Current issues in Mathematics
Summer 2008
Introduction
This paper is written to accompany the opening plenary session at the MEI conference on
July 3rd 2008. It looks at three particular areas of current concern for mathematics
education in England.
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The proposed timing of changes to A Level
•
Mathematics in the level 3 diplomas
•
The design of the proposed scheme for two GCSEs
The proposed timing of changes to A Level
Under present plans, there will be two GCSEs in mathematics from 2012, with teaching
for the new qualifications starting in 2010. Many people see this as a window of
opportunity with the possibility of students learning more mathematics and engaging
better with the subject. If that proves to be the case we can expect many more students
wanting to continue the subject to AS and A Level, and also more wanting to do
mathematics associated with other post-16 qualifications.
It is almost inevitable that from 2012 onwards, students entering Year 12 will have
different knowledge, skills and attitudes; if they do not, the whole exercise of moving to
two GCSEs will have been a lost opportunity. However, just how these changes will
manifest themselves will remain to be seen until they happen; that is until 2012 at the
earliest and, more reliably, 2013. It will then be possible to design post-16 courses that
are appropriate for this new generation of students, building on their experiences.
The year 2013 has special significance since this is the date proposed for a general post16 review. The timing would seem to be perfect for mathematics.
Not so under present plans. New AS and A Level mathematics syllabuses will have been
introduced in 2011, just in time for the 2013 review to set up a second set of changes. If
put into practice, this proposal would be very damaging.
•
After just one year the new syllabuses, based on out-of-date information about
the incoming students, would no longer be fit for purpose.
•
They would be incompatible with the idea that we should be designing
coherent pathways for students.
•
Changes are always expensive to implement, both in financial and human
terms. To bring in one change knowing that it will shortly be replaced by
another would be a waste of resources.
Current issues in Mathematics
MEI, Summer 2008
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It would be possible to justify changes in 2011 if the existing syllabus was clearly
unsuccessful but this is far from the case. The Curriculum 2000 syllabus resulted in a
disastrous fall in student numbers and so was replaced by the present one in 2004. This is
proving fit for purpose. Teachers are happy with it and student numbers have recovered
to pre-curriculum 2000 levels, with further increases in the pipeline.
Why change a syllabus which is manifestly successful ? The lesson of Curriculum 2000
is that it is all too easy to make things worse rather than better.
Recommendation 1
Any plans to change A Level Mathematics in 2011 should be delayed until after
the 2013 review.
If the 2011 changes were to go ahead, a number of other issues would come to the
surface, including the major problems that would arise if it were decided to try to move
from a 6- to a 4-module structure. These questions will be much better subsumed into a
later review.
Mathematics in the level 3 diplomas
As the diploma programme takes shape, the quality of mathematics taught and learnt
post-16 appears to be increasingly at risk.
When the diplomas were first proposed many people expected them to be aimed at the
same students as existing vocational courses; those currently taking AS and A Levels in
mathematics would continue to do so but the mathematics available to the generally
weaker students who would now do the diplomas might well be better than at present.
This is not, however, how the diplomas are being designed. Instead they are being
targeted on the best students. It is claimed that a suitable diploma will equip a student to
go to any of the top universities. Furthermore the diplomas are to cover subject areas, like
engineering and science, where the usual route into degree courses had previously been
through A Levels.
In the present design, students learn the mathematics through special units within the
diplomas rather than through A Level. This sets up serious potential problems. Indeed it
would not be an overstatement to say that a successful diploma programme would have a
devastating effect on mathematics.
Imagine a situation where the diploma programme has really taken off; all 16-19 students
are on diploma courses and so A Levels have been phased out. The only mathematics
available is within the diplomas. What would this provision look like ?
Current issues in Mathematics
MEI, Summer 2008
3
•
The greatest amount of mathematics would seem likely to be the 240 guided
learning hours in the Engineering Diploma (60 hours for the compulsory unit
and 180 for the Additional and Specialist Learning unit). This is significantly
less than the 360 hours for a standard A Level Mathematics course and under
half of the time for a student taking a Further Mathematics qualification.
Consequently it would no longer be possible for students to attain current
standards in post-16 mathematics.
•
There would be no natural supply route for those going on to read
mathematics at university. The only mathematics available to students would
be designed to meet the diploma needs of engineering, science etc. and would
be taught within the confines of those courses. Nothing even resembling the
present Further Mathematics would exist.
•
Present syllabuses, with the availability of units from a variety of strands and
to a considerable depth, allow many students a rich mathematical experience.
This will be lost to diploma students; for example those doing all the
mathematics available in the Engineering Diploma will only meet quite trivial
statistics.
•
The diplomas are intended to be about education rather than training,
providing a gateway for students to go on to university courses. The fear is
that when they do so, students will find they have missed out on some of those
fundamental concepts of mathematics that are more easily assimilated when at
school or college.
•
The delivery would be fragmented with a multiplicity of mathematics courses
for the different units in the various diplomas. Consequently there would be
more lessons to be covered and existing competent teachers would be spread
more thinly.
The question “Why is there not a Mathematics Diploma ?” is sometimes asked. The
answer is that no one would want to present 16 to 19 year olds with a diet of solid
mathematics; even if such a diploma were available, it is far from clear that any students
would opt to take it.
Since good mathematics is crucial to the state of the nation, the diploma programme as
presently designed cannot be successful in the long term. It either has to be adapted or to
fail.
