Mathematics

As a country, we’re not very good at Maths – Dick Evans explores some of the reasons for this and suggests how we “could do better”.

It’s one of those national concerns that con tinues to attract press attention usually following critical inspection reports and is associated with the weak numeric skills possessed by students whether in school, college, university, employment or society in general. Whichever way you analyse the problem and its causes it is one of the most serious elements within the educational and training world.

As the world becomes more scientifically and technologically based the underlying weakness in mathematics must surely undermine our ability to compete internationally and reduces our competitive edge in areas of endeavour that require numerical and mathematical skills. The problems exist across all sectors of education and training whether it is at the community level including basic numeracy and financial literacy, school, FE, HE and work-based level. The causes must include a cultural dimension as it has been such a long standing problem which has precipitated a number of perplexing and at times contradictory outcomes. There is a marked reluctance, indeed almost a hostility, to the area of mathematical concepts and aspects that are numerical especially, in England. People seem to readily accept that they are ‘not good at maths’ and equally worrying are not prepared to do any thing about it. The Moser report highlighted the massive level of adult innumeracy in this country and the subsequent government action to create a number of national strategies and organisations seems to have produced little lasting impact on reducing the levels of innumeracy. Recent Ofsted and ALI reports continue to highlight the crisis in numeracy and mathematics teaching. So let’s look at each of the sectors of education and training to assess the current state of numeracy and mathematics.

Basic Skills – Numeracy.

The National Research and Development Centre for adult literacy and numeracy (NRDC) has recently called for a great debate on numeracy. It stresses that numeracy has up to now been seen as secondary to literacy. More attention and resource has been given to the latter even though the level of innumeracy is higher than for illiteracy. But the problem is far more serious in numeracy with 23.8 million adults who have numeracy skills at level 1 or below (1). Yet the survey reported an interesting contradiction namely that people over-estimated their numeric ability as well as their ability in literacy. Many people appear to excuse themselves by saying that most calculations are now performed for them e.g. electronic cash registers, automatic petrol pumps and electronic calculators carry out the operations. The greater use of calculators has raised some fundamental questions/ about the teaching and subsequent learning and understanding of mathematical operations e.g. why? how? and the importance of estimation. Recently attention has been drawn to the problems in understanding personal finances and a national programme has been launched to address the issues around financial literacy. Clearly a lack of understanding of how to calculate simple and compound interest along with other equally important computations has led to much of the current concerns about personal debt. In spite of the national ‘Skills for Life’  (SfL)programme and a great deal of additional funding this country continues to reside at the bottom of most international league tables in mathematics and annual surveys reveal little improvement and where progress is shown our international competitors show greater improvements.

Schools.

The problems here are longstanding and systemic and seem to be immune to solution. There is now an ever-accelerating downward spiral caused by the shortage of qualified teachers and too few young entrants to the profession. Ofsted reports continue to highlight the lack of real and lasting impact of such initiatives as the numeracy hour in the primary sector and the painfully slow improving pass rates at the various SATs and GCSE levels.

Most graduates in mathematics do not enter teaching and those who do go into the private sector with the result that the state system witnesses a growing crisis in recruitment and retention of teachers. Over 30% of mathematics teachers do not possess degree or equivalent qualifications in the subject. Many teachers come to teach the subject as a result of the shortages – the classic and extreme example is the arthritic PE teacher. Poor teachers produce students with poor mathematical skills and so the downward spiral is generated. Very few careers teachers have any qualification or knowledge of mathematics, which surely leads to partial guidance into areas of employment that require numerical skills e.g. engineering and science. Obtaining precise details of the number of qualified teachers in schools continues to be a problem and this further complicates the development of strategies to plan and manage teacher supply. Too often the mathematics curricula are inappropriate and the associated assessment regimes often further distort the teaching and learning opportunities for those who find the subject difficult. Research has shown that the current curriculum is failing the top 8% and the bottom 30% of the learners and that for the remaining much of the mathematics is still seen as irrelevant and unattractive. The majority of students drop mathematics after GCSE and do not take the subject at GCE AS/A level – interesting to note 50% of students aged 16 fail to gain a grade C in the subject.

