Mathematics Teaching

HL Deb 19 January 2005 vol 668 cc781-818

3.14 p.m.

Lord Peston

rose to call attention to the state of mathematics teaching in schools; and to move for Papers.

The noble Lord said: My Lords, today's debate is motivated by the report, Making Mathematics Count, which was written by Professor Adrian Smith. His report was on post-14 mathematical education. I intend to view today's debate more broadly to include all school mathematical education. I also add a sort of declaration of interest; namely, that Professor Smith is Principal of Queen Mary, University of London, where I spent a very large part of my academic career.

When I say that I want to look at this more broadly, I want immediately to mention mathematics in primary schools, and to assert that much of the problem of mathematics and mathematical ignorance arises from lack of teaching or poor teaching when young people first come into contact with elementary calculation. But having said that, I should also add that most people—and not least employers—are confused because they believe that mathematics is just calculation. What is much more important is serious mathematics, which, as an intellectual discipline, is one in which rigorous proof is of the essence and calculation is hardly more than incidental.

Certainly we want everyone to be numerate in a calculation sense. I do not doubt that it is important for performance in the workplace that people are numerate in that way. But the reason for doing maths in schools is wider and deeper than that. It is to give young people direct experience of deductive, rational argument in its purest form. That is important for everyone and not merely for those who go on to become professional mathematicians, pure scientists or engineers.

The obvious analogy in my judgment is with English poetry. I imagine only a minority—probably a tiny minority of adults—read the poetry of Keats and Shelley, let alone Milton, and they probably think that Bob Dylan is a serious poet, but I am certain that all young people should at least be acquainted with the very best that English literature has to offer. I would say the same is true of mathematics. It is a subject for everybody.

Having said that, I recognise a point that will probably have been made by one of the many distinguished scientists who adorn our Benches—if any of them had bothered to turn up for today's debate—namely; that no serious study of natural science or engineering, or indeed nowadays of my own subject of economics, is possible without a proper grounding in mathematics. If that does not happen in school, it is not in the least surprising that the number of prospective students of science is lower than it might otherwise have been and that one ends up eventually with university science departments closing.

The general point, however, is that all students at school—and not merely those going on to do A-level—should be taught by people who have a proper understanding themselves of mathematics and who have been trained to teach the subject. I note with a degree of alarm in Adrian Smith's report his discovery that there are apparently very significant numbers of teachers in schools qualified to teach mathematics but who do not teach it; they do other things.

In that connection I must draw your Lordships' attention to the fact that training places for teachers of maths in teacher training colleges, or whatever they are called now, are regularly unfilled despite the valiant efforts of government to offer financial incentives to people to take up the places. The reason is that what little research we have shows that the average rate of return to an investment in maths degrees is higher than in other subjects, but that is because these mathematicians are not employed in schools or education more generally.

Again, as Adrian Smith points out, if income is what matters in people's job choice, then the finance industry is enormously more attractive than education. I must add that, compared certainly to when I and probably most of us were at school, the typical schoolteacher—and this is more general than just mathematicians nowadays—is subject to criticism from all sides and therefore the notion that they can compensate for lack of income with job satisfaction becomes more and more far-fetched.

I might add that the current policy, which seems to be supported very widely, of placing more of the cost of higher education on students must lead them to place more emphasis on lifetime income in deciding what to do after graduation. In the case in point, mathematicians will have an incentive to look elsewhere than schools for employment. While they may have a desire to enter public service, it becomes less and less affordable for them to do so. All of that must be placed in the context of the most recent research that I have looked at, which appears to indicate that not merely are the returns in teaching lower than can be earned in other work—I shall be interested to hear what my noble friend the Minister has to say about this matter and about the subject in general—but the gap has grown in the past 10 years.

I have already indicated that while basic numeracy is important it is far from what mathematics is really about. I make a similar point about data handling, which again shows how out-of-date I am. When I went to school I would not have had the faintest idea what the words "data handling" meant. I gather that it is now a very important part of the syllabus. It appears that data handling is quite different from what one might understand by statistics, let alone probability. The report says that the data handling component of GCSE ought to be re-examined and the time spent on it reduced. I am bound to say that I very much agree with that. In particular young people need to be taught rather more about matters such as spurious accuracy in data. My own test for innumeracy is the solemn reading out of figures—frequently by Ministers, I say to my noble friend—to several decimal places when the underlying data are hardly accurate to five percentage points.

I revert to pure mathematics as an intellectual discipline. As an amateur who loves pure mathematics, I regard it and mathematical logic as part of the greatest expression of the human intellect and the human imagination. It stands alongside serious music—that is, classical music—and literature as the true flowering of our civilisation. It is deeply to be regretted that so few young people in school have any acquaintance at all with pure mathematics in its strict sense. To take an obvious example, it has been known for 2,000 years that root two is not a rational number. But I wonder even how many A-level students would understand what I have just said, let alone be able to reproduce the proof that was known to Pythagoras and others.

I looked at current A-level papers in preparing for this debate. They, too, seem to be much more about calculating, albeit at a more advanced level, than any requirement to prove anything fundamental and in a rigorous form. My other worry about A-levels, at least as regards the papers that I have looked at, is that I discovered that I could do all the questions on the papers. I am bound to say that tells me absolutely that standards must have fallen. Therefore, I certainly support Professor Smith's recommendation that we need to strengthen the curriculum in a way which makes it more stringent and a much better test not only of the intellectual ability but also of the intellectual input, if you like, of the students doing these courses and these exams.

I conclude as I began. Professor Smith's report is of great importance and he is to be congratulated on it. However, it does not lie in his hands, or even in your Lordships' hands, to do anything about it. That is the task of government and it should be at the top of the department's priority list. I beg to move for Papers.

3.24 p.m.

Lord Lucas

My Lords, it is a great honour to follow the noble Lord, Lord Peston, who I have admired for many years, albeit from a distance. I am very glad that he has chosen to raise this subject in debate.

I am good enough at mathematics to know that I am not a mathematician, that I have my limitations and that I fall short of being able to enjoy the sort of beauty that exists in pure mathematics. However, I am close enough to see it and I am close enough to understand it in others. So I have to trudge along in the field of computation. Indeed, I have spent most of my life in the field of computation. I suspect that most of us do. Very few people really get the chance to exercise pure mathematics. It is a wonderful thing to be able to do. I would like to be able to do the Times crossword better than I do. One gets a lot of pleasure out of these intellectual exercises. However, it is not really the substance of life for most people, and certainly not for most students.

My recent exposure to the subject has comprised helping my children through their GCSE mathematics. They are both competent practitioners and I have not had to struggle too hard but I was struck by the grim syllabus we have evolved for mathematics. As the noble Lord, Lord Peston, says, it has none of the joys of pure

mathematics. As someone for whom mathematics is a beautiful thing, you cannot get any joy out of it. Nor can you get any practical use out of it as someone for whom mathematics is a tool. If you look at some of the things that people are asked to learn to do, and the sort of questions that they are asked in examinations, you just think, "Why?". What earthly joy or what earthly purpose has all this?

I have been an accountant and a merchant banker and studied physics at university, but I have never used most of the stuff that is in a modern GCSE syllabus. Even in my life it has not been necessary. As I say, calculating the volume of a cone is not something which brings much joy, albeit that I cannot think of a purpose for it at the moment. It seems ridiculous to me that we should have allowed ourselves to get into this pass because mathematics, and a better understanding of mathematics, would be useful to us if we taught the right kind of mathematics.

If, as the noble Lord, Lord Peston, said, we ended up with a better understanding of statistics, it would double the quality of Ministers overnight. We endlessly see articles written on the basis of scientific papers and then spouted on ministerial Benches—my party when in government was as bad in that respect as this Government—but when you get down to the research paper itself, there is some statistical technique being used to amplify data so that the result you are getting in words bears no relation to the result that is there in figures. My favourite example is the Tennessee Star Project on class sizes, which constituted the great proof that you need small class sizes to provide good education. When you got down to the paper itself, you found that if you halved the average class size, you got a 1 per cent improvement in results. Yes, it was statistically significant because they had carried out the research with lots of pupils and it was absolutely certain that this was a reliable result. However, it was not a useful result because you could find better ways of spending money and improving education than doubling the cost and getting a 1 per cent improvement.

I refer to the aversion we have in our society to risk and our failure to understand what risk is. We are happy to go out and buy a lottery ticket but shrink from the ordinary risks of everyday life to the point at which we deny ourselves many pleasures and greatly increase the cost of others because we do not have a rational understanding of risk. That is all based on mathematics and there is absolutely no reason why the mathematics we teach in schools should not have some relationship to the mathematics that we use in life. That would give children some pleasure in being able to use this subject in a way which would reinforce their willingness to learn it and their appreciation of its usefulness.

There is very little relationship in mathematics to the common applications of science that people see. The mathematics behind computer games is fascinating stuff. A book entitled, In Code, was published recently about number theory and the basis for encryption. It is a totally readable book. It demonstrates the fascination that people have with the application of mathematics in real life. But there is none of that in the syllabus. There is no connection between the properties of numbers and the fact that they might have a use.

I know that at the end of the day we want mathematicians who wander off into their abstruse spheres and think high thoughts, but most of us, if we are going to learn mathematics, will benefit enormously from having it connected. There is no reason why mathematics cannot by linked sensibly with other subjects. Surveying or architecture would be fascinating subjects to study at GCSE level. You would get your element of mathematics and an element of appreciation plus history. Crossing the subject boundaries like that and involving mathematics suddenly gives you an understanding of why geometry might be a useful subject rather than the dreadful, dry, purposeless questions which sit in mathematics papers.

As the noble Lord, Lord Peston, implied, you are never going to get great mathematicians to teach mathematics. Anyone who is zip at the subject is in the City or somewhere else earning a great deal of money, not least because they are capable of doing original work there. They are capable of tackling something which is new and producing a new result. Even if they are not capable of inventing a new mathematics, most mathematicians want to be involved in doing something new, which is where you are given the opportunity rather sitting down in front of a class of 14 year-olds and doing what you did 10 years ago.

If we want people to teach mathematics with relish, we ought to allow it a human side that connects it with real life and which allows it to be taught well and with an enthusiasm that is transmitted by people who, as the noble Lord, Lord Peston, said, have the expertise to teach mathematics, but whose main interest may well lie elsewhere—in a subject such as economics involving people, albeit quite remotely if you are doing classical economics. None the less, economics, politics, history, languages and other great subjects, all relate to people and the pleasures of real life.

