tables based on test results an accurate reflection of how well schools are performing?


They may be an accurate reflection of how they are performing as measured by tests, but results should be viewed in relation to the context of the school and the many other aspects of educational 'performance' that are not measured by tests.

2.7 To what extent is there 'teaching to the test'?

It is commonplace, particularly in the years when high stakes tests are taken, but it is a pervasive element in many schools in mathematics for much of the time.


2.8 How much of a factor is 'hot-housing' in the fall-off in pupil performance from Year 6 to Year 7?


No comment.

2.9 Does the importance given to test results mean that teaching generally is narrowly focused?


2.10 What role does assessment by teachers have in teaching and learning?


Teacher assessment linked to national tests is not popular with mathematics teachers, a high proportion of whom were pleased with the recent decision to abandon GCSE coursework. More generally there are serious problems with any form of coursework because of the ease of plagiarism from the internet and the difficulties associated with the level of 'help' that is acceptable. Teacher assessment also puts unfair pressures on teachers when so much hangs on the results of examinations.

The future

2.11 Should the system of national tests be changed?


As far as mathematics is concerned the major concern in the medium term should be to reduce the unreasonable burden on students and teachers that the current national assessment system imposes. The impact of Key Stage tests and examinations for GCSE and AS and A level and accompanying accountability measures needs to be reduced. I would suggest that Key Stage tests should either be abandoned, as in Wales, or else be made optional for schools so that they could choose how best to use them. With GCSE, AS and A level the existing system has its merits, although there is an urgent need both for a review of the role of QCA and the awarding bodies and for carefully considered changes at a detailed level. These are, to some extent, happening with the current consideration of Pathways for mathematics following the Smith Inquiry[4]. However, such changes need to be managed much more effectively than has been the case in recent years. League tables should be abandoned because they greatly exacerbate the strong pressures on teachers to 'teach to the test' with all its ill effects.

2.12 If so, should the tests be modified or abolished?


See 2.11.

2.12 The Secretary of State has suggested that there should be a move to more personalised assessment to measure how a pupil's level of attainment has improved over time. Pilot areas to test proposals have just been announced. Would the introduction of this kind of assessment make it possible to make an overall judgment on a school's performance?


This is unlikely to be satisfactory as a way of judging performance and will add greatly to the 'teaching to the test' which is such an undesirable by-product of the current system.

2.13 Would it be possible to make meaningful comparisons between different schools?

Credible comparisons would be difficult to make.

2.14 What effect would testing at different times have on pupils and schools? Would it create pressure on schools to push pupils to take tests earlier?

The idea that students should be tested 'when ready' would add greatly to all the existing pressures to move students on in ways which are detrimental to the development of secure mathematical understanding and the interest in mathematics which encourages further study.

2.15 If Key Stage tests remain, what should they be seeking to measure?


These tests can provide a rough guide to the level in the National Curriculum that students can work with comfortably, but they would be more effective if they were taken in a much less pressured environment than currently.

2.16 If, for example, performance at Level 4 is the average level of attainment for an eleven year old, what proportion of children is it reasonable to expect to achieve at or above that level?

It is wrong to speak of an average level of achievement, because that is something that changes over time. There is no way of answering the question as to what proportion of students might achieve at level 4 and above. There is no inherent reason why it could not be a lot higher, but achieving that would involve deep changes in our cultural attitudes towards education and the way our education system operates, so that a much higher proportion of students had a much more positive attitude towards their education in general and to mathematics in particular.


2.17 How are the different levels of performance expected at each age decided on? Is there broad agreement that the levels are appropriate and meaningful?


The decisions were made in an arbitrary way and only provide a rough guide as a rank order of performance which gives some indication of future potential.

Testing and assessment at 16 and after

3.01 Is the testing and assessment in "summative" tests (for example, GCSE, AS, A2) fit for purpose?

Whilst we should constantly seek to improve the quality of the tests we use, the current format of tests is adequate subject to two provisos. The first is that in mathematics there is a need for more problem questions which are presented in an unstructured format. The second is that papers should be designed so that the mark that is the threshold for the lowest pass grade on any paper should never be less than 50%. It is unsatisfactory that anybody should be deemed to have 'passed' a test where more than half has not been completed adequately

3.02 Are the changes to GCSE coursework due to come into effect in 2009 reasonable? What alternative forms of assessment might be used?

Yes, but it is not clear what alternatives are being proposed for mathematics in terms of different types of questions to assess aspects which were originally supposed to be assessed with coursework.

3.03 What are the benefits of exams and coursework? How should they work together? What should the balance between them be?

For reasons indicated previously assessed coursework has been too problematic to be retained in mathematics. However, it is crucially important that the sort of tasks encouraged by coursework do form a significant part of all students' classroom experience.

3.04 Will the ways in which the new 14-19 diplomas are to be assessed impact on other qualifications, such as GCSE?

It is not clear what the impact will be since information about the assessment of diplomas as they might impinge on mathematics is not available.

3.05 Is holding formal summative tests at ages 16, 17 and 18 imposing too
great a burden on students? If so, what changes should be made?

Ultimately it would be good to move to a situation where the only national summative testing took place at the end of full-time compulsory education, which will eventually be at age 18, as in many other countries. In the meantime it would be a useful step to move away from any formal testing that was certificated at age 17, except perhaps for repeats of GCSE.

3.06 To what extent is frequent, modular assessment altering both the scope of teaching and the style of teaching?

Modular assessment has some benefits in giving students short term goals, but, unless structured very carefully, it does not encourage approaches which give a coherent overview of a subject.

3.07 How does the national assessment system interact with university
entrance? What does it mean for a national system of testing and assessment
that universities are setting entrance tests as individual institutions?

The fact that universities find it necessary to set their own entrance tests shows a lack of confidence in our existing system which they clearly feel does not give them adequate information about the ideas that students understand and can use with confidence. This goes back to earlier references that were made to achieving 'long lasting learning'.


May 2007

[1] Ofsted (2006) Evaluating Mathematics Provision for 14-19 Year Olds

[2] Black and Wiliam (1998) Inside the Black Box. Raising Standards through Classroom Assessment King's College London

[3] Assessment Reform Group (1999) Assessment for Learning: Beyond the Black Box University of Cambridge School of Education

[4] Smith, Professor Adrian Making Mathematics Count February 2004