Examination of Witnesses (Questions 726
- 739)
MONDAY 19 APRIL 2004
PROFESSOR ADRIAN
SMITH
Q726 Chairman: Professor Smith, we
are very grateful that you have come to meet the Committee. As
you know, we are very interested in the findings in Making
Mathematics Count and we are also right in the midst of a
full inquiry into the skills of our nation and this is by way
of finding out some signposts to where we are going to go in this
inquiry. Would you like to say anything about your inquiry to
open up or would you like to go straight to questions?
Professor Smith: I am happy to
do either. The remit of the inquiry you will have seen from the
report itself. You will know that this is an inquiry into post-14
mathematics education prompted by certain sets of specific concerns.
But I would say both retrospectively and perhaps I felt at the
time that the world does not start at 14 and so one should not
take there to be an implicit premise that we have sorted it pre-14
and that the problems are post-14. The remit was post-14 and I
was aware of the dangers of straying into other territory where
I neither had the time nor the resource nor the expertise at my
disposal. But I would say just as a warning that there is a wider
context pre-14 which could bear further scrutiny.
Q727 Chairman: The whole world seems
to be in a bit of a tizz about mathematics and science teaching.
It seems to us that there have been a number of inquiries recently
taking place. Did you find that in the work you were doing you
bumped into all sorts of other people who were trying to come
up with answers? We have just had the Roberts report, for example.
Professor Smith: Yes. In fact,
I suspect that there is a direct line in terms of the prompting
for my report from the Roberts report. As you will know, the Roberts
report was a wider inquiry into the supply of scientists and engineers.
Many of the issues that it identified are relevant to mathematics
and I have drawn attention in the report to the commonalities.
Many of the findings and suggestions in the Roberts report will
find echoes in my report. However, I have argued that there is
something rather more special about mathematics, not only if you
take the conclusions of the Roberts report, that there are grave
difficulties in a number of areas of science and engineering,
but also because mathematics underpins most of those areas, so
it is an even more basic problem. I have added to that the fact
that there were studies done, and I am referring in particular
to one report, Mathematics Skills in the Workplace, which
is looking at rather different levels from the heady research
and development level that Roberts was focusing on in science
and engineering, where again mathematics is all-pervasive and
crucial. There is a third strand to that. If you look at employment
and life chances and all the rest of it there is a lot of data
which indicates that those who suffer from numeracy and literacy
deficiencies tend to suffer all the way along in terms of health
and employment and so on. So the spectrum of concern raised by
the mathematics problem coincides in part with the Roberts report
and with general concerns about science and engineering but also
has more specific elements that we could talk in more detail about
later if you wish.
Q728 Chairman: Do you think, looking
across the international perspective, that we are congenitally
less able to be good at mathematics? There are two problems, are
there not? There is teaching people to be numerate and to understand
even the maths that are available to them for their financial
understanding of their world through to developing talent in mathematics
and becoming teachers and academics. Is it the congenital argument
or do we just have lousy teaching?
Professor Smith: In all the areas
where one would have liked to make some crisp intellectual statement
international comparisons are extremely difficult. School systems
vary such a lot, the curriculum varies tremendously. There are
some international studies. I do not know if you are aware of
PISA and TIMSS in particular.
Q729 Chairman: We are very familiar
with them.
Professor Smith: The messages
are so conflicting if you look at it statistically. The Royal
Statistical Society had a half-day meeting on this that you might
want to pick up on outside the framework of these meetings, where
it looked at the statistics of trying to make these international
comparisons. What a lot of the reporting does is concentrate on
averages but there are very interesting messages in the variations,
there are huge variations. If you look at Japanese performances
they tend to be very closely clustered around the mean, so it
is almost as though you have got a cloned cohort of Japanese learners,
whereas if you look at America and Britain we have huge variances.