You can see that, too, in the way the sciences are dealt with. The most popular science is biology, then chemistry and physics because you are getting more and more remote from real life. The physics syllabus is the one I followed when I studied physics. I liked it, but that is me. I can really understand why people do not want to know about the motions of vibrating springs or calculate what is happening to them. It is not something which has resonance, as you might say.

We ought not despair of mathematics or pupils, but we ought to look at what it is we are asking them to learn. We should start from the base and say, "Let's find ways in which we can give them some insight into the joys of the subject and the extraordinary beauty of the patterns and the way in which mathematics can move you from one place to another without seemingly having to understand what lies in between". It is an extraordinary thing to be shown. If we take them on a journey which involves something of real life rather than artificially constructed problems about steam engines, or whatever else might amuse the problem setters, we will really start to capture people and give them the feeling that it is something in which they wish to be involved.

If we go down that road we will find that people whose main subject is not going to be mathematics have picked up enough of it to enhance what they intend to do and the decisions they will take in their daily lives. We will have built a stronger foundation for the general teaching of mathematics. If that occurs, I shall be absolutely delighted. But the core to it is reforming the Qualifications and Curriculum Authority because that is where all these difficulties and drudgeries arise. We need much more innovation there. If I were to suggest one thing to the Government I would say, "Abolish it" and let us have examinations set and invented by people who really care about these things. Let us have some innovation and forward thinking. Let us have some diversity because all we have at the moment is stasis and decay.

3.34 p.m.

Lord Sheldon

My Lords, the noble Lord, Lord Lucas, has prompted me to consider for myself what use one is making of one's adventures into perhaps the higher realms of mathematics. In my case it is the probability theory from time to time just to see what the chances are of this or that. One makes use of that. One almost wants to turn to a blackboard, which is not there, when one is thinking about these things.

My congratulations to the noble Lord, Lord Peston, are not just conventional. He has introduced a subject that is very rarely debated in either House. He has pointed out that mathematics is not just calculation, which it is essentially for most people, but that a much wider use can be made of it. We perhaps should take that into account when we consider the work done at universities in teaching some of our young men and women.

It is right to say that there is the real problem of the cost to students of taking university courses. It is a very serious problem in the context of mathematics, which is a great expression of intellect. Mathematics is not the easiest route to earning the kind of money needed to repay the cost of university study.

For myself, mathematics is probably the only discipline which would be unaltered in any parallel universe which may exist. It is this abstraction which one finds so fascinating and which impels one's enthusiasm. It has a fundamental role in the practical aspects of our industry, economy and all parts of our practical world. I believe that although many other disciplines are necessary, mathematics as well as English are very special. They stand out above all others. Although they are all important, we need to take into account what Smith says in his report at page 14, paragraph 1.15. He points out that, in many respects [mathematics] is 'special' and that we must be prepared to consider, particularly in terms of organisation, structures, and investment, that different approaches and prioritisation may be required for mathematics That is wholly right and very important indeed.

I was an engineer in my younger days and I took a number of qualifications including an external degree at London University, which included a very high level of mathematics. I became particularly interested in the mathematics side of my studies. There was a lecturer at the college evening classes that I attended who was the eighth wrangler of Cambridge University in his day. He gave one a feeling of the greatness of mathematics and stimulated interest, which is vital to anybody who wants to regard mathematics as a serious and fascinating subject.

By contrast, another lecturer would put down equations on the blackboard without setting out their meanings. The contrast between these two kinds of instructional education is particularly important in showing that the one can enthuse a person wanting to look at mathematics and the other can regard it as a conventional background to the kind of work that that person is undertaking. This contrast showed me the importance of the subject and that how it is taught is so important to how students can be enthused.

Like the noble Lord, Lord Peston, in preparation for this debate, I have been looking at certain aspects of mathematics. I was looking at some differential equations to see just how much I understood them at this rather remote time of my life. I understood what they were about. I realised the concept of it all, but much of the detail I had lost long ago.

From the note that is produced by the Mathematical Association we can see the decline in student numbers. On page 23, in table 2.2, in the very important report Smith report, we see that the teachers qualified in mathematics have declined from 46,500 in 1988 to 30,800 eight years later. That is an enormous decline. Given the numbers interested in the subject and in university education, one might have expected to see a big increase.

I know there are problems about what is included, but it shows the decline in the numbers of those wanting such detailed knowledge of mathematics in their background. Also, 20 per cent of those who are teaching have no post-A-level qualification. Clearly, that is wrong. One needs to have quite considerable expertise to interest students and to create sufficient enthusiasm in them. The Mathematical Association, in a useful response to the post-14 mathematics inquiry, in paragraph 3.6, deals with the decline in A-level results. We see that in 1989, 12.8 per cent of students studied mathematics but that figure fell to 7.7 per cent in 13 years. That decline came in the late 1980s, but we have seen a further decline in more recent times, which is of great concern to us now.

Why has that happened? I believe that the decline in manufacturing industries may play a part, but another cause may be that the discipline of mathematics is different from that of other subjects taught in schools. In many subjects, an examination question can be answered in different ways; one can modify one's answers and still be broadly right. Mathematics is a much tighter discipline. There is usually only one way to produce an answer.

We have seen the perils of too frequent examinations. How can we repair the damage? The frequency of examinations is one aspect. Assuming a teacher has a certain amount of enthusiasm and background knowledge, frequent examinations do not allow a teacher to develop the broad approach that is required.

Are employers doing enough to influence the decline? They can play an important role by the very demands that they make on the students to study certain aspects to provide for a career structure that will be of use to them. Looking at paragraph 1.7 on page 12 of the very good and most valuable report of Professor Adrian Smith, we see that major employers in the engineering, construction, pharmaceutical, financial and retail sectors all make clear their continuing need for people with appropriate mathematical skills.

Given that pressure, I would have thought that there would be much more interest and enthusiasm for undertaking mathematics, just to meet the requirements of potential employers. Unfortunately, that has not happened. Why are they not demanding the standards that I am sure the schools and universities will be able to meet?

The next question is: should mathematics be compulsory after the age of 16? The Mathematical Association, in paragraph 2.1 on page 5 of its very useful report that has been sent to us, considers the possibility that there should be compulsory mathematics education for all students beyond 16. Although that is attractive, it should be carefully weighed as a priority against the need to improve substantially the quality of learning up to the age of 16. It is said that the quality of learning is central to the contribution that mathematics can make to this country's future. That is probably right.

The Roberts report, published in April 2002 pointed out the mismatch of the supply of young people for science, engineering, financial services and computer sectors. So there is a failure to meet the requirements.

On the suitability and qualifications of teachers, the report points out that 50 per cent of maths teachers are over 50 years of age. The figures are not exact because two kinds are taken into account, but it shows quite clearly that the maths teachers in this country are much older than teachers of other subjects. The worry is that the shortage of qualified teachers to come will lead to problems. Figure 2.2 on page 30 of Professor Adrian Smith's report shows that vacancy rates in maths are much the highest in a whole range of subjects. That cannot be right. It concerns our future industrially, commercially and in wider areas. We need to encourage people much more than we have done so far and attract to this important discipline many more young people than we see at present.

3.46 p.m.

Lord Wallace of Saltaire

My Lords, I hope that in the wind-up speech we shall hear a great deal about how the Government are taking the recommendations of the Smith report further. It is an extremely valuable and highly detailed report and it makes some important recommendations. I shall touch on some of them. In no sense am I a mathematician, but I declare a parental interest as the father of a son who is embarking on a PhD in pure mathematics in the United States. If there are opportunities here still for people like him, I hope that, when he has finished, he will be attracted back from the United States.

One of the first things that Professor Smith says in his report is that maths is important "for its own sake". It involves logic and calculation; the enjoyment of mathematics seems to me to be an important aspect which, I regret to say we are in danger of losing as a result of changes to the school syllabus. The proposals that maths A-level should shift more towards functional mathematics and away from pure mathematics seems to me to be part of what is wrong.

It is important to remember the number of different functions that mathematics plays in our society and economy. Professor Smith refers to logic, calculation, relevant work skills, the gateway to many other subjects, engineering, computing and even economics. I cannot resist saying to the noble Lord, Lord Peston, that we persuaded our son to take an economics course at an American university, where he is currently, with the thought that he may do something a little more relevant in the real world. His conclusion is that economics, as now taught, is muddled mathematics.

The report makes it clear that in Britain there is a crisis in maths teaching at all levels. Universities have suffered a decline in numbers studying the subject. From the latest figures that I have, I am happy to see that that decline appears to have stopped, although the numbers going through are not sufficient to sustain mathematically qualified teachers in schools.

A number of university maths departments are now surviving by, in effect, providing service teaching for other departments and the Government have to recognise that the system of university funding provides perverse incentives to reduce not just chemistry departments but also maths departments. There are three or four international-quality maths departments in universities in this country.

One of the objectives of all those concerned with higher education in this country should be to reverse that decline and to increase that number. The report suggests that regional maths centres should be developed as part of the national centre for educational excellence in mathematics. Those regional maths centres should be linked closely to regional universities. That means that there needs to be a top-class maths department in every region of this country, which sadly is not the case at present.

We have seen the figures on teacher supply; we understand what is happening in secondary schools where the number of those going on to A-levels is sadly declining. One of the teachers who taught my children, who has become a teacher-administrator, having worked for the QCA since then, tells me that one of the biggest problems is that too many students between the ages of 14 and 16 see mathematics as boring and obscure and more difficult than other subjects; therefore something

that you should get out of as quickly as possible and do something that will get you a better grade. How do we reverse that?

I declare a different interest as a shareholder in Filtronics, a company with its headquarters in Saltaire. It employs maths graduates and it works in narrow band electronics. Filtronics attempted to stimulate maths teaching and qualified mathematicians who it could recruit in West Yorkshire through a six-year scheme, in which it worked with relevant university maths departments and schools to provide small bursaries of £750 to people who stayed on at the age of 16 and studied maths. It underwrote schools with fewer than 10 students in their A-level maths classes to carry on teaching the subject at that level rather than to take the easy way out and stop it. It also sent professionals into schools to talk to 14 year-olds about why maths is fun and why maths is useful in your future career. They claim that over six years and at a cost of £125,000 a year they have enormously increased the throughput of students staying on to study maths in schools.

That is one experiment done by a particular company with particular assets at its disposal, but clearly we must learn from it. We must get practitioners into schools; we must get universities and schools working together much more; and above all we must enthuse that crucial group of 14 to 16 year-olds to understand that it is worth continuing with the subject. We ought to encourage the Government to engage not just business, but banks, which after all recruit a great many of these people, to work in partnership with them to get that enthusiasm going.