Many international comparisons e.g. with East Europe, Indian sub-continent show how poorly we perform although to be fair the US and now Japan are experiencing difficulties in recruiting and retaining mathematics staff. One reason for the recent increase in off-shoring call centres to India is the high level of literacy and numeracy skills possessed by the workers many of whom are graduates in disciplines that demand numerical capability.

Post-16 Providers.

The shortage of qualified teachers of mathematics and numeracy in post-16 providers is even more critical than in schools. There has been a mass exodus from colleges of specialist teachers in mathematics, science and engineering in particular over the past decade or so and very few new entrants into colleges. The absence of an effective management information system (MIS) in post-16 providers for recording and reporting the professional details of teaching staff makes any planning nigh impossible. The issues associated with MIS in FE have been known and well documented since the incorporation of colleges in the early 1990s and now with an extended post-16 sector the problems are even more critical. Without accurate information no meaningful action can be taken to address the acute problems with the supply of teachers let alone establishing re-training programmes.

Colleges and training providers have to pick up the problems students possess with poor achievements in mathematics and numeracy and who enrol for a wide range of subjects or programmes that require numeric or mathematical skills. Many enrol on vocational programmes e.g. modern apprenticeships, technician and craft provision. Too often these students cannot see the need for numerical skills or mathematics, after all who needs maths to be a caterer/ hairdresser/ plumber etc – I have taught these students and it presents some great challenges in convincing them of the value of these skills even those that are relevant to the profession or trade.

Compensate for school problems.

Colleges and training providers have to recognise and then compensate for the inherited problems from school whether the students are progressing on to GCE AS/A levels or vocational programmes. In addition they have to deliver the key skill of application of number to students who are often reluctant and cannot see the relevance of this and the other key skills. Couple this with a shortage of sufficient qualified teachers, poor learning support and inadequate resources little wonder critical inspection reports are common place. The recent fiasco over Curriculum 2000 (C2k) and AS’ mathematics in particular brought about a significant dropout from the A2 stage of C2k in mathematics and the subsequent problems this will cause will resonate for many years. Another worrying feature is that the current initial FE teaching qualification does not provide sufficient support or preparation for people entering the profession.

Teaching numeracy and Mathematics does present different challenges resulting from the views and perceptions real or imagined by the students of the subject. These perceptions have been recorded from a number of surveys over the years and have elicited the following recurring comments:

• The subject is difficult and most teachers seem uninspiring and unable to make it interesting and exciting as other subjects.
• Mathematics is boring, difficult and irrelevant.
• It does not enhance my earning power -other jobs are better paid.
• I can get by without maths
• I am not good at mathematics.

It will be interesting to see what recommendations the Tomlinson review will make in regard to the examination structures post-14 and how these will address the problems in a number of key subjects e.g. mathematics, modern languages, design and technology.

Higher Education.

For a number of decades university admission tutors and lecturers have complained about the inadequacy of mathematical knowledge and skills of students studying such subjects as engineering, the physical/biological sciences/ construction. Many have developed comprehensive diagnostic testing regimes and now provide additional learning support facilities in order to identify deficiencies and to introduce remediation programmes to help the students. One of the problems identified by these diagnostic tests is the omission in the National Curriculum mathematics syllabuses of key subjects such as algebra and elements of geometry and trigonometry. In addition other key difficulties are identified including weaknesses in the students ability to use key mathematical skills such as technical facilities, (the ability to perform numerical and algebraic operations), and a marked decline in analytical powers when it involves more than one operation. These concerns and subsequent developments in the university sector are expressed in ‘Tackling the Mathematics Problem’ (2).