If we see something we like, for example, in PISA we are 8th in
OECD countries, we take great pleasure in that, and then we forget
to say that in TIMSS we are 20th out of 38. Disentangling these
messages is very difficult. I did have an expert report written
for me which compared and contrasted different systems, but by
the time you have factored in different school organisations,
different ways of looking at the curriculum, different paces and
different ages at which you do things, different expectations,
different assessment structures, you have got so much noise in
there that it is very difficult to take out the messages. Bear
in mind that the end product of my report was to try and make
practical recommendations to make the world a better place. There
is no point my saying that if only we had the teenage culture
of Singapore all would be well, so what are the practical means?
Again, if you look historically you will find that that the Singaporeans
and the Koreans do amazingly well at these things but there is
a totally different youth and school culture. A few years ago
the eastern Europeans would have done extremely well but there
is little point my saying that the absence of good television
programmes, discos and play stations is the answer to the problem.
Q730 Chairman: What about the quality
of teaching? Indeed, you have touched on it. Are there not modern,
more innovative ways of teaching mathematics? In teaching IT they
use different methods entirely. Are we still rooted in a tradition
that is not very good in terms of adding value?
Professor Smith: There are serious
issues about teaching which I have gone into in some detail but
you have to unpick them. It is in part the supply of qualified,
competent, charismatic, knowledgeable teachers who inspire and
there are big issues around that supply which I have set out at
length. There are issues around just the way one organises curriculum
assessment. Let us take post-16, for example. There is a widespread
view that somehow we have ended up modularising things into little
bits and testing each little bit as we go along, and so a number
of teachers would say that we are teaching for the test; we are
no longer really involved in an exciting, inspiring teaching and
learning process. There are a number of elements to this, including
modes of delivery. Do we make enough use of IT? There is teacher
supply. What goes on in the classroom will be constrained by curriculum
and assessment structures and I have made a lot of comments about
those. I do feel, and it is echoed by a lot of the responses to
the inquiry, that probably we are way behind in mathematics in
innovative modes of delivery. I have drawn attention to some particular
projects where people have, for example, put the whole of the
GCSE syllabuses up on the web. It seems to me very difficult to
document this in any evidential sense. You have generations of
kids like my own son for whom, over the period 12-18, private
study became less something he did in the corner of a room with
an angle poise lamp and a book and much more to do with surfing
the web and pulling together information. It would seem to me
highly likely that there are more amenable forms of acquiring
information through self-study which we have not properly researched
and adapted to, although there is a particular example at the
Thomas Telford School which has put all the GCSE stuff on the
web. There are other examples of distance enhancement and use
of ICT, but there is, one would have to say, no definitive evidence
base which says that we have put this in place, we have measured
this before, we have measured this afterwards. It is very elusive
to find anything that demonstrates that you can radically change
the teaching and learning environment or that the teaching and
learning environment has been radically changed for the better
by ICT except in small projects. I really do think there is a
need for a lot of concerted research and evaluation that pulls
together initiatives by various bodies, typically centred around
charismatic individuals, charity-funded for a few years. What
we do not do is go round afterwards and find out what worked and
then properly fund it and implement it across the board. Going
back to the international question, there are very specific national
things to do with teacher supply, to do with the way we organise
the curriculum and assessment, and to do with attitudes and investment
in resources for novel kinds of teaching. On all of those fronts
we have problems, but to look somewhere for some international
paragon of a model that one could pull over—
Q731 Chairman: Are there any other
countries that have this potential enormous gap in the numbers
of qualified maths teachers as one generation retires?
Professor Smith: Let me creep
up on that one. If you look carefully at my report you will see
a cry of angst about just how difficult it is even to get data
in the UK on the numbers and qualifications of teachers, and there
are not very easily accessible sources in other countries, so
my response would be partly anecdotal. To get to be a maths teacher
in France, for example, you have to go through all sorts of terrible
examination hoops and then you get posted to whatever part of
the country the Government decides to send you, so there is an
entirely different attitude and culture there, but there are countries
like the Netherlands which are similar to us. When my report came
out I was approached—and I do not think this was a confidential
approach—by somebody who was going to be in London from
the Netherlands equivalent of the Department of Education who
asked if we could get together because they have the same problem
and were thinking of doing a similar exercise. The Australians
have encountered a similar problem and the United States has got
it in spades and is launching a similar investigation. There is
an all-pervasive general problem about generating interest and
getting children as they move through the education system to
be committed to and to take up the study of maths, science, engineering
across many western countries. Some of those things will be culturally
and organisationally different in different countries and, as
I say, the main focus of my report was looking at the structures
and the approaches we have in the UK and asking the question,
"What could we change to practically do better?", which
is a slightly different question than undertaking a more abstract
and academic exercise.