What other remedies do we have? Clearly, at university level the Government must make clear that maths departments are part of the core of any university, and to some extent they need to be treated differently from some other departments in funding terms. There is a general problem with the funding of particular low-level recruitment departments in universities, but we must not let maths go the way that chemistry is in danger of going.

I note a number of experiments with teaching internships for maths undergraduates, which is a way of providing them with some additional funding and showing them that teaching and learning can go well together. As it happens, my son taught in Uganda for a summer at the end of his first year of university because one of his schoolteachers had gone off to Uganda to teach maths. It made a huge difference to his understanding of the subject, and he enjoyed it enormously. Again, that is the sort of thing that the Government and others could be encouraging. We should be sending more practitioners into schools, and we should be teaching the history of mathematics much more at that level, because that is part of what explains to students why maths relates to real life. That would help the flow into A-levels from there.

Professional training for the many teachers who have come into maths from other subjects is clearly important. I trust that in the wind-up we will hear much more about what is going to happen about a national centre for excellence in maths teaching, and how it and the regional centres will be set up.

There are other things that one can do. My son was lucky enough to be entered by one of his schoolteachers in a not-bad comprehensive for the Maths Olympiad, a major scheme that gives extra assistance to bright students from different places, and he went through to the finals. I regret to say that only three students from state schools had got through to the last 20, which tells us something about the quality of teaching in independent and state schools. Some teachers from independent schools were extremely helpful at that stage. When we come to debate the Charities Bill, perhaps the Government might like to consider asking our independent school sector to run extra schools for bright children from the state sector at weekends or in the holidays. I know from the experience of friends that the independent sector pays its maths teachers far, far better than state schools. We could ask them to do that as a contribution to the public interest.

It is clear that we must encourage good maths teachers not to rise too quickly, as too many of them do, to become assistant or deputy heads because they are very good at constructing the timetable while no-one else can. Instead, they should stay on as senior teachers with the benefits that they can gain from that. It is also clear that we should be doing more to attract people who have pursued other careers to return to teaching in their 40s and 50s. The City of London pays mathematicians and physicists extraordinarily well—I declare a different parental interest in that—but they want to push you out by the time you are 40. Incidentally, by the time you are 40 you do not want to continue working 10 to 12-hour days. We should be trying to develop schemes to encourage those people to return to maths.

I repeat that maths is the core of education as much as is English; numeracy, logic and calculation stand alongside literacy as skills that we should encourage all children to learn, not only because they are useful, but for the joy of learning.

3.57 p.m.

Lord Barnett

I am delighted to congratulate my noble friend Lord Peston on introducing this debate and moving the Motion, which is not, incidentally, on pure mathematics. It is on mathematics which, in my experience, most people think of as pure arithmetic rather than pure maths. In fact, in my studies for an accountancy qualification, pure mathematics never entered into it. Equally, as Chief Secretary to the Treasury, in my experience pure maths never entered into anything—I see a former Permanent Secretary who can perhaps confirm that. Arithmetic may just about have entered into my work as Chief Secretary over the years.

The importance of maths has been emphasised by many, not least by Professor Adrian Smith in paragraph 0.12 of Making Mathematics Count: The Inquiry regards it as vital that society fully recognises the importance of mathematics; its importance for its own sake, as an intellectual discipline; for the knowledge economy; for science, technology and engineering". There is no reference to economics—I do not know what my noble friend has been doing all these years. Economics was not mentioned by Professor Adrian Smith in his excellent report.

Most of this debate has concentrated on education in secondary schools and universities. In practice, many experts believe that the problems that have arisen stem from failures in primary schools; right from the beginning. Indeed, some experts have said: The introduction of numeracy hour into primary schools may have damaged children's long-term understanding of maths". I am not sure about that, but it came from a government-funded report on research by London University, although I gather that the actual research was done by two students from the University of York. They argue that children may have been taught bad habits, and they refer to what is called "quick-fire mental arithmetic sessions". It is a long time since my primary school days, but I am sure that we had quick-fire lessons, which I do not think did me any harm throughout my career, either as an accountant or as Chief Secretary. I should be interested to know whether the Government have a view on the matter, or whether they let it go by.

The "experts"—I put the word in quotes—fear that falling numbers of maths students at A-level stem from primary level, where unqualified staff simply do not understand the subject they are teaching. That is rather disturbing, and I hope that the experts are wrong. I shall be glad to hear whether the Minister thinks they are wrong.

I turn to the excellent report on secondary education produced by Professor Adrian Smith, which was published as long ago as February last year. It follows a review by Sir Gareth Roberts, which was carried out, I assume, following an instruction from the Chancellor of the Exchequer, while Professor Smith's report was sought by the Chief Secretary to the Treasury. I do not know whether there are implications that that report was requested by the Chief Secretary rather than the Secretary of State. I see that Professor Adrian Smith sent his report directly to Charles Clarke, who was then the Secretary of State for Education and Skills. I assume that he sent a copy to the Chief Secretary because funds were required. I hope that that does not signify a significant change in who should control education or any other departmental expenditure.

The report, which has been mentioned often in the debate so far, refers to the deeply disturbing fact that many believe there is a major crisis in the teaching of mathematics. Professor Smith noted three major areas of concern. First, the curriculum and qualification framework has failed and fails to motivate students. Secondly, there is a serious shortage of specialist maths teachers. Thirdly, there is a lack of support for the infrastructure.

Professor Smith makes some 44 recommendations—I shall not refer to them all. There are three areas that are worth considering. First, in Chapter 1, entitled, "The Importance of Mathematics", he recommends the creation of a high-level post. I am glad that the department has advertised such an appointment. I shall

be glad to know whether that appointment has been made, or whether the temporary person put in charge, Anita Straker, has been made permanent.

Secondly, Chapter 2 refers directly to one of the central points in the debate so far, entitled: The Supply of Teachers of Mathematics. The issue of pay and other incentives has been referred to already, not least by my noble friend Lord Peston, who pointed out that the financial incentives are not in favour of producing more maths teachers. The question of paying more to provide such teachers will no doubt concern our right honourable friend the Chief Secretary. I do not know whether some discussions have already taken place, but no doubt the Minister will tell us. Chapter 6, headed, National and Regional Support Infrastructure, is the third issue referred to by Professor Smith in his covering letter. There are 18 recommendations under that heading. I shall refer to just one in the time available. Paragraph 6.1, recommends that the work of the National Numeracy Strategy … be continued and built upon, and that resources for mathematics are ring-fenced", for precisely this part of the problem. Again, I shall be glad to hear from my noble friend whether anything has been done in that regard.

As I said, it is now nearly 12 months since the report was published. We have had a sort of reply—I say that because it is a pretty generalised initial response from the department. It refers to a schedule of work, a 10-year investment programme and a five-year strategy, which we shall have shortly—I should like to know when.

There is too much generalisation in that initial response. To be told that it is dynamic, and so on, is all very nice, but we need something more specific in response to Adrian Smith's excellent report. We are told that there will be an incorporation of vision. I am all in favour of vision, and of incorporating it all over the place, but it is not an adequate response to a serious report.

The initial reply says that the Government will invite tenders by March 2005 for the establishment of the national centre for excellence in the teaching of mathematics. That would be a useful start, but will it be in March, which is now very close? I am glad to see that my noble friend is nodding. Such a centre for excellence could be very useful if it worked effectively.

We are told that there will be an increase in the value of the golden hello. It would have to be a pretty substantial increase to persuade many to stay in teaching mathematics rather than taking up accountancy, where they might feel that there would be a better personal financial reward, even with a small golden hello. No doubt my noble friend will tell us what she has agreed with the Chief Secretary in this regard.

We are told that there will be a development of excellent teacher status, giving top teachers access to salaries of more than £35,000 a year. The Government make it sound like such a huge salary, but how many top teachers will get even that modest £35,000 a year? It will sound a lot to many teachers, but it will not sound a lot to those who have gone to work in other parts of the economy rather than carrying on working as excellent teachers whom we so desperately need.

We are also told to expect the final report in the autumn of a working group that is being set up to sort out the proposed model for delivery of mathematics within a diploma framework. Maybe I have missed it, but I have not seen that yet. I assume that the report should have been published last autumn rather than autumn 2005.

Generalised answers in the initial reply are fine, but it is time that we had specific answers. I have read, as has my noble friend Lord Sheldon, the questions put by the Mathematical Association. I cannot refer to too many of them, but a couple are well worth mentioning. Recommendation 2.2 on the question of teacher supply requires, as suggested by Professor Smith, that a, revised form of SSCSS [Secondary Schools Curriculum and Staffing Survey], requiring a mandatory response …should be designed and undertaken as soon as possible. I hope that we will get it as soon as possible.

I want to end on a more constructive note. In doing so, I declare a non-financial interest as chairman of a non-financial charitable trust, called the Education Broadcasting Services Trust. It has been working closely with universities to produce a disk and a website, which will advantage many in the field. The programme has been running for only a year, but it already gets 10,000 hits per day. It gives pupils and students the opportunity to be taught by major national and international teachers. Help is being given by the Higher Education Funding Council and the likes of the Gatsby Foundation that do a marvellous job in the area.

I gather from the initial response of the Government that they are interested in using the web. Could they provide a little help, although not necessarily to the Education Broadcasting Services Trust? Many other organisations want to work in the area and do a first-class job. I would like to hear from my noble friend that she could get a bit of money—an extra few million pounds from the Chief Secretary, which would really only be petty cash—to help in this vital area.

Baroness Farrington of Ribbleton

My Lords, I draw noble Lords' attention to the fact that there has been a miscalculation in the allocation of time for this debate. We are actually five minutes short, so no one must overrun their time.

4.10 p.m.

Lord Moser

My Lords, perhaps whoever did the calculation did not do mathematics at school. I also thank the noble Lord, Lord Peston, for introducing the subject, which is of enormous importance. I have a personal reason for thanking him. A little more than 50 years ago, I was teaching mathematics at the London School of Economics, and one of the more promising students in my classes was young Maurice Peston. I feel now that I did not totally waste my time.

Enough has been said to underline the importance of mathematics for me to be very brief on that aspect. It is a wonderful discipline in its own right. It underpins almost all other disciplines, whether physical, medical, social or economic. It is crucial for an understanding of everything that goes on in business, the financial sector and everywhere else, and of the evidence adduced for issues of health, food, taxation and so on. It is at the core of our ordinary life.

