A Level Mathematics
Courses as a Foundation
for Degree Studies
A teacher’s perspective
Outline of presentation
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Brief outline of changes over last
25 years!
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Current Maths A Levels
Further Maths Networks
Have Maths A Levels got easier or have
standards risen?
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Broader educational factors
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Future changes
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Summary
Exam Boards
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AQA
 Edexcel
 OCR
 WJEC
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All courses are modular; different schools
impose different levels of ‘modularisation’
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Subject Criteria set by QCDA
(Core material for A Level Maths only)
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Regulated by Ofqual
AS Levels and A2 Levels in:
• Maths (C1, C2, C3, C4 + 2 applied)
• Pure Maths (C1, C2, C3, C4 + 2FP)
• Further Maths (FP1, FP2 + 4 other)
Modules available:
C1-4, S1-6, M1-5, D1-2, NM(2), FP (3)
Other Maths AS/A Levels:
• Use of Maths
• Statistics
Overview of Changes to Maths A Levels
The first core for A Level Mathematics was introduced from
1983; it contained only pure mathematics and was intended
to form 40% of the syllabus. It led to overly large syllabuses
which led to a decline in the numbers of learners taking
mathematics; a smaller revised core was introduced in
1995. With the introduction of Curriculum 2000 (in which
the norm is that in the first year learners take four GCE
subjects rather than three), the core was again revised, this
proved too demanding and was followed by a reduction of
one-fifth in the numbers taking A GCE in Mathematics. In
response to this drastic fall, a revised core was
introduced in 2004 which spread the existing pure
content over four units instead of three and reduced
the number of applied units from three to two. Since
2004, there has been a substantial and continuing growth
in numbers taking A GCE Mathematics (and proportionately
an even greater growth in the numbers taking A GCE
Further Mathematics).
Taken from
ACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009
 Modularisation
 Introduction
 Minor
of Discrete/Decision Maths
changes to content of modules at
various stages
Changes to Further Maths
Prior to 2004 AS in Further Maths had to include a
compulsory unit Pure Maths 4, which required as a prerequisite A Level Core Maths; AS FM could only begin
after A Level Maths had been completed.
From 2004, the ‘replacement’ compulsory FP1 module
was designed to be taught alongside the new AS Core
Maths content.
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Broader content
Allowed, individual schools, to teach A Level Maths and Further
Maths students together for the A Level Core Maths component.
Affected course content of the full A Level in Further Maths.
See MSOR Connections Aug 2004, Vol 4 No 3
http://www.furthermaths.org.uk/manager_area/files/Offering_further_mathematics_as
_part_of_the_A_Level_curriculum_Final_Report_Dec_07%201%20.pdf
Focus on Increasing Uptake of Further
Maths in Schools and Colleges:
Further Maths Network
Further Maths Networks (DfES funded, with centres managed by MEI)
set up in 2004. Importantly facilitated teaching of Further Maths by
external tutors and coordinated teaching of Maths at different schools.
The FMSP has three strands:
Student Support - helping to provide access to Further Mathematics
tuition for all students.
Teachers' Professional Development - enabling more teachers to
teach Further Mathematics and Level 3 mathematics within diplomas.
Communications and Marketing - promoting mathematics and raising
awareness of the benefits of studying mathematics beyond GCSE.
http://www.fmnetwork.org.uk/
Further Maths A Level
Students may not have choice over which modules to
study
Students may be taught in mixed ability groups
Lessons may not be timetabled in normal hours. May have
to travel to different centre to ‘share teachers’; may have
reduced contact hours.
A Level GCE Entries
Year
1989
All
Subjects
661591
All Maths
%
Subjects
84744
12.8
Further
Maths
n/a
1994
732974
64919
8.9
n/a
1999
783692
69945
8.9
n/a
2004
766247
58508
7.6
5720
2006
805698
63252
7.9
7270
2008
827737
73684
8.9
9091
Taken from ACME Position Statement on Qualifications
in Mathematics at Level 3 from 2011 February 2009
Have Maths A Levels got Easier?