Q732 Valerie Davey: You began early
by saying that there was a wider context and I recognise that
that was not the subject of your report. However, given that you
have reflected on it, have you anything to add in the context
of what we should be doing, let us say, 0-14, and are there issues
which have come to light or things which you have been prompted
to think about or talk to other people about which you would like
to share with us as important in as much as at 14 they obviously
do not come as a blank cheque; they come with that earlier experience?
Professor Smith: I will, of course,
answer but with a slight disclaimer that that was not the main
focus of my report.
Q733 Valerie Davey: I fully recognise
that.
Professor Smith: My total immersion
in the literature and realities is not quite the same as post-14
and so you need a health warning around some of the things I would
say.
Q734 Chairman: But, Professor Smith,
when we looked at early years education we were the first Committee
to appoint a clinical psychologist to advise us on the development
of a child's brain, in other words, on what is a good age to start
teaching children to do certain skills. We understood from our
technical advisers that it was not a good thing to push children
to do tasks such as learning writing too early. Is there any evidence
that that would be the case in teaching mathematics?
Professor Smith: I know of none.
There have been a lot of studies about the acquisition of various
kinds of mathematical and other skills. I know of nothing that
we do in primary schools that is radically awful or damaging or
dangerous in that respect. What I was going to focus on was something
else. Let me take the primary phase first. You will know that
in response to concerns about the acquisition of numeracy and
literacy skills, the national strategies were set up. In some
sense, without being rude to anybody, the very fact that such
things were set up means there is a whiff of the remedial about
it, that we have not got it right and we need to make further
input into it to make it better. Of course, a lot of that was
focused on what you might call Continuing Professional Development
for teachers. In some measure at the primary level that has been
quite effective but the fact that that intervention was effective
you could read as saying that we perhaps did not have a cohort
of primary school teachers with the kind of competences in their
own understanding and competence in mathematics and the teaching
of mathematics that was ideal. The fact that we put in an intervention
and development and things got better demonstrates that. Let me
remark in passing that if you look later on in my report there
are concerns people express at what is the real competence that
you have achieved if you scrape a C at GCSE maths, and just let
me remind you that that is the threshold qualification for training
to be a primary school teacher. If we are looking longer term
at the problem and we note already (and this might be a contentious
thing to say) that the effect of the numeracy strategy intervention
begins to tail off, all this goes back to teacher supply and the
qualifications of teachers. I would say, and I am saying it with
my earlier health warning that this was a post-14 report and I
am not an expert in this area, that it does seem to myself and
others bordering on the shocking that grade C at GCSE is regarded
as a sufficient level of competence to become a primary school
teacher.
Q735 Valerie Davey: Could we come
on to the element of motivation, which I think is those early
years, and the14-plus? It may well be apocryphal but I read that
the young people on the streets of Rio de Janeiro could calculate
the currency exchange quicker than a calculator. They knew the
value of the coins they were given immediately. That is a motivation;
they needed it. I think in the old days, dare I say, we needed
it more than perhaps young people do today with their calculators
and the till roll and all the rest of it. Let us now go to the
14-plus. What is the motivation for young people to learn mathematics?
Professor Smith: Could I come
back there because I made some remarks about primary but I did
not make remarks about Key Stage 3, 11-14. Let me briefly say
there that one of the clear effects of the shortage of specialist
mathematics teachers is that organisationally, and you can understand
exactly why this would happen, if you have a limited amount of
confident, competent specialist maths teaching resource in an
11-18 school you are likely to put it in the 14-onward phase.