I do not really distinguish between numeracy and mathematics. Numeracy is a core part of mathematics. A lot of mathematics is to do with numbers, and pure mathematics is to do with abstract matters, but numeracy is a part of it. I shall come back to that in a moment. For the ordinary citizen's life—to understand what goes on in a mortgage, banking, league tables and political announcements about taxation—an understanding of numbers and how to deal with them is crucial.

What is sad about the necessity for this debate, rather than about the debate itself, is that the concern with the state of mathematics in our society—it is not just in education—has been well known for decades. The Robbins report, with which I was involved, has been mentioned. We drew attention to it 40-odd years ago, and we were not the first. Since then, every educational inquiry of which I can think has highlighted mathematics as a key concern. The National Commission on Education—it was chaired by the noble Lord, Lord Walton—drew particular attention to it. There have been task forces and endless conferences, and somehow it needs a crisis to get a government into action.

The crisis is that, for most of the 1990s, mathematics has been in decline in the world of schools and A-levels. That has been known for 12 or 13 years. One-third of universities now say that they have to put on remedial courses in mathematics to enable students to cope with the subject, so the problem is not new. Given that, all that one can do is at least to welcome that this Government have commissioned the Smith report, and that they have appointed the chief adviser on mathematics, Professor Hoyles. That is good news.

The Smith report has been referred to by all speakers as excellent. The professor is a statistician, so he knew what he was doing. It focuses on teacher vacancies—the worst of any subject in schools—curriculums and the approach to teaching and learning. I do not need to repeat what other noble Lords have said. I want to talk about the fact that the problem, sadly and in a mysterious way, is much more deep-seated than can be coped with, even with good reforms in schools.

I notice that, in welcoming the report, the most recent Secretary of State, Mr Clarke, referred to numeracy and the importance of improving that part of the mathematical equipment. That makes me really worried, because the problem of dealing with numbers goes right through society. Where it comes from is a bit of a mystery, more in this country than in any other, certainly in Europe. I know from my decade as head of statistics in this country that there is more discomfort in the presence of numbers than was ever recognised by

any of my European or even American colleagues. They could not understand why we were so concerned with improving trust in statistics and with misuse of statistics.

I offered my resignation twice as director of statistics because governments of the day were inclined to misuse figures. In one case they did so rather innocently, and in the other they did not understand what the figures said. That is all around us. I remember at that time talking to the head of a very major FTSE company. I happened to say something about compound interest, and he said, "I have problems with compound interest". Then he corrected himself, saying, "To be honest, I have problems even with simple interest". What worried me about it was that, in a way, he was boasting. He was not ashamed. Such a statement would never be heard from a top industrialist in a European country.

I have often asked myself where that slight discomfort and boasting that one is not good with numbers comes from. I think that it comes from a school ethos that regards someone who is uneducated in classics and perhaps theology as truly uneducated, but does not feel the same about someone who is uneducated in mathematics. So there is a very serious problem that goes through the rest of society.

I became really concerned about the matter because—I must declare an interest—of something in a report that I wrote for the Government four years ago. It was called A Fresh Start and was about literacy and numeracy, examining both problems. The numeracy problems are much deeper than the literacy problems. Although there are definitional problems, if you take what is internationally regarded as the definition of severe innumeracy—people who cannot multiply two figures together and certainly cannot calculate change in the supermarket—24 per cent of the adult population are deeply and seriously innumerate. That leads to what other colleagues have been saying about mathematics. It is a very deep-seated problem. In Germany the equivalent figure, with the same test, is 7 per cent.

I come to my conclusions. In tackling the problem of mathematics in education now, priority number one is to implement the Smith report. Other noble Lords have focused on priorities including teacher supply, teacher retention, pay and the constant monitoring of what is happening with such an urgent problem—Smith suggested it should be once every two years. The immediate response from the Government was a little on the vague side as the noble Lord, Lord Barnett, said. I did not feel that the Government were grasping the problem with any real urgency. There will be too many inquiries, committees and so on. I would like the Minister to say that this matter will now be one of serious urgency within the educational strategy. I also hope that Professor Hoyles, the new chief adviser for mathematics, will focus on it.

Priority number two is that I hope that Professor Hoyles will focus, secondly, on primary schools. There is a lot to be done to get children of that age through numeracy, to experience the joy of figures and how they relate to everyday problems on television, on evidence for food and health prices and so on. Children are responsive to that, which could lead to a different approach to mathematics at secondary school—an approach based not on fear and boredom but on excitement.

If, as a result of the debate, the Government take the problem more widely through society—dealing also with family problems, because of the importance of parents in that particular game—then the noble Lord, Lord Peston, will have been justified in choosing the subject.

4.22 p.m.

Lord McKenzie of Luton

My Lords, I welcome this debate, initiated by my noble friend Lord Peston, as it raises important issues for our time. Any debate about education could be fully absorbed into the wider issues of the fundamental purpose of education policy: how much it should be about encouraging and empowering individuals to develop, to learn about learning, to become citizens in an increasingly complex and diverse society, to develop values and reference points and to experience achievement and fulfilment. That debate could be about the narrower issues of education associated with specific attainment and with acquiring skills and knowledge for employment.

Whatever the philosophical starting point and at whatever level, it is hard to overstate the importance of mathematics. As the report by Professor Adrian Smith, to which other noble Lords have referred, states, mathematics is important for its own sake as it helps to discipline the mind and develops logical and critical reasoning and problem sharing. It is essential for the development of the knowledge economy and forms the basis of most scientific and industrial research and development. The attainment of basic mathematical skills—whether they are called numeracy or calculation—is vital for everyday living, enabling individuals to participate in their communities, workplaces and places of leisure just as does their ability to communicate by language or, increasingly, to master the empowerment of ICT. If it does not lower the tone of the debate, a game of darts cannot be played without some mathematical skills.

To compete economically, we need to have more people engaging with mathematics at the highest level. To remain a cohesive and inclusive society, we need to enhance numeracy skills for all those currently at school and for those adults whom prior systems have failed. Mathematics is not just a narrow academic pursuit; however beautiful, it has to be part of the mainstream of our lives.

In preparation for speaking today I not only read the report of Professor Smith, but undertook a brief ring around of my local community to obtain an update on how various companies and organisations currently assessed this issue. I spoke to the LSC, the chamber of business, some employers, one of our secondary schools, the LEA and our sixth-form college. I should disclose that I serve on the governing body of the last two. The feedback is obviously anecdotal but there is undoubtedly a theme from business expressing concerns about the competencies in mathematics which is entirely consistent with the messages from the Smith analysis.

The individuals to whom I spoke referred not so much to the more sophisticated, higher level competencies but to more basic abilities to deal with problem solving, percentages and multiplication. One of our locally based airlines, for example, referred to some of their finance personnel not having a sufficient appreciation of numbers to be always able to gauge intuitively whether the outcome of a computation is right or wrong, or whether the order of magnitude is correct. They may be very competent at handling ICT systems but are not always good at recognising erroneous outputs which derive from incorrect inputs. The company sought to overcome that by encouraging its finance staff to take professional exams. There is a particular issue in ensuring that we reap all the benefits of technology—and the speed and ease of computation that this can bring—without losing core competencies around the understanding of numbers. I would not advocate a return to such far-off days but when I was studying for my accountancy exams, as an articled clerk, the advice I obtained from my principal in preparing for them was to practice adding up columns in the telephone directory.

These messages about competencies were echoed by the LSC, which was concerned that mathematics education in the past had not done enough to equip young people for employment—in particular, whether the curriculum was robust and flexible enough for some to succeed. Employers were having to backfill this deficiency. Our local sixth-form college—in fact, the first such college in the country, now with beacon status—has an open access policy and requires all of its students to study for the GCSE in maths and English if they arrive without those qualifications. This is both to develop core competency and in recognition that it is necessary for better access to higher education. Nevertheless a question was raised as to whether achieving grade C at GSCE is a truly adequate preparation for A-level.

The issue for schools, particularly secondary schools, is the shortage of sufficiently qualified specialist mathematics teachers. That of course is the paramount issue arising from Professor Smith's report, as other Lords have said. Secondary schools which do not have a sixth form suffer a particular disadvantage in this respect, as there is a natural and understandable tendency for maths specialists to go to schools and colleges where they can engage with students following AS-levels and A-levels. At a local level, LEAs and schools can and do develop programmes which attract teachers into the area, but they are essentially bidding them away from other areas. This of course does not help the national picture. There is, of course, no better way to enhance the numbers of students taking mathematics at a higher level than confronting them with enthusiastic, skilled teachers who have a passion for their subject.

Great emphasis has been placed on enhancing teaching skills, which must be absolutely right, but we should not overlook issues of learning. Understanding that young people have different learning styles should be an integral part of good teaching in any subject, including mathematics. Professor Smith's report does set out concerns over the curriculum and assessment for mathematics and how it is perceived to be a disproportionately hard subject. Again, other noble Lords have referred to that. This has influenced pupils' subject choices post 16, and has discouraged youngsters from continuing with the subjects. In this regard, his proposals to redesignate GCSE mathematics as a double award seems particularly sound. Finding more space in the mathematics timetable by switching teaching and learning of statistics to other disciplines also has some interesting possibilities.

An issue with which we have been grappling locally in the LEA is the differential performance in mathematics, particularly of students who do not have English as a first language. I am not sure whether we have solved or unravelled this matter, but it relates to the language in which the problem is expressed. If the nuances of that cannot be readily understood, it is difficult for youngsters to participate fully.

We should recognise that there are positive developments, despite the changes which we face. Professor Smith concentrates on post-14 issues, but we know that mathematics teaching does not start there. It starts in primary schools, where significant progress has been made since 1995, when the trends in international mathematics and science surveys showed that maths test scores for 10 year-olds in England were falling below the international average. More recent studies have revealed that mathematical attainment for England's year five pupils is now well above the international average and only a little behind the highest performing countries in the world.

However, more needs to be done and further progress will be hard to achieve. That will be greatly helped by more support for primary teachers to help them develop a wider understanding of the subject matter, greater skills on how to teach maths and using technology to enhance learning. The emphasis on post-14 development should not detract from that. We need to help primary teachers gain confidence to stretch young people. Neither should we ignore the progress that has been made at key stage 3, where the percentage of students who are attaining level 5 or above in mathematics has increased from 67 per cent in 2002 to 73 per cent in 2004—albeit that the 2004 outcome is a little behind target.