However, the problems can easily be solved. The content of, for example, the
mathematics units in the Engineering Diploma matches closely that in AS and A Level
units; it would be quite possible to make the match exact so that diploma students would
be taking AS and A Level mathematics units. It would then be possible for them to take
extra units and claim qualifications in AS and A Level Mathematics and Further
Mathematics. This is a sensible way to use the modular (or unitised) structure we already
have in place. Units from other subjects could also be integrated into relevant diplomas.
A counter-argument to this proposal is that the teaching approach for AS and A Level is
theoretical and so ill-suited to diploma students who should learn the subject in context.
This needs careful consideration.
Current issues in Mathematics
MEI, Summer 2008
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•
The key to learning mathematics successfully is good teaching.
•
Teaching in context can amount to no more than drilling students in the
techniques to use in particular types of problems; in such classes students do
not learn or understand the relationships within mathematics and so are unable
to use it in unfamiliar situations.
•
Good teachers always try to use approaches that will motivate their students
and have a variety of examples at their finger-tips to meet their particular
needs.
•
However, many mathematics teachers have limited knowledge of the way the
subject is used elsewhere and would welcome high quality resources
containing more context-based examples that they can use.
The last of these points shows a way of turning the current situation to advantage. In
September (2008), the first diploma courses will start and many of those teaching the
mathematics are going to need support. This could include the provision of good contextbased materials; indeed the Royal Academy of Engineering has instigated work to do just
this for the Engineering Diploma. If that happens across all the diplomas, mathematics
teachers will have a rich and helpful new resource.
Recommendation 2
It must be recognised that the current design of diplomas is not sustainable.
Changes will be needed if the standard of mathematics in our schools and
universities is not to fall drastically.
Recommendation 3
Appropriate AS and A Level units in mathematics (and other relevant subjects)
should replace the existing diploma units.
Recommendation 4
During the lifetime of the diplomas that are now being introduced, every effort
should be made to use them to develop good context-based mathematics teaching
resources.
It would be wrong to leave the subject of the new level 3 diplomas without drawing
attention to the highly unsatisfactory compulsory Principal Learning mathematics unit in
the Engineering Diploma (Unit 8). This is intended to provide a basic mathematics course
for everyone, including the weaker students many of whom will probably have achieved
grade C through the Foundation Tier GCSE.
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The content of Unit 8 is the equivalent of about 2 units in AS Level Mathematics and so
about 120 guided learning hours would be devoted to it. The same material in the
diploma is only allocated 60 hours. Even quite strong students will not be able to cope
with it in that time, let alone the rest. Many students will be unable to come to terms with
this unit and so will not learn enough mathematics to support either the rest of the
diploma or their own progression beyond it. The diplomas are meant to increase
participation; this unit will have exactly the opposite effect, disenfranchising students
who are capable of benefiting from the diploma as a whole. Clearly more funded time is
needed for many students taking this basic unit
Recommendation 5
A funded year-long bridging course should be available for those who enter the
level 3 Engineering Diploma without very strong mathematics.
The design of the two GCSEs
Present discussion is often focused on two aspects of the proposed introduction of two
mathematics GCSEs and a Functional Mathematics qualification.
•
The form of the assessments
•
Ensuring that all suitable students have access to both GCSE qualifications
These are obviously important matters, but they seem to have diverted attention away
from the key underlying question of how to ensure that the new provision results in more
students learning more mathematics.
Before that question can be answered, it is first necessary to consider (and admit to) the
shortcomings of the present GCSE. These can be summarised in terms of its outcomes.
•
Among the stronger students, too few are sufficiently inspired by the subject
to continue it to AS and A Level. About 80% of those who “pass” GCSE, with
grade A* to C, immediately drop mathematics.
•
Many weaker students do not engage with the subject; they see it as being not
for them and so learn very little. Some are turned off mathematics for life.
•
Few students leave GCSE with any level of functionality in mathematics.
Each of these points needs to be addressed specifically in the design of the new scheme.
¾
There should be a marked increase in the proportion of the age cohort
continuing mathematics to AS and A Level. That means that the new scheme
has to be more motivating than the existing GCSE. This will not happen on its
own; it needs to be more interesting and exciting for more able students.
¾
There needs to be a big improvement in the level of engagement of all
students. This will require very serious thought, leading to changes in both the
pedagogy and assessment, and possibly the curriculum too.
¾
The introduction of a Functional Mathematics qualification is intended to
improve students’ functionality. However, it should not be necessary; the
GCSE provision, if appropriately designed, should equip students with
Current issues in Mathematics
MEI, Summer 2008
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functional skills. One measure of success for the new GCSEs is that they
should render the Functional Mathematics qualification redundant at this
level.
Recommendation 6
It should be made clear how the design of the new GCSE provision is expected to
overcome the weaknesses in the present system and so result in a significant
improvement in students’ quality of mathematics and their approach to it.
QCA are conducting an on-line survey into views on the two GCSEs. It is obviously
really important that as many teachers as possible use this opportunity to make their
views known.
Conclusion
There are other major concerns in mathematics education, like the shortage of teachers
and public attitudes to the subject, but these are long-term issues with no quick solutions.
By contrast, the three matters raised in this paper are all short to medium term issues
where reasonably easy ways forward are readily available. However, they will affect
every young person in future cohorts, many more than once.
Appropriate action, as outlined in this paper, will help to ensure that more young people
to have a good experience of mathematics, and this in turn will make it easier to address
the long term issues.
Current issues in Mathematics
MEI, Summer 2008