There is a lot of evidence, and you will find it in Ofsted reports
as well, that in some areas maybe up to 50% of the lessons being
taught at Key Stage 3, 11-14, in mathematics are being taught
by non-specialist maths teachers. Anecdotally, what people will
tell you over and over again is that we are not doing too badly
at the job in primary school in enthusing and getting skills,
and then we go and knock the stuffing out of them between 11 and
14. I cannot evidence that in any particular scientific way but
I can draw attention to the fact that the 11-14 phase is where
you are most likely to get non-specialist, non-properly qualified
mathematics teachers.
Q736 Valerie Davey: Contrary to the
motivation element in a way, the best lesson I was ever taught
happened to be a maths lesson. We ended up by being told that
we had just proved Pythagoras's theorem. I can remember that lesson
as clearly as anything, just those last words at the end, "You
have just proved Pythagoras's theorem". Is it relevant? We
had no motivation but it was a brilliant lesson which I shall
always remember, and again it comes down to inspired teachers.
I think what you are saying and what is coming over very clearly
is that getting the motivation comes from the teacher and the
impact of how people share ideas.
Professor Smith: I think that
is absolutely crucial but the curriculum and the packaging also
play a part. There is universal agreement that as mathematics
and its applications expand there is a tendency to stuff more
and more into the curriculum, so you get an over-packed curriculum
and you are moving too fast for most people. You do not get enough
time to acquire fluency and practice. All these things are relevant,
the kinds of things that are available in the free-standing
mathematics qualifications, understanding personal finance and
so on; I think we could do a lot more creative things in motivating
kids. A lot of schoolchildren who are sitting there holding the
mobile phone will go home to play video games. Nobody tells them
that those things are based totally on mathematics.
Chairman: Professor Smith, I have a sneaking
desire to ask you to cross-examine Val Davey on about that particular
theorem, but I do not think we have time.
Q737 Mr Gibb: Can you just outline
for the Committee what the mathematics problem is that you have
been reporting?
Professor Smith: I think problems
rather than problem. If you want to focus just on two bullet points
following on from the Roberts report, if you look across science,
engineering, technology, they are underpinned by mathematics,
so there is a need for mathematics skills passing through those.
At that level you are talking primarily of the problem of the
bottleneck at 16. If you look at the numbers, and I will round
up these numbers for the purposes of illustration (these are not
the right numbers), about 500,000 children sit GCSE mathematics.
I lie; it is actually 600,000. About 50,000, a tenth, currently
pass through the A-level phase and then let us say 5,000 (in fact
nearer 4,000) go on to do degrees. Between 16 and passing through
to doing mathematics degrees at university you have got a hundredfold
decrease. There was already a worry about this problem. There
is a bottleneck. There are not enough people coming through to
acquire those higher level skills, the underpinning of science,
engineering, technology, the wider knowledge economy, the IT and
finance industries. The other aspect is that if you take those
who come off the conveyor belt at 16 you have got employers saying
that they either do not understand or that the abilities, the
skills, the competences that people have acquired are not what
employers want or are not at the level that employers want. There
are difficulties with the transition from 16 to A-level and then
universities will say, engineers will say, physicists will say,
maths departments will say, that post-A-level, people who have
done mathematics simply do not have the fluency skills that you
would associate with having acquired an A or a B at A-level mathematics.
You have got both a supply problem, the numbers doing it, and
also concerns from what you might call some of the end users,
about the competences that have been acquired. You put the two
together and you can say there is a problem.
Q738 Mr Gibb: But if we had the Minister
before us, like we will on Wednesday, he would cite PISA and say
that Britain is 8th in the OECD countries in terms of maths, so
there is not a problem. How do you counter David Milliband's comment
on Wednesday in answering that question?
Professor Smith: Even if we forgot
to tell him that we were 20th out of 38 in TIMSS, which I am sure
you would tell him, neither of those tells you about the supply
problem, does it?
Q739 Mr Gibb: Leave the quantum aside.
Let us look at the quality of the output. What is the answer to
that?
Professor Smith: If you then look
at your end users, whether they be employers or universities,
and their documented criticisms of the lack of competences, those
are real. They are a different source of complaint and analysis
than anything measured by PISA, so you might end up saying, "We
might have come 8th in PISA. That just shows how terrible others
are".
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