The continuing decline in student enrolments in mathematics will bring about the closure of around 6 departments of mathematics in the university sector this year. Link this with the closure of 70 departments of engineering and science over the past 6 years, all subjects requiring a high degree of mathematical content and you will see the approaching crisis in these strategically important subjects.

Work-Based Provision.

This area is the most neglected and suffers a dearth of research and subsequent development into this important area. What limited research exists highlights that too often employers and employees do not recognise what mathematics is involved in the job or more worrying what level of mathematical skills are required within the workplace. This stark fact presents the training and college providers who often have to prepare students for the work place with major problems. The challenge is to make the content of the programme interesting and relevant to the student and equally important to prepare the future employee to be competent in the workplace. One real problem at present is the insistence in the Modern Apprenticeship programmes that all students pass all of the key skills and that includes the application of number where the pass rate is truly abysmal. This on-going difficulty is proving a real problem in the recruiting and retention of students on the MA programmes. Successive reports by both ALI and Ofsted have highlighted the problems with the application of number key skill and its impact on success rates and has caused real concerns within the provider networks e.g. colleges and training organisations. If we are serious about creating a successful apprenticeship route the issue of application of number needs to be reviewed and the programmes required for the acquisition of essential numeric skills and mathematics configured in a way that possesses relevance and is fit for purpose. Too often a great deal of the mathematics taught at all stages is redundant and seldom used subsequently by the majority of students whether they enter work or progress on to FE/HE.

General Observation.

How many popular books are on mathematics or indeed how many films are made around the subject there are a few exceptions like ‘A Beautiful Mind.’ The whole area is seen as distant and disconnected from real life. Science seems to be more acceptable but this does not seem to attract more people into these subjects especially teaching. So is it a cultural issue? (Personal note: I seriuosly think it is a cultural issue!)

In order to begin to address some of the key causes of innumeracy, weak numeric skills and poor achievement in mathematics the following need to be considered:

• Formulate a national strategy for adult numeracy.
• Carry out a fundamental review and subsequent radical reform of the schools and college curriculum that creates programmes that are fit for purpose – this will clarify what numerical/mathematical skills are essential for particular programmes of study e.g.non-vocational, vocational.
• Fully investigate the possible benefits of ILT and ICT in the teaching and learning of numeracy /application of number and mathematics.
• Improve career guidance to make people more aware of the economic benefits of a qualification in mathematics.
• Carry out a fundamental review of teacher recruitment/ training/re-training and investigate the issues associated with retention of mathematics teachers.
• Make certain the various stages of the edu-cation/training system are more fully aware of what each is doing in regard to mathematics.
• Reduce the amount of assessment associated with the national curriculum and the post-16 qualifications framework – it distorts the teaching and learning process and diverts the limited and valuable teacher resource that should be focussed on the pupil/student.
• Tackle once and for all the issues around the recruitment and retention of mathematics teachers – move away from short term solutions e.g. employing overseas people and supply teachers, golden handshakes and handcuffs.
• Review salaries and conditions of service for teachers of key shortage subjects.

Let’s try and end on a more positive note. A great deal is now happening in mathematics education. The post-14 mathematics inquiry, chaired by Professor Adrian Smith, reported on 24th February and made a number of important and radical recommendations. In addition an independent committee the Advisory Committee on Mathematics Education (ACME), chaired by Sir Christopher Llewellyn Smith, continues its work on a series of important projects associated with the subject e.g. CPD for teachers and currently on assessment. There has already been a positive result following one of ACMEs recommendations namely to establish a National Centre of Excellence for Mathematics supported by a network of centres based around England to support maths teachers.

These websites are well worth visiting: mathsinquiry.org.uk and acme-uk.org

References:

• (1) “The Skills for Life”. (SfL) Survey DfES Research Brief RB490 (TSO, October 2003).
• (2) “Tackling the Mathematics Problem”. Institute of Mathematics and its Applications, London Mathematical Society and Royal Statistical Society. October 1995