The Mathematical Association - supporting mathematics in education

Whilst the problems relating to mathematics teaching in schools and colleges have many similarities to those of science teaching, there are many particular difficulties associated with learning and teaching mathematics. It has a high profile as a result of its great importance to our society both in underpinning a wide range of disciplines and in providing many of the elementary skills needed in everyday life and in employment. It does need separate consideration, a fact that has been recognised in setting up the Smith Inquiry whose report Making Mathematics Count[1] was published in February 2004.

The Mathematical Association, in its evidence to the Smith Inquiry, highlighted three key issues which are closely interrelated. These are reproduced below and are as valid today as when they were written in early 2002.

1. The recruitment and retention of mathematics teachers is a matter for very serious concern. Radical and sustained measures over many years are required following an analysis of the underlying causes of this very real crisis facing mathematics.

No matter what form proposals for reforming mathematical education take, effective implementation will only be possible if there is a substantial increase in the number of mathematics teachers with sufficient understanding of the subject and the enthusiasm and skill to teach it well. Without progress on this issue, real improvements in standards simply cannot be achieved.

2. The quality of teaching and learning of mathematics needs to be greatly improved. The content of the mathematics curriculum is broadly acceptable and does not require substantial change. The problem is not what is taught, but how it is taught, or, much more to the point, what is learnt.

A period of curricular stability is needed to allow real progress in improving the quality of teaching and learning by reducing the pressures on teachers so that they have time to think and plan and engage in sustained professional development. This would help to create the conditions which are necessary for success in easing recruitment and retention problems.

3. The current system of assessment and all the accompanying targets and league tables are having substantial ill effects on the teaching and learning of mathematics. A radical shift away from the current dominance of tests, examinations, targets and league tables is essential if standards in mathematics are to be improved.

The excessive emphasis on tests and examinations has the very serious effect of skewing all classroom activity towards the short term goal of maximising test results. Important aspects of mathematical learning that are hard to assess become optional in the eyes of both students and teachers. A substantial reduction in statutory testing is necessary if the quality of teaching and learning is to be improved and would contribute greatly to creating an environment in which mathematics teaching is a more congenial task.

The measure of our success is the extent to which mathematics lessons that stimulate interest and boost confidence become the common experience of all students, so that they are able to acquire knowledge and skills with understanding and can apply what they have learnt to a wide variety of challenging situations.

Prior to the publication of the report mathematics had experienced a serious setback when there was a disastrous decline in the number of candidates taking A level as a result of the changes that followed from Curriculum 2000. Whilst there have been modest improvements in numbers since there is, so far, little sign of a rapid return to the numbers prior to those changes which had already been in decline over at least the previous ten years. Smith proposed that groups be set up to consider ‘pathways’ for post-14 mathematics, but other aspects of government reform are hastening change so that the potential good work that had been set in train is being undermined by further piecemeal changes that are not part of a coherent strategy.

There is a serious and long standing shortage of secondary school mathematics teachers which includes a significant hidden shortage caused by the employment of many teachers with weak subject knowledge and inadequate training in teaching the subject. It is difficult to quantify these shortages because of the lack of good data, but a recent report from NFER[2] has noted that 24% of those teaching mathematics are non-specialists.

The problem is further exacerbated by the difficulty in retaining good mathematics teachers in the profession. A small scale research project has been set up by The Mathematical Association and funded by the Gatsby Foundation. Its report Career Patterns of Secondary Mathematics Teachers[3] has just been published. It draws attention to the important characteristic of mathematics teachers whose major source of career satisfaction is linked to their love of the subject and their wish to communicate that enthusiasm. Disillusionment sets in when the demands of the job make it impossible to sustain that enthusiasm. Many factors influence this, but those concerned with pupil behaviour, workload leading to lack of time and the pressures created by the assessment and accountability systems and by constant changes were commonly mentioned by the teachers and former teachers who contributed to the research. Supportive schools and departments and opportunities for professional development contribute significantly to career satisfaction, but the relentless pressures clearly take their toll on morale, health and the opportunity to lead a normal life.

There is an urgency about tackling the issue of retention, which could begin by acknowledging and then acting upon the fact that many aspects of government policies exacerbate the problems. Many of the difficulties that lead to poor retention also contribute to the problem of recruiting sufficient people into the profession.

There is a remarkably wide consensus about the content of the mathematics curriculum at all levels, but much less agreement about how it should be taught. The National Secondary Strategy has had a variable impact: whilst it provides a structure and a range of ideas that have helped many teachers, it is seen by others as very prescriptive and that is unhelpful in getting the best out of thoughtful and creative teachers.

Moreover many teachers feel seriously constrained by a system that is increasingly controlled from the centre and dominated by the assessment and accountability system, which encourages a narrow 'teaching to the test' which focuses exclusively on rehearsing skills and solving standard problems. This compromises the enthusiasm of both teachers and students, fails to develop students’ ability to think independently and detracts from their enjoyment of mathematics, which in turn leads to fewer students wishing to take the subject beyond year 11 and the next generation of parents conveying their distaste for mathematics to their children.

Much more needs to be done to give teachers frequent opportunities to renew their enthusiasm by reflecting on mathematics and the problems of teaching it effectively. Whilst much rhetoric focuses on the value of teachers working together as a team and engaging in professional development, there is little sign of resources being made available on a sufficient scale so that teachers have the time to engage with these valuable activities throughout their careers. The National Centre for Excellence in Teaching Mathematics (NCETM) is an immensely valuable initiative, but its activities will make little impact unless teachers are given adequate time to engage with what it has to offer.

The issues highlighted in the earlier sections are more critical than buildings and resources although many mathematics teachers are pleased to acknowledge that they have benefited greatly from the expenditure on buildings and ICT resources in recent years. However, there is an urgent need to reduce class sizes. This issue is critical to teacher’s morale and the difficulties they commonly face in creating a classroom ethos where learning can take priority over wrestling with the problems of pupils’ attitudes and behaviour.

Good teachers are the key to raising standards and improving attitudes towards mathematics. We need government policies that create the conditions in which all teachers feel valued and where they feel able to pursue the difficult task of teaching mathematics free from excessive interference and pressure and, above all, with the time to do the job well.

[1] Making Mathematics Count: the Report of Professor Adrian Smith’s Inquiry into Post-14 Mathematics Education February 2004 The report can be downloaded from www.mathsinquiry.org.uk.

[2] National Foundation for Educational Research (NFER) Mathematics and Science in Secondary Schools: the Deployment of Teachers and Support Staff to deliver the Curriculum January 2006 The report can be downloaded from www.dfes.gov.uk/research.

[3] Smart, Teresa and Tickly, Clare Career Patterns of Secondary Mathematics Teachers The Mathematical Association June 2006