Access to Further Mathematics at AS and A Level

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Access to Further Mathematics at AS and A Level

• Seminar, University Loughborough, 20 April 2005

How we can improve the mathematics skills of all
students who wish to progress to
mathematics-related degrees and also stretch and
inspire the most able.
Charlie StrippMEI, Mathematical Association
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About Further Mathematics

• Further Mathematics is an AS/A-level
  qualification which both broadens and deepens the
  Mathematics covered in the standard AS/A-level
  Mathematics.

• Further Mathematics was originally designed to
  stretch and inspire the most able and give a
  strong preparation for maths-related degrees
  (Engineering and Sciences, as well as Mathematics
  itself).

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Why do we need to support Further Mathematics?

• Mathematics, Engineering and Science Degree
  courses often assume a level of mathematical
  fluency beyond that achieved by students who have
  only completed A-level Mathematics.

• Talented students may be turned-off mathematics
  if they are not sufficiently inspired by the
  standard A-level Mathematics course.

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Why do we need to support Further Mathematics?
In 1980, 15000 students took A-level Further
Mathematics. This has declined to about 5000
entries per year.
Main reasons for the decline

• Small classes are expensive to run

• Shortage of suitably qualified staff

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Why do we need to support Further Mathematics?

• There is a serious equal opportunities issue
  here. Students lucky enough to attend a school
  or college which can offer Further Mathematics
  can do it. Others, equally keen and able, cannot.

• In order to address this problem MEI, funded by
  the Gatsby Charitable Foundation, set up a pilot
  project called Enabling Access to Further
  Mathematics.

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The MEI Pilot Project
A project specifically designed to find
alternative models for the successful delivery of
Further Mathematics.
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Vision of the Pilot Project

• The country is covered by groups of schools,
  colleges and universities, working together to
  offer Further Mathematics to students in their
  area.

• Every student who can benefit from Further
  Mathematics will have access to study it.

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How the Pilot Project works

• Students learning is managed by a project tutor,
  through a Further Mathematics Lead Centre.

• Students study is structured using
  purpose-written web resources.

• The web resources are used in conjunction with
  MEI textbooks.

• The MEI Project Coordinator and the project team
  offer training, support and advice.

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How the Pilot Project works
Linking institutions

• The pilot Lead Centres work with local schools
  and colleges to provide their students with
  Further Mathematics tuition.

• The pilot Lead Centres also organise Study
  Days, which may be attended by students from
  schools who provide Further Mathematics teaching
  in-house.

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Linking institutions
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How does the tutoring work?
Project tutors can enable students to study
Further Mathematics when teaching/tutorial
support is not available at their school/college

• The tutors are linked to project Lead Centres.

• The tutor must have a contact to liaise with in
  the students school/college Maths department.

• In some cases a combination of in-house and
  external tutoring is appropriate.

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How does the tutoring work?

• There are a several models. What works best
  depends on local circumstances.

• Tutors visit students in their schools

• Students attend their Lead Centre

• Videoconferencing

• Email, fax and telephone

A combination of these techniques is often most
appropriate and effective.
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Income

• Schools/colleges can claim qualification funding
  from the LSC for students using the project,
  exactly as they do for other AS/A-levels. Current
  funding is roughly 800 per student for each year
  of AS/A-level study.

• Lead Centres charge schools for tuition at a rate
  that means that schools and colleges can
  break-even, once textbook costs and exam entries
  have been paid.

• Obviously, by improving the mathematics provision
  to their students, schools and colleges are doing
  much more than breaking-even educationally!

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Pilot Further Maths Centres

• Initially five Lead Centres were involved

• We now have 11 Centres, at various stages of
  development, tutoring a total of over 200
  students.

Dr Challoners Grammar School (Bucks), Exeter
College (Devon), Hertfordshire LEA, University of
East Anglia/Norfolk LEA, University of Leicester,
University of Loughborough, UWE (Bristol),
University of Leeds, University of Manchester,
University of Warwick, University of Wolverhampton
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Does it work?

• Feedback from students and teachers has been
  extremely positive.

• The results have exceeded our expectations.

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Does it work?
Students and teachers also report very valuable
side-effects from the supported self-study Lead
Centre tutoring model

• Students performance in their standard
  Mathematics AS/A-level is enhanced.

• Students learn to learn more independently.

• Students have the opportunity to meet and work
  with students from other schools and colleges who
  are keen on Mathematics.

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The Further Mathematics Network

• The Further Mathematics Network is a national
  expansion of the MEI Access to Further
  Mathematics pilot project.

• The aim is to set up 40 50 Further Mathematics
  Centres, to cover the whole of England.

• These Further Mathematics Centres will be based
  on the Lead Centre model established during the
  pilot project.

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The Further Mathematics Network

• Through the Network, ALL students who would
  benefit will have the opportunity to study for
  Further Mathematics qualifications.