The Government should be commended for responding positively to a range of Professor Smith's recommendations, including improvements to pay, however inadequate these may be deemed by some noble Lords, and teacher training bursaries for mathematics graduates. A new national centre for excellence in mathematics and a chief adviser, the "maths tsar", has been appointed to oversee the implementation of the strategy and to raise the profile of the subject.

Changes to the curriculum, particularly to the prospect of being able to achieve a grade C or higher, whichever tier is followed at GCSE, will be generally welcome. The debate about where statistics fits into the new arrangements will undoubtedly be lively. Despite the clear progress which is being made, we should be realistic about how much needs to be done if we are truly going to make mathematics count. This must be a long-term project that is sustained by clear consensus in the mathematics community, as well as by politicians. It is an endeavour in which we must not fail.

4.32 p.m.

Lord Tunnicliffe

My Lords, when I was a schoolboy, I was very bad at reading and writing. Frankly, I am not very good at them now. For me, the word processor and the spell check have been a salvation. However, I was good at sums. I did sums, pursued them and was introduced to the wonderful world of mathematics, which, if you have not been there, is almost impossible to describe: the magic of algebra, the fascination of trigonometry and geometry, the understanding of rate of change and, in Newton's words, the "summation of infinitesimals".

So I was good at sums, which, by then, we were calling mathematics, and I went to study it at University College, London. I did not have a good first day there, because the provost stood up to say that anyone who did not go on to take a PhD would be a failure. The college staff's sole role in life was to create graduate researchers. So I took that knowledge away and thought, "Well, there are other things to do at university". Indeed, I learned to fly, to run a small business and, en passant, obtained a maths degree. But that left me, throughout my life, with the question: how much had that degree contributed to the world that it opened up for me and the successes that I gained?

So I thought that I should participate in this debate. Like everyone else I turned to Making Mathematics Count by Adrian Smith. It was a superb report which, although long, considers three general areas—the shortage of teachers, the failure of the curriculum and the lack of resources for continuing professional development. I disagree with the noble Lord, Lord Barnett, on the response, which, curiously, was also called Making Mathematics Count, published by the Government.

The responses to the first and last points were good. The moves that the Government have made to counter the shortage of teachers and the moves promised on continuing professional development were quite good. Perhaps I may assure the noble Lord, Lord Wallace, with anecdotal information from my pub, where we do not, in general see too many burned-out city types although we have an individual who spent half a career in information technology. He found that the arrangements available to change career to have been flexible and rewarding and he is now a couple of years into what he sees as a rewarding career as a mathematics teacher.

However, he faces one crucial question from time to time from pupils—"Sir, why are we doing this?". The area of fiercest criticism in the report and of least satisfaction in the response was the key issue identified in the overview, where it states that, the failure of the current curriculum, assessment and qualifications framework in England, Wales and Northern Ireland to meet the needs of many learners and to satisfy the requirements and expectations of employers and higher education institutions". The most acute failure in the curriculum identified in the report relates to AS levels. The words are extreme and identify a serious reduction in children moving forward to take A and AS levels as a result of the restructuring. The response by the Government, which starts on page 42 of their report, sets out a programme to counter this issue and calls upon the QCA to take action to counter this problem. I hope that the Minister can say how that programme is progressing, because the impact of the present A/AS curriculum is significant.

Briefly, I should mention the broader issue of what I would call the demand side of the equation. Professor Smith's report covers well the supply side—what is right and what is wrong with it. But the demand side—regarding what sort of mathematicians we need—is covered less well by the Government's response. The ability to create mathematicians, who are not a well defined group, depends on a scarce resource. It depends on mathematicians who are willing to be in teaching. While the Government are doing good things to try to improve that, they will be up against the fact that anyone who is good at mathematics is generally extremely employable. To employ well that limited resource, a curriculum that is appropriate to the needs of society is crucial.

We also need to motivate young people. We must give my friend in the pub the answer to, "Sir, why are we doing this?". We must be able to say to that young person, "It relates to your future work. You will find this useful. It is part of a total package".

While I have considered this problem for 30 or more years, I am privileged to have discussed this matter with the new chief adviser for mathematics, Professor Celia Hoyles, who was, at that time, Dean of Research and Consultancy at the Institute of Education—an institution with which I have had a relationship through my wife. Professor Hoyles and I had a long discussion about the question, "What do industry and society need from maths education?". I thought about that for some time and after our conversation I realised that I could not answer the question. I am in a pretty good position to answer the question. I have had a wide and varied career and I am a maths graduate. I realised that the question would require much more research than we presently carry out.

It was easy for me to say that none of my maths degree was at all relevant to my career. Indeed, just to ensure that I was not too numerate, the largest number I met during the years of studying for my maths degree was 34. Suddenly, I realised that, as I look back on my career, there is a whole series of subtle skills and subtle ways of

thinking about things—an ability to be able to communicate with other people's specialties for which maths equipped me. We therefore need to invest in understanding the demand side of the equation. We need a different set of mathematicians to do mathematics research. We probably need similar mathematicians to get involved in fundamental physics research, and so on.

As one comes from that rarefied position among engineers, relatively few engineers need to be at the cutting edge of mathematics but they do need to be good practitioners and able to use mathematical tools. It was said earlier that, in business and commerce, people could not understand compound interest and that sort of numeracy. There is something bigger than numeracy. It is about how things behave, how things lever, and so on. Yes, those skills probably are quite important but how much is that in demand and should you be putting scarce resources into it? In wider industry, there is the need to be able to cope with computation and numbers, but to what level and in what areas?

Finally, as has been mentioned, the modern citizen cannot exist and judge without some understanding of mathematics, numeracy and, particularly because they are the common language of our world, statistics.

The specific recommendation 1.3 in Professor Smith's report recommends the setting up of an advisory committee on maths research and industry. That committee, or something like it, is essential. The present decision-making in maths education is dominated by mathematicians and educators. We must bring the demand side of the equation into the debate.

Summing up, I think that this is a very good report and it is a pretty good response. In those immortal words, it is "good in parts". There is an urgent requirement for the QCA to address the A/AS problem. It is urgent that we develop and understand the curriculum changes necessary to motivate our young people and to create the skills for the modern world of work and for modern society. I would particularly like to hear the Minister's comments on the extent to which the Government will help in setting up the ACMRI.

4.42 p.m.

Lord Dearing

My Lords, I apologise for being absent from the Chamber during three of the speeches, but I am very grateful to the noble Lord, Lord Peston, for introducing this subject. I can think of no subject that is in greater crisis or where there are more grounds for concern than in mathematics.

In 1996, I was invited by the then Government to conduct a review of qualifications for 16 to 19 year-olds. My research showed me that there was no subject where there was more dissatisfaction from employers, and, for different reasons, the universities, than in mathematics. The noble Lord, Lord Peston, referred to a problem that goes back decades. With employers, I found that it went back for at least a centuryߞand we have not resolved it.

The noble Lord, Lord Moser, referred to 24 per cent of our people being innumerate. My understanding of the term is that it means those people have, at best, what is expected of an average 11 year-old. It is appalling. They cannot function effectively in the ordinary business of life. As for students—and this is part of the problem—too many of them find it difficult, boring, and not relevant to life as they see it. It is passing them by. Wherever I look, there is dissatisfaction.

When we look at the teaching side of it, reference has been made by the noble Lord, Lord Peston, to the number of teachers who are qualified to teach maths but who do not do so. Although the noble Lord was not absolutely certain about it, I think that the figure in Adrian Smith's report was 25 per cent. It would be very interesting to research in depth why that is so, because it is a serious problem: we have a serious shortage.

Reference has been made to the shortage of maths teachers. It is about two and a half times as great as that in Europe. We have a shortage of about 30 per cent, in terms of schools saying, "We do not have the qualified teachers to give the students what they should have". In Europe the figure is 12 per cent. However, we have 25 per cent who could be teaching maths and who have chosen not to.

When I deserted mathematics nearly 60 years ago, I had accomplished what was then called the School Certificate with some credit in mathematics. I knew about Pythagoras and I could probably do the proof, if given half-a-crown! I could do the unapproachable height problem in trigonometry and use the cosine and the sine. I could even do the odd quadratic equation. I went for a job when I was 16. It was a temporary job: male clerk, grade 3, in the tax office. I went to the Labour Exchange and I got a green card to introduce me. Off I went, with my good marks in the School Certificate. The guy I met sat me down at a desk. He sat on one side and I sat on the other. On my side was a great, long column of numbers. He gave me back the green card. I was not suitable. I could not add up that long column! I needed to practise on the telephone book! There is a problem between the ordinary everyday needs and mathematics of the kind to which the noble Lord, Lord Lucas, referred.

I am glad that the Minister is not commenting on the Tomlinson report, because the Government's reply is in gestation and the last thing we want is to hurry it. I am very concerned that we achieve a consensus on this before making any changes, because that is the best gift the politicians can give to education.

One of the good things about the Tomlinson report is that it suggests—as other noble Lords have suggested, including this one in his report in 1996—that we need to develop the basic competencies in number, functional mathematics, if you want to call it that, communication, and IT. The report proposes that in order to gain one of his diplomas—which he sees all kids doing at their appropriate levels—you have to reach the required standard in those three areas. It is a mastery test. You cannot compensate for doing badly in one area by doing well in another: you have to reach the required standards. For those three core subjects there are about 30 per cent of the marks for what we now call the A-levels.

Adrian Smith proposes that you should get more for mathematics than for the average subjects. I do not agree with the "snitching" point which was referred to. However, what Tomlinson proposes is that you do supplementary mathematics to get extra marks and credits. By that means, you can move towards what Smith wanted, namely, more reward for the work—which motivates students—without, as he suggested, solving a problem by just doubling it and shifting data-handling to poor old geography or biology. Trust mathematicians to think of something as unacceptable to biologists, et cetera, as that!

I believe that Tomlinson has something here, recognising that every man and woman requires this functional ability in the basics of mathematics and then to reward and encourage those who can—and most could, if there were good teachers—go on to gain extra credits in that subject. There is more corn for effort. For those for whom the joys are beyond the horizon, they can do what they can see is relevant.

Perhaps I may now come to one or two reservations about Tomlinson, in relation to the Smith report. Smith is concerned that you do not stop at 16, having got your credit in maths, and do not do any more in terms of A-levels. He wants to find ways of encouraging students. Tomlinson, as I see it, is not providing that motivation, which I think is a pity.

Generally, if there is a problem, do not blame the customers: have a look at the product and its delivery. Yes, I agree with Smith. One has to look at the curriculum. For those doing vocational subjects, I strongly believe that it is no good expecting them to enjoy doing maths in the abstract.

