The Final Report of the Working Group on 14 to 19 Reform

‘The Tomlinson Report’

A copy of the report, which was published on 18th October 2004, may be downloaded from www.14-19reform.gov.uk or a free copy may be obtained from DfES Publications at 0870 000 2288.

Some comments from the Mathematical Association

The report identifies a set of admirable aspirations which will be widely acceptable:

• raising participation and achievement;
• getting the basics right;
• strengthening vocational routes;
• providing greater stretch and challenge;
• reducing the assessment burden;
• making the system more transparent and easier to understand.

These are supposed to be achieved through a ‘unified framework of diplomas’, based on learning programmes comprising ‘core learning’ and ‘main learning’, with an ‘extended project’ as a major feature at each level.

The success of reforms is dependent on the details being thought through properly alongside the general principles. However, as far as mathematics is concerned there is a serious lack of attention to the necessary detail in the report as to the practical implications of the proposals and the appropriateness of some of the measures. There is a very real danger that structures will be imposed which will, at best, do nothing to raise participation and achievement in mathematics and, at worse, will cause an already difficult situation to deteriorate further.

Pedagogy is the key factor in raising standards in mathematics. It is vital to create a system that encourages good pedagogy. That requires much more than changes to content and structures and it has to take place against a background of serious problems with recruiting and retaining mathematics teachers and a lack of time for teachers to engage in professional development on a significant scale. Change must take pragmatic account of these continuing constraints and give priority to what will make a real difference to the quality of the mathematical experience of students.

We make comments below on the three of the above headings which have the most immediate bearing upon mathematics.

1. Getting the basics right

1.1 Splitting the mathematics curriculum into two parts, identified by the report as ‘functional’ and more ‘theoretical’ or ‘conceptual’, was possibly implied by some of the pathway models discussed in the Smith Report, but there are strong arguments against dividing the curriculum in this way. It is a serious mistake to imagine that there is some part of mathematics which relates to the real world which does not require a theoretical or conceptual underpinning. The constant difficulty that many students have in handling simple ideas with number is at least at much to do with a lack of conceptual understanding and a suitable level of fluency as it is to do with a failure to see any ‘real world’ purpose for the ideas. The proposition that applications to real world contexts is inherently motivating is not self evident - good mathematics teachers use a wide variety of problems and puzzles at all levels as a valuable source of stimulus and motivation as well as a means to develop fluency, understanding and problem solving skills.

1.2 Since the Key Stage 4 National Curriculum is apparently to remain as the programme of study until the age of 16, we do not see that anything is to be gained by dividing mathematics between ‘core’ and ‘main’ learning. The report, like the Smith Report, says little about the precise content of what is referred to as ‘functional’ mathematics and is vague about how credit would be divided between ‘core’ and ‘main’ learning in mathematics. Mathematics should be taught and learnt as a unified subject: the Association does not support moves to introduce artificial subdivisions between the practical and the theoretical.

1.3 Beyond Key Stage 4, it is not clear from the report how changes in structures will help in resolving the serious difficulties that arise in making suitable provision for the many students who currently fail to achieve what is regarded as the benchmark of a grade C pass in GCSE mathematics. Renaming this as a component of the core at intermediate level does not of itself provide a means of preventing the perceived failure at 16 and the disillusion that comes with subsequent attempts to master the same material in order to achieve what is regarded as a pass.

1.4 It is not clear from the report whether there is an expectation that some element of core mathematics would be taken by all students after the age of 16. The proposed advanced diploma requires mathematics at intermediate level, but is not clear as to whether success in the intermediate diploma is sufficient or whether further study at this level is expected.

1.5 The report gives the impression that what is currently offered at A level will remain largely unchanged. That will be very welcome in the light of the many difficulties that mathematics at this level has encountered in recent years. The welcome recent encouragement for A level Further Mathematics in the DfES response to the Smith Report will likewise, we hope, be readily incorporated in an advanced diploma.

2. Reducing the assessment burden

2.1 We welcome the recognition that steps are needed to reduce the ‘burden of assessment’. Reducing or removing the requirements for coursework will be a useful step towards this in mathematics. However, the continuation of high stakes examinations with timed written papers at age 16, as well as at 18, in mathematics, linked to performance measures, targets and league tables, will continue to lead to all the undesirable effects produced by narrow ‘teaching to the test’. The report does not highlight these aspects of the ‘burden of assessment’ for mathematics as one of the components of ‘core’ learning and it fails to make any recommendations that will significantly change the current situation, particularly at intermediate level.

2.2 The report recommends a move to 4 modules for A level as a measure to reduce the assessment burden. Equal weighting of such modules would create a serious problem for mathematics in the light of the 2:1 pure/applied split which was agreed following the problems created by Curriculum 2000. Four modules weighted 2:1:2:1 would be acceptable in the longer term, but in the short term further change when recent changes are only just being implemented is not desirable.

2.3 The report states that a pass at any level should indicate some mastery of knowledge and skills. That is an aspiration to which we subscribe fully. Current examination practice does not ensure this, because threshold marks for a pass for GCSE grade C in mathematics, for example, are far too low. The report fails to face up to the problem of how current practice is to be changed in order to achieve the desirable end of demonstrating mastery. In the long term the problem is associated with improving the quality of teaching and learning and the cultural climate in which these take place, but in the shorter term it would be necessary to reduce dramatically the volume of content or else to accept that far fewer students will achieve the nationally accepted threshold. Both alternatives are unlikely to be politically acceptable.

3. Providing greater stretch and challenge

3.1 The proposal to introduce A+ and A++ grades and the incorporation of AEA into A level seeks to address the very real problems of discriminating between the ablest students at A level and challenging them suitably. However, extending the grade range in this way is likely to devalue the lower grades. Further detailed debate is needed to find a sensible way forward so that all students can demonstrate mastery at some level and so that the ablest students can demonstrate their skill at solving demanding problems rather than their ability to score high marks on what to them should be routine tasks.

3.2 There is no indication in the report how greater stretch and challenge could be incorporated into the way in which current National Curriculum programmes of study are taught and assessed. The Mathematical Association has consistently argued that able students require a programme which deepens their understanding and challenges them to solve demanding problems, rather than accelerating them along a path through more content. This view was strongly endorsed in recommendation 4.5 of the Smith Report: ‘This extension curriculum should be firmly rooted in the material of the current Programmes of Study, but pupils should be presented with greater challenges.’ Some formal assessment of such an extension curriculum would be vital to ensure its acceptance as an essential part of the mathematical experience of all able students. The Tomlinson Report has nothing to offer in this respect at the intermediate level: the only acknowledgement of the issue at this level seems to imply that greater stretch and challenge would be achieved by moving on to material required for advanced level. This is precisely the acceleration model that the mathematical community has argued against so strongly.

Conclusion

Whilst we endorse many of the aspirations of the Tomlinson Report, we are disappointed by the lack of detail in the proposals, particularly in the way that they relate to mathematics. We have serious concerns about:

• the lack of any clear definition of ‘functional mathematics’ or any consideration of the implications of splitting mathematics at Key Stage 4 into components;

• the failure to face the real issues linked to ‘teaching to the test’ which arise from the effects of the assessment burden on core subjects;

• the problem of changing current examination practice so that a ‘pass’ indicates a real mastery of an appropriate range of knowledge and skills;

• the redefining of grades at A level;

• the apparent endorsement of acceleration at intermediate level.

In spite of its very serious reservations about aspects of the report, the Mathematical Association looks forward to working with all those involved in striving to improve the quality of mathematical education for all 14 to 19 students.

19.11.04.