• The setting up of the Network will be supported
  by DfES funding and managed by MEI.

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Further Mathematics Centres

• A Further Mathematics Centre is a collaboration
  between institutions, which could involve one or
  more of LEAs, universities, colleges and schools.

• These institutions work together to coordinate
  the Further Mathematics provision in their region.

• Each Further Mathematics Centre is managed by a
  Further Mathematics Centre Manager.

• Schools, colleges and students served by the
  Centre form its membership.

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A wider role for the Further Mathematics Centres

• The Further Mathematics Centres will also need to
  engage with pupils in Key Stage 4, to encourage
  uptake of Mathematics post-16. This might be
  through enrichment work, or by supporting the
  study of a qualification such as the Additional
  Mathematics FSMQ.

• The Centres may also contribute to the continuing
  professional development (CPD) of teachers in
  their area, linking with the National Centre for
  Excellence in Mathematics Teaching.

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Further Mathematics and the 2004 AS/A level
Mathematics reforms

• A disastrous fall in numbers of students taking
  Mathematics at A level, (approaching 20)
  following the introduction of Curriculum 2000,
  has led to AS/A-level Mathematics being reformed,
  to bring its level of demand in line with other
  AS/A-level subjects.

• This is in line with recommendations made in the
  Roberts review, Set for Success, commissioned
  by the Treasury, which reported in 2002.

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SET for Success Recommendation 2.11
It is essential that pupils have a broadly equal
chance to achieve high grades in science and
mathematics as they would in other
subjects.Without this, fewer pupils will choose
to study science and mathematics at higher
levels.The Review is firm that arguments about
the merits of levelling up or dumbing downare
a distraction if pupils generally find it more
difficult to achieve high marks in science and
mathematics, this needs to be corrected.The
Review believes that this can and should be done
without compromising the core knowledge and
skills needed for studying science and
engineering
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Further Mathematics and the 2004 AS/A-level
Mathematics reforms
However, when commenting on the previous
AS/A-level, the Smith Inquiry report, Para 4.37
states the distribution of grades suggests
that the more able are insufficiently
challenged and the least able are frequently
overstretched.
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Further Mathematics and the 2004 AS/A-level
Mathematics reforms

• Without an increased uptake of Further
  Mathematics, the AS/A-level reforms will
  exacerbate problems for the most able. Almost 40
  of students completing A-level Mathematics last
  summer achieved a grade A the new A-level
  Mathematics is less demanding for the most able.

The good news

• As part of the reforms, most of the awarding
  bodies have taken the opportunity to reform their
  AS/A-level Further Mathematics qualifications, as
  well as the standard AS/A-level Mathematics.

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Further Mathematics and the 2004 AS/A-level
Mathematics reforms

• Previously AS-level Further Mathematics was
  effectively harder than full A-level Mathematics
  and virtually impossible to complete in year 12,
  because it relied on knowledge of the whole of
  the A-level Mathematics core

• The new AS-level Further Mathematics is a true
  AS- level and is designed to be taught alongside
  the standard AS-level Mathematics in year 12.

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Further Mathematics and the 2004 AS/A level
Mathematics reforms

• The new AS-level Further Mathematics is primarily
  a broadening option, introducing useful new
  topics (complex numbers, matrices) and
  reinforcing general mathematical fluency. It
  should be available to ALL students who wish to
  study for a maths-related degree, not just the
  very best.

• The full A-level Further Mathematics is both
  broadening and deepening and should be available
  to the most mathematically able and all who wish
  to study for a Mathematics degree.

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Further Mathematics and the 2004 AS/A level
Mathematics reforms

• The reforms provide a real opportunity for a
  large increase in the numbers of students taking
  both AS and A-level Further Mathematics, if they
  can access teaching.

• The Access to Further Mathematics Pilot Project
  has shown that it is possible to organise
  effective Further Mathematics teaching for
  students, even if their own schools and colleges
  cannot offer Further Mathematics directly.

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The effect the FM Network can have on Mathematics

• The Further Mathematics Network, combined with
  the new structure for AS/A-level Further
  Mathematics can boost the numbers of students
  taking Further Mathematics enormously.

• All students who would benefit from AS/A level
  Further Mathematics will be able to study it.

• OfStEd will be able to criticise any
  schools/colleges whose students are not
  encouraged to take Further Mathematics.

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The effect the Network can have on Mathematics

• Universities will be able to ask for Further
  Mathematics explicitly in their Offers, which
  will increase demand from students to study
  Further Mathematics.

• Links with school pupils at Key Stage 4 will
  boost numbers choosing to study AS/A-level
  Mathematics.

• The result will be a significant increase in the
  take up of AS/A level Mathematics and Further
  Mathematics and in the standard of pre-university
  Mathematics.