I recall going into a college and seeing GNVQ students in art and design. The idea that mathematics was relevant to them was beyond their comprehension and perhaps that of their teacher. It could be explained to them that, "Look, you might run your own little business. You have got to be able to cost a job". "Oh yes". "You have got to be able to do budgets. Oh, and you need to allow for overheads". "Oh, that is per cents, is it?". If one does that, one can get them into mathematics. A good aspect of the Tomlinson report is the proposal that while what you learn is the same, it is contextualised to make it relevant.

As regards teachers, I do not think that we shall ever solve this problem unless we get teachers who are very good. Good teachers will get pupils. Therein lies a very large part of the problem whereby 25 per cent of people who are qualified choose not to teach. That needs to be researched.

Other noble Lords have suggested the "golden hello". With tuition fees, we especially need a really good, attractive "golden hello". Yes, there should be reward for those who are excellent teachers; that is, not for being promoted to a supervisory job, but to stay as a first-rate teacher on the classroom floor. The rewards must be there. Continual professional development of high quality must also be there, so that teachers know that their professionalism is cherished and will be enhanced. They are very important guys who should be rewarded for achievement.

We shall never solve this problem until we solve the problem of why teachers are abandoning the subject and not enjoying it. Rewards are part of that, but enjoyment of the job, which turns on the curriculum, is very important. Perhaps we should take notice of the real opportunities from information technology. I believe that this has been looked at time and again. We have an excellent report from Adrian Smith and an interesting vehicle for development of those proposals through Tomlinson. Now is the time, after due consideration, for the Minister to stand up, before many weeks have gone by, and tell us what she will do.

4.53 p.m.

Baroness Sharp of Guildford

My Lords, I should like to join others in thanking the noble Lord, Lord Peston, for initiating this debate. He and I have long tried to contrive to secure a debate on the Smith report. I am delighted that we finally have.

I was very taken with the speech made by the noble Lord, Lord Tunnicliffe, when he spoke about the subtle skills that he learnt from his degree in mathematics. That is summed up in the letter that Professor Smith sent to Charles Clarke when he introduced his report. He wrote: Mathematics is of central importance to modern society. It provides the language and analytical tools underpinning much of our scientific and industrial research and development. Mathematical concepts, models and techniques are also key to many vital areas of the knowledge economy, including the finance and ICT industries. Mathematics is crucially important, too, for the employment opportunities and achievements of individual citizens". That is enormously true. One of the great dangers for this country is that if we fail to produce these mathematical skills, the knock-on effect of our not being able to undertake scientific research to keep up with ICT in other countries is enormous. We have a horrible phrase that I have used as an economist in relation to being able to understand knowledge; namely, the "absorptive capacity". The concept is that if we do not have scientific research that takes us to the leading edge of science, that is fine because 95 per cent of research is done in other countries and we can use that. But we cannot use the research if we do not have the tools. Mathematics is a key tool for making use of the research. If we fail in mathematics, we can fail abysmally.

Are we failing in mathematics? On reading the report produced not very long ago by the EPSRC, which looks at the relative excellence of maths in this country and elsewhere, the answer is "no" and that we are holding our own internationally. But I was brought up sharp by the figures that the Mathematics Association produced in relation to A-level entries. I had not taken them in. Are noble Lords aware that in 1989, 85,000 young people took A-level mathematics? In 2002, which was admittedly a very bad year because of AS-levels, that figure nevertheless had fallen to 53,000. 1 repeat: 85,000 in 1989, and by 2002 that figure was down to the 50,000 mark.

If we do not have young people taking A-level mathematics, what chance have we of them taking mathematics at university? Combine that with our serious shortage of teachers. Yes, I congratulate the Government, who are now recruiting 2,500 teachers of mathematics a year. But are noble Lords aware of the shortfall? Of those currently teaching mathematics in our schools, 25 per cent have no qualification or only a very weak qualification in mathematics. That is in the Smith report.

We have a shortfall of 30,000 teachers in mathematics. Recruiting 2,500 teachers a year, particularly as after five years something like 50 per cent of them have fallen by the wayside, is not enough. You have to look only at the balance—disproportionately, those teachers of mathematics are in the 45-plus age group—to realise that we face a very serious crisis. We need to do something about it. The question is whether the Government are doing enough about it.

The key issues are those raised by the Smith report; that is, the supply of teachers, continuous professional development and pedagogy. Let us look first at the supply of teachers. We are in very serious danger of falling into a vicious circle whereby because we are not producing enough teachers who are competent to teach the subject and inspire people, we are not getting the young people going through to A-level; we are getting them into university, but we are not producing enough university graduates to fulfil the teaching profession. Unless we can shake that up, we will not cope with it.

I was struck by a report from a group at the London School of Economics about the future shortages of teachers and their age profile. It noted that, Now the shortage of teachers looks set to become even more of a problem as large numbers of people currently in the profession near retirement. Shortages are especially acute in subjects like maths, science". One of the answers that the Government give is, "Ah, but we are moving to performance related pay and that is such a good thing". The report says that performance related pay, may not be the best vehicle to improve teacher performance, since the outcome of interest—pupil achievements—is multi-dimensional and depends on the efforts of a group of teachers rather than individuals. Evidence from elsewhere in the world tends not to support PRP schemes. In fact, over time, most schemes for teachers have collapsed and there is evidence that the ability of PRP to motivate staff is limited". So I think that we have to be quite careful about looking to something like PRP to motivate where we want to go.

How far have the Government gone with the survey that we need? One of the problems with the Smith report was that those who were writing it did not have even the figures that they needed. They did not even know how many teachers were properly qualified. How far has the secondary school staffing proceeded? Where are the Government going with that? That is a very important question.

I turn to CPD—continuous professional development. I am sorry—the awful part about the education world is all the acronyms that one gets into. CPD is desperately important, all the way up from the nursery school right through to the secondary school.

I ask again: are we doing enough? What about the national centre of excellence? What is happening to that proposal? What about the regional centres which go along with it? We really need to know much more about what is happening. The programme needs to be accelerated because we really have to get moving on this problem, which, as I indicated, is very serious.

I come lastly to pedagogy. I agree strongly with the noble Lord, Lord Tunnicliffe, who, I think, said that we had not talked about it very much, although we had talked around it a great deal. This issue is a fundamental problem. It takes us back to the point of the noble Lord, Lord Moser; namely, that 24 per cent of adults in this country are innumerate. As he said, that means that they cannot do simple calculations. On top of that, we have to bear it in mind that 30 per cent of those who spend 10 years studying mathematics in our schools come out with no qualification. Surely, that is an indictment of our schools.

Yet people say that the answer lies in teaching that is more relevant to everyday society. We have to be careful about moving in that direction. The noble Lord, Lord Dearing, talked about the Tomlinson report, but the Mathematical Association has great reservations about it. I have to say that I share its view when it states: 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 as 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". Are noble Lords aware that one can get an A grade in GCSE maths without doing any algebra? That is where we have got to. It requires a real questioning of what we mean by teaching mathematics. There is a great danger in thinking that we can teach arithmetic and that it teaches people the logical skills of mathematics that are so important.

The noble Lord, Lord Moser, raised the whole question of why people have such a hang-up about teaching mathematics. That is a vital question to tackle. We have not done enough research on it. It is fundamental to the way in which we teach the primary school, and even the pre-primary school, curriculum. It is an area where we need a lot more research and a lot more thinking. We need also to move as quickly as we can because there is a crisis. In their response to it, the Government have been totally complacent. They are operating only in the teacher supply area, which, so far as it goes, is quite good but is not nearly enough. Even we in this debate today have been too complacent.

5.4 p.m.

Lord Hanningfield

My Lords, I too congratulate the noble Lord, Lord Peston, on securing this important and timely debate. I welcome the opportunity to contribute from this Bench. The tremendous and learned contributions that we have heard today show the enormous value and expertise of this House. We could not have had a better debate on the problems of mathematics.

Like the noble Lord, Lord Tunnicliffe, I was quite good at maths at school. It was called arithmetic then. However, I did not go into the academic world as he did. I became a farmer and a politician. Perhaps if I had followed the academic route, I might have been able to make as valuable and learned a contribution as many other noble Lords have done today.

I have known the noble Lord, Lord Wallace of Saltaire, since my early twenties. If someone had told us then that we would be debating maths together in the House of Lords, we would not have believed it. Other noble Lords referred to their background, so I thought that I would mention that.

As everyone has said this afternoon, the state of mathematics in our schools—a matter that has been raised time and time again—is something about which we should all be concerned. The fact that around a third of pupils emerge each year without a qualification in mathematics that is valued by employers and by society gives some idea of the problem that we face.

I must state from the beginning that what I say is no criticism of maths teachers. They do a magnificent job, often in trying and difficult circumstances. The problem does not lie with them. All the speakers this afternoon have highlighted that fact. In fact, as most noble Lords have said, the problem is that we have far too few maths teachers. Furthermore, we have too many teachers who are not actually trained in maths but are expected to teach the subject. I was interested to hear the noble Lord, Lord Dearing, say that there were 25 per cent who could participate in teaching maths. That says something that we should think about.

Pupils in schools and the general public seem to be less interested in the subject year by year. It is now possible to see that the decline in maths as a subject and in the quality of provision has a significant impact on the country's economic and educational well-being. Everyone has quoted reports and figures this afternoon, so I shall quote some.

The second round of the OECD's programme for international student assessment, which involved more than 250,000 15 year-olds in 41 countries, showed in December 2004 that the UK had fallen from fourth to eleventh place internationally in science; from seventh to eleventh place in reading; and from eighth to eighteenth place in maths. In only three other OECD countries—Turkey, Luxembourg and Mexico—were more pupils held back by a shortage of well qualified and experienced teachers. The shortages were especially marked in maths, in which subject heads estimated that 41 per cent of pupils were hindered by a lack of appropriately qualified teachers, and in science, where the figure was 35 per cent.

The National Audit Office also reported on adult literacy just before Christmas. It concluded that 26 million people of working age had levels of literacy and numeracy below those expected of school leavers. The UK has a higher proportion of adults with a low level of numeracy than 13 other developed countries. Only six countries did worse: the Republic of Ireland, Hungary, Slovenia, Poland, Portugal and Chile. The number of adults without adequate numeracy skills is still growing by 100,000 a year. Those figures, which are dramatic, underline a lot of what has been said this afternoon.

The Tomlinson report has been talked about this afternoon. Mike Tomlinson learnt from employers and universities that they felt that they had no guarantee that someone who had obtained a top grade in GCSE maths was any good at the subject. Although 94 per cent of GCSE students sit maths, only 50 per cent achieve a grade C or above. Ninety per cent drop the subject at 16. The Smith report, to which everyone has referred this afternoon, highlighted a 25 per cent drop since 1991, and the number taking A-level maths has dropped too.

The number of young people studying mathematics and physical sciences is in sharp decline. That is particularly worrying when the demand for graduates and postgraduates in mathematically orientated subjects is, as we heard this afternoon, rising. In particular, science-based industries, financial services, telecommunications and information technology all require graduates in maths-based subjects. A-level entries for all subjects rose by 7.4 per cent in England, Wales and Northern Ireland between 1991 and 2003. However, entries fell by 18.7 per cent in chemistry, 24 per cent in maths and 29 per cent in physics.

A recent report in the Financial Times stated the obvious fact that the subject that lay at the heart of science and technology and played a vital role in economics, social science and medicine was maths. People want maths A-levels. Those who obtain A-level maths will probably earn 10 per cent more on average than those who do not.

As I have said, many noble Lords have referred to the extremely good Adrian Smith report. He concluded that the Government's record on maths provision was not good, as we know, and no doubt the Minister will respond to that later. But let me repeat what has been said by several noble Lords because these issues are very important. Professor Smith said that the real problem is that there is a shortage of maths teachers in secondary schools—a point made by the noble Baroness, Lady Sharp, and by many other noble Lords during the debate—and that approximately 30 per cent of teachers currently in post are under-qualified, the highest maths qualification for some teachers being only A-level. Young people are not stretched enough by either the current GCSE or A-level courses. As many noble Lords have said, the curriculum is not adequate.

Professor Smith's report states that priority must be given to the supply of maths teachers, a point made several times today. This cannot be done quickly, as we know, particularly given the small number of maths graduates each year. Nevertheless, he suggests that much can be done to improve the skills of those already teaching the subject. However, he concluded that, in the long term, maths teachers must be offered significant extra pay to attract more graduates into teaching and to strengthen the signals to young people that maths teaching can be a remunerative career worth choosing.

We have heard about the Government's response to the report—no doubt the Minister will add more later—and the proposal that maths teachers should get a £1,000 premium on the normal £6,000 bursary. In addition, from this year, the "golden hello" given to trainee maths teachers who continue into schools should rise from £4,000 to £5,000. Several noble Lords have commented on the "golden hello" and I ask the Minister to tell the House how far these reforms have been implemented and what impact they have had in reforming the teaching of maths, including the recruitment of additional maths teachers. I should be grateful, too, if the Minister could up-date the House on the establishment of the national centre for excellence in the teaching of mathematics.

We are doubtful whether a £1,000 premium will have a significant impact on enticing maths graduates into the profession. What is likely to be more important is how they perceive the teaching profession. To a certain extent, I agree with the noble Baroness, Lady Sharp, on that. Working conditions, reduced bureaucracy and excellent opportunities for continuing professional development are most important.

I am the leader of Essex County Council. One of our senior officers is Dr Puleston. His wife, Michelle, teaches in a comprehensive school. I asked her to give me her personal views and to obtain the views of other maths teachers in the school. The collective answer from this group of maths teachers was that there was a lack of time. Teachers are spending the vast majority of their time with all year groups preparing for examinations, with realistically little opportunity to encourage the investigative and thinking skills that would develop good mathematicians.

Teachers would like maths to be fun. They would like to teach pupils to love maths for maths' sake, or to think about the subject in such a way that they understand it. However, due to the pressures they face, they are teaching their pupils to achieve a particular level at key stage 3 or to achieve a particular grade at GCSE; they are not teaching pupils to love maths.

Examinations test processing skills, so teachers teach pupils how to process and how to get through examinations. This is not fun or stimulating for many students; it does not make them want to study maths further. It also does not enable them to use the maths that they have studied in the future if they have not fully understood what they are doing. So teachers feel rather disenchanted about the way they have to teach maths in schools. Teaching pupils in this way, with such an emphasis on examinations, is turning students off maths.

There are also concerns about the examinations themselves—a point made by several noble Lords today—and the curriculum that enables them to participate.

This has been a valuable debate with important contributions. I have been most impressed by the emphasis that all noble Lords have laid on how we can make maths more fun; on how we can get pupils involved at a primary level—or even a nursery level—so that they go into future education wanting to enjoy

it. I was quite good at maths because my parents enjoyed it and it was in our culture and in our thoughts; maths was part of our lives. I hope that we can inculcate that attitude into young people, and many of today's valuable contributions will help that. We need to help the teachers, as I have pointed out, to enable them to help children and young people to enjoy maths.

It has been a great debate. I hope the Minister will be able to give the House some answers.

5.15 p.m.

Baroness Andrews

My Lords, this is a maths debate so I shall try to give some answers. It has been a hugely enjoyable debate. It goes to show that maths can be fun, a theme that has run throughout the debate. I am indebted to my noble friend Lord Peston. I am glad that he has realised what has clearly been a long desire to have such a debate—quite rightly so—and I am sure that it has lived up to his expectations. It has been extremely good.

Noble Lords have been extremely diffident, not to say modest, about their mathematical abilities and achievements. They have then gone on to show that there was no reason for them to be so at all as they all seem to be particularly expert in different ways. I am probably the only Member of the House who has a real reason to be modest. It has felt to me like being in a collection of senior wranglers, with the senior wrangler par excellence sitting directly behind me. I hope that I, too, can live up to expectations.

The language of our debate has been extremely stimulating and generous. We have had mathematics compared to poetry but not yet to music. I shall make that connection, however, because it is often the case. Certainly maths is absolutely fundamental to our intellectual life in every respect. From the Greeks and Romans and the Persian mathematicians to the success of the Titan space mission last week maths affects every single application; it is the purest form of intellectual activity.

Yet, paradoxically, which is where the challenge presents itself, mathematics affects the informing and underpinning of the ordinary processes of everyday life, its common languages and experiences. In that paradox lies the challenge of the pedagogy: how to stretch and challenge the most able; how to give the less able confidence, in school and beyond; and how to ensure that not only the teaching environment but the learning environment produces the stimulation and the confidence that creates the mathematicians of the future. So that is the challenge the Government face.

As to the Smith report and how we responded to it, far from being fitful in our response we very much welcomed the report. It was an excellent, coherent report. We have accepted the vast majority of its recommendations and are working our way through them. We have publicly expressed our satisfaction. The implementation is being overseen by a programme which is based by the DfES's own Director General for Schools. Celia Hoyles, who is heading up the programme, is also a board member. So, far from lacking a sense of urgency, we are combining urgency with coherence in our response, and I hope I can go on and prove that.

It is interesting to know that Professor Smith was a close colleague of my noble friend. His challenges were to maintain motivation past compulsory education and then beyond A-level; to ensure that we have a system which understands the skills needed for a changing world, how the curriculum can respond and—this is particularly interesting—what mastery of the subject means. This is a particular challenge in a subject that is moving so fast, where the frontiers are so broad and where the definitions pose such problems. Thirdly, of course, there is also the challenge to create the optimum environment for teaching and learning.

I was particularly struck by the reference of my noble friend Lord McKenzie to different teaching styles—learning to learn. Having been involved in education for some years, I have become more aware of how much emphasis is now going into the notion of how we learn to learn. That is particularly critical at the edge of mathematics.

Indeed, the noble Lord, Lord Moser, was right to say that this is not a new debate. I shall not quote from the Cockcroft or the Robbins reports. I merely say that, The failures in arithmetic are mainly due to the scarcity of good teachers". That is from an HMI report of 1876. I am sure we could find a Tudor quotation as well.

Just as the problem is complex, long-standing, problematic and exercises our best brains, so do the solutions. That is not an excuse; it takes a long time to create a better culture in which to have confidence in, understand and value mathematics. We cannot do it alone. I agree with my noble friend Lord Barnett that it is the Government's responsibility, but as other noble Lords have pointed out, it is also the responsibility of other partners including industry, QCA and the voluntary sector. I take my noble friend's point that the Gatsby Charitable Foundation has done excellent work in stimulating mathematical research, and many other voluntary organisations do so as well. However, the noble Lord, Lord Moser, is right that we are confronting a profound cultural issue which goes to the heart of what people think they can learn and what they can master to live their lives.

The broad policy areas identified in the Smith report included the failure of the curriculum and qualifications framework; the quality of the teaching and learning experience; the difficulty of the subject; the failure to excite and provide appropriate motivation, to which so many noble Lords referred; and the lack of awareness. There are also the issues of difficulty in recruiting and retaining mathematics teachers and of professional development, to which the noble Baroness, Lady Sharp, referred. The report calls for a profound cultural change.

Those are our challenges and we are wrestling with them. It is not simply a question of how to incentivise mathematics teaching and learning for the brightest but how to make it relevant and exciting for all our children in school. So I am very pleased that my noble

friend Lord Peston talked about primary education. My noble friend Lord Barnett and the noble Baroness, Lady Sharp, talked about the foundation stages and the importance of what we can do to give the very youngest children confidence in and understanding of maths. I am referring not to numerical skills but to showing that shapes, numbers, perception, ratios are fun and enjoyable, because that enjoyment will go with them to the next stage.

The story is good when it comes to primary education. The mathematics performance at year five in primary school, according to the Trends in International Mathematics and Science Study, has increased by 47 scale points since 1995, the largest increase in any country. The increase is also evident across the range. The report that my noble friend Lord Barnett quoted from found that most teachers thought this was a success. It was not an entire, or indeed an original, judgment of our numeracy strategy, as I understand it. It was a synthetic study, which has to be considered in context. We should put it against our Ofsted and our international findings, which show that there have been significant improvements.

Having said that, we have a long way to go. I do not deny it, and there is no trace of complacency in anything I say this afternoon. Most recently, 74 per cent of 11 year-olds have reached the expected level of attainment—up one percentage point on 2003. In fact, we are focusing our teaching and learning in primary schools by introducing a much wider range of guidance and materials across the curriculum precisely to address the issues which noble Lords have raised about content, creativity and enjoyment, particularly for those who find the subject more difficult. We are looking hard at how to extend the range of materials. We are also developing central points of mathematics expertise within the new primary networks. That will lead to 1,500 to 2,000 primary maths centres nationwide. We are also increasing the impact of the primary leadership programme, making mathematics compulsory in the associated training programme. For unqualified teachers in primary school, that is a series of very specific responses.

My noble friend Lord McKenzie talked about the key stage 3 strategy. That is extremely important, because we have to keep the motivation and the confidence alive. The transition between key stages 2 and 3 has very often led to a loss of confidence for young children going to secondary school.

Our key stage 3 strategy is very specific, and we are seeing a real impact. The number of pupils achieving the expected level at key stage 3 has risen by 7 percentage points since 2001. I was very interested in what the noble Lord, Lord Wallace, said about excellence programmes and innovative programmes such as the Millennium Mathematics Project and the Olympiad.

We are looking, in transition and beyond, at a range of innovative programmes for the gifted and talented, in both primary and secondary schools, which will bring out their mathematical skills. A lot of very interesting work is taking place in the teaching of maths, such as brain gym, gifted and talented programmes, after-school clubs—very dear to my heart—out-of-school learning programmes and holiday schemes. We are looking at ways in which particularly enthusiastic young people and those who are good but are not confident can build on their skills outside school hours. So I think we have somewhere to go there.

Baroness Sharp of Guildford

My Lords, will the noble Baroness comment on the fact that for these more gifted children at key stage 3, that is not assessed within the curriculum? The curriculum is being developed to have, in effect, a further maths element—an extension element—but because it is not being assessed, it is not carried through in all schools and, to some extent, the children themselves write it off.

Baroness Andrews

My Lords, I know that the National Association of Mathematicians has made that criticism. While the extension programme is very new, that is possibly true, but we are seeing a transfer of technique and content into the mainstream curriculum from many of these programmes. I should have thought that that was very likely, but I will certainly give it some further thought.

Let me turn to the curriculum and assessment issues raised by the Smith report and by noble Lords. What has been said this afternoon is correct: maths has the highest entry of all GCSEs. Some 50 per cent of the cohort obtained grade A^* to C and 91 per cent obtained A^* to G. The Smith report pointed out that the current GCSE structure seemed to have a lot of disincentives built in. Many young people could not achieve a grade C in the first place and there was also the double award effect, as my noble friend said. Some were unprepared to make the transition to A-level. The perception was that the content of A-level was too large to be mastered. Those are very specific criticisms, to which we have responded.

We have been presented with an opportunity in terms of the GCSE. We expect very shortly to take a decision on the QCA's authority about the introduction of a two-tier maths GCSE. It has been piloted over two examinations. Rather than having a three-tier GCSE, a two-tier GCSE looks very likely, which will give all candidates access to grade C. It will also ensure that those who attain grade B are tested on higher grade material. That will, in itself, inspire many more to go on to A-level.

In terms of A-level, we have addressed the issue of an overloaded, demotivating curriculum. As of last September, we have revised the AS and A-level specifications and the core content is now distributed over four rather than three units, with two applied units. That will help to address the drop in A-level numbers, to which many noble Lords have referred, not least my noble friend Lord Tunnicliffe, who asked specifically what was happening in this field. QCA is monitoring the position; it is also monitoring those who get good GCSEs but do not go on to take A-levels and those who start but do not finish. So we are addressing the point very specifically.

The QCA has an enormous programme of work. I do not agree with the noble Lord, Lord Lucas, that we should abolish it. It is an extremely important and creative body. It is looking at a whole range of longer term issues to do with GCSEs: the content and size of the curriculum; the impact of technology on the mathematics curriculum; the use of ICT in maths; and statistics and data handling. It is looking at many aspects in order to clarify the amount of teaching time needed, taking on board what the Tomlinson report said about the load of casework and how we might address that. That is going to be in the longer term.

I have spoken a bit about the high achievers, and where in fact we hope that that will lead us.

The noble Lord, Lord Dearing, raised the issue of the Tomlinson report in a very courteous and understanding way, and discussed the relationship between that and the Smith report. He did a brilliant analysis of the relationship between the two reports. We shall have to wait for the White Paper, which I am sure will not be too long in coming, to see how those two sets of imperatives will sit together. The Tomlinson report referred very much to the core of functional competencies and the main learning programmes—and I am sure that we shall draw on what the Smith report said.

On that theme, the QCA is expected very shortly to let contracts for the first phase of development work on potential models for a curriculum assessment model, which will have a course of functional maths.

Higher education was something that we touched on very briefly. We are very much aware of the need to maintain and improve our levels of recruitment to maths teaching. Feeding through the system as we do, I feel sure that we are actually better placed than we were. We are also very alert to the situation in science and engineering departments; that is why the former Secretary of State, Charles Clarke, asked the Higher Education Funding Council to advise us on how we might maintain the profile of key subjects such as maths and sciences in the higher education sector. We look forward to receiving that feedback. For those who get to university and cannot cope with the maths, the Higher Education Academy provides support for providing them with additional skills.

I move swiftly on to the second major issue—the importance of the charismatic teacher, the one who makes all the difference. Many noble Lords have referred to that issue. How do we get the very best teachers in sufficient number? I do not want to conceal or diminish the problems, but nor should I underplay what the Government are doing and how seriously we are taking the matter. Although the number of vacancies for maths has fallen by almost 40 per cent during this Parliament, there are still more vacancies than for any other subject. But the picture is improving; recruitment is up by 60 per cent since 2000, and we have more people starting teacher training this year than there have been on record for 15 years—that is, 2,500. This is the fourth year of successive rising achievement.

Yes, I can tell the noble Lord, Lord Hanningfield, that we believe that the bursaries, which now amount to £6,000, are making a difference. That sum will rise to £7,000 in September, just as the "golden hello" will rise from £4,000 to £5,000. However, we believe that it is not just higher pay that encourages recruitment; the noble Lord, Lord Hanningfield, was right to refer to the workload, for instance. We are trying to address that by training a cadre of specialist higher level teaching assistants, for example, and by reducing bureaucracy wherever we can.

The good news is not only that we are recruiting more teachers at initial teacher training. A TTA report is due out tomorrow, and I believe that I can anticipate it without taking too many risks. It shows that there is a whole cadre of people coming from sectors such as banking, who are taking early retirement from those sectors and coming into teaching. I recommend that we all read that report very closely. As for age profile, we are also introducing graduate teachers from other professions. But the pay has gone up, and we have schemes such as the advanced skills teaching programme, which will keep teachers teaching and not administrating.

The crucial point, as the noble Baroness, Lady Sharp, pointed out, is continuous professional development. The noble Baroness said that a cultural shift was required, and I believe that it is absolutely vital. We are grasping the nettle, and our five-year strategy is full of it. But the National Centre for Excellence will involve the establishment of a nationwide network of quality subject-specific continuing CPD opportunities. This is our big chance; this is our opportunity to look at mathematics, across the whole range of what we want for the future. Our approach will provide strategic direction but it will also actually get down at the sharp end to what we want in terms of the best quality teaching and content. I hope that all those measures together will address some of the problems raised by the noble Lord, Lord Moser, about basic skills.

Sadly, I have to finish there; it has been a bit of a gallop, but I have come a sort of full circle. The noble Lord, Lord Tunnicliffe, asked what sort of mathematicians we wanted in future. That is the key question, and I have no glib answer to it. But we do want to see mathematicians who are fit for purpose, whatever that purpose may be; who are literate in all forms of mathematics at the frontiers of knowledge but are also able to manage their own business in daily life. We believe that the appointment of Professor Celia Hoyles as chief adviser in mathematics with the Department for Education and Skills will make a big difference. She is very committed to raising the profile and the value of maths—that, plus the national centre, which will be putting out tenders in March. I am pleased to say that we are well on track with that.

We are doing what we can. I am sure that there is more to be done, and noble Lords have pointed out that there is more to be done. But with the scope and determination that we have, we are in with a chance of addressing some of the basic problems which we have faced for so long.

I am conscious that I have not answered all questions, including the one about the staffing survey. But when I have not been able to answer a question I am very happy to write to noble Lords and to circulate the letters. I thank my noble friend Lord Peston on behalf of all noble Lords.

5.35 p.m.

Lord Peston

My Lords, in the few moments that we have left, I shall rectify a gap in my speech. This point was in my speaking notes, but I decided not to mention it in the hope that another noble Lord would do so. Professor Smith's recommendation 2.6 was that consideration should be given to the introduction of new mathematics teacher certification schemes, with the aim of increasing the overall supply of teachers appropriately qualified to teach at least some part of the curriculum. That struck me as an exceptionally good recommendation and, since no other noble Lord has underlined it, I shall just draw it again to my noble friend the Minister's attention.

The noble Lords, Lord McKenzie and Lord Tunnicliffe, pointed out that learning maths is hard. The other point is that teaching maths is hard. That is the other thing that we have to bear in mind. Going back to my days as a teacher, I remember year after year, since all that you needed to know in economics was demand and supply, making remarks like, "Well, the equilibrium is where the demand curve intersects the supply curve and that is the solution of a pair of simultaneous equations". Everybody would look at me blankly, so I would say exactly the same again and they would still look at me blankly. But then in those days, before the reforms of the present Government and their predecessor, professors were completely above criticism—so if the students did not understand something it was just too bad! That is the difference between what I used to have to do and what maths teachers in schools have to do now, so I am deeply sensitive to their problems.

In response to the comment made by the son of the noble Lord, Lord Wallace of Saltaire, I really do agree with him. I still read the academic journals. An article will have an interesting opening paragraph, written in English; then it will have a dozen pages of mathematics and then the same opening remarks repeated in equivalent English, though not identical. So you read the opening remarks and say, "That is a very good point and it is obvious what follows". Then you go to the end, and you have the ethical dilemma of deciding whether to read the 12 pages of mathematics in between. I have never cracked that, because I know that it is my ethical duty to do it but I also know that the maths is there because the chap has not the slightest chance of getting his paper published in an academic journal unless he includes in it maths that most people cannot understand. So that is a serious question.

I conclude, however, with a remark on darts, which was raised by my noble friend Lord McKenzie. I swear that I read in the paper not long ago that there was a crisis in the darts business because far too many darts players cannot work out the score and, in particular, cannot work out what double they need to win. I am certain that I read that somewhere. So we have a maths crisis in darts, as well as everywhere else.

It remains to me to thank all noble Lords who spoke. I am a lifelong learner, and I learned a great deal today from noble Lords. In addition, I thank my noble friend the Minister. This is about as difficult a subject to respond to as one can imagine, and she did an outstanding job in addressing your Lordships' House. My Lords, I beg leave to withdraw the Motion.

Motion for Papers, by leave, withdrawn.