Research evidence/QCDA reviews
Media opinion
Teachers’ views
My perceptions:
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Some changes to the course content
Structure of exam papers/mark distribution
Predictable questions
More scaffolding
More limited algebraic solutions, less requirement to solve problems
One quarter of the Core Maths material is higher level GCSE material
Retake culture
Teachers better able to ‘teach to exams’
Context: Encouraging more pupils to take Maths to a higher level, whilst a
wider range of A Level subjects are now on offer; some of which are not as
academically demanding
Changes to Course Content
FP1: AS module for Further Maths post 2004 (Edexcel)
Inequalities
Combining D1/C4
Series
Sums of finite series
Complex numbers
Numerical solution of
equations
Iteration formula, linear
interpolation, interval
bisection, NewtonRaphson
First order differential
equations
Requires C4
differentiation
Second order differential
equation
Extension to C4
Polar coordinates
P4: AS module in Further Maths prior to 2004 (Edexcel)
Coordinate systems I
Now in FP2
Requires C4
Coordinate systems II
Now in FP2 (except polar
coordinates in FP1)
Requires C4
Complex numbers
Most in FP1
Linear algebra
Not in FP1 or FP2
(using matrices)
Integration
(standard forms and reduction formulae)
Requires C4 integration
Now in FP2
Vectors
Extension of C4
Numerical methods
For solving differential
equations
Requires C4
Proof
Not in FP1 or FP2
OCR MEI C3 June 2009
(marks per question)
OCR MEI P2 June 2001
(marks per question)
Q1
14
5,4,5
Q2
15
1,5,5,4
Q3
16
2,3,9,2
Q4
15
3,5,3,4
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
3
8
3
3
7
5
7
18
18
3
5,3
3
3
3,4
5
4,3
5,2,3,6,2
1,3,7,7
OCR MEI June 2001 P3
OCR MEI June 2009 C4
Difficulties comparing questions
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Changes to unit structure/content
 Context of mark scheme and grade boundaries
is missing
 Same topic but level of difficulty may depend on
question position
 Question may be set to meet a different
Assessment Objective
Assessment Objectives
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AO1: Recall, select and use mathematical knowledge,
concepts and techniques in a variety of contexts. (30%)
AO2: Construct rigorous mathematical arguments and proofs
through use of precise statements, logical deduction and
inference, including ..extended arguments ..to substantive
problems in unstructured form. (30%)
AO3: Use of standard mathematical models to represent real
world situations.. discuss assumptions and refinements of
models. (10%)
AO4: Comprehend translations of common realistic contexts
into mathematics, use of results and calculations to make
predictions. (5%)
AO5: Use of contemporary calculator technology and other
permitted resources accurately and efficiently. Understand
limitations and, give appropriate accuracy. (5%)
QCA/Ofqual Reviews
1995-1998:
 Decline in algebraic manipulation skills
 Increase in structuring of questions
 No increase in reasoning/problem solving
1998-2004:
 Greater consistency across awarding bodies, but greater variety of
routes
 Questions more ‘accessible’ but greater degree of structuring
 Increased exam time led to greater thoroughness, but also greater
predictability
2004-2007:
 Greater consistency across awarding bodies, number of possible
routes became more consistent
 C1 helped address gap between GCSE and A Level
 C4 provided more rigorous assessment
 Still over structuring of questions
 Limited coverage of AO2
Have standards risen?
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Increased use of interactive and ICT based
resources e.g. autograph/omingraph for
visualizing transformations, polynomials and
trigonometric functions etc
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Greater access to web resources e.g. mei.org
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Extended teaching: revision courses, tutors
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Improved diagnostic assessment and target
setting
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Improved teaching through CPD
Broader educational factors which might affect the
depth/breadth of Mathematical Studies?
 Throughout secondary school an increased number of subjects are
being covered or are available e.g. ICT, citizenship, RE often
compulsory
 More able pupils expected to extend in all areas (G and T agenda);
some take 12-14 GCSEs
 In year 12, pupils take 4/5 subjects. Common to take a mix of
subjects (e.g. humanities and sciences)
 Increased focus on e.g. target setting days, enrichment activities,
leadership activities
Most courses are modular, time out of main teaching, increased
focus on exam practice, overall examination times have increased
Wide variety of teaching styles across schools, increasing
emphasis on team working and use of ICT and other interactive
resources/activities; perhaps less independent study
Maths lessons generally more tutorial based than lecture based;
difference in year12/13 between Science and Maths in this respect
Greater access to:
Past exam papers
Solutions
Mark schemes/exemplar materials
Teachers have little control of availability of these resources
Throughout secondary schools; strong emphasis on achieving
target grades
New A* Grade
The A* grade will be awarded to candidates who have achieved:
An A grade overall in their A Level, and 90 per cent of the maximum
uniform marks (UMS) on the aggregate of their A2 units.
It should also be noted that the percentage of A* grades is likely to vary
from subject to subject, as does the percentage of A grades awarded each
year. The new grade is not being awarded to a set percentage of the total
candidates or a set percentage of those who achieve an A grade – it will
strictly be awarded according to the rules set out above.
Changes in allocation of unit
grades to A Level Maths and
Further Maths
 http://store.aqa.org.uk/admin/library/EU34
_MAR08_SUBJ.PDF#gce_math
Changes likely from 2012
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2 units at AS Level and 2 units at A2 Level for A
Level Maths (no change FM)
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33-40% Applications (A Level Maths)
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No decision as yet re content of ‘Applications’
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Fixed content for Further Pure AS and A Level
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The style of some questions, particularly at A2,
may be different to the current examinations to
incorporate 'stretch and challenge' and the
inclusion of 'proof' and unstructured problemsolving questions
More details of possible changes
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QCDA Draft subject criteria for new mathematics A
Levels http://www.qcda.gov.uk/qualifications/3971.aspx
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4 Maths A Levels proposed (AQA):
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A Level Maths
A Level Further Maths
A Level Use of Maths
A Level Use of Statistics
http://web.aqa.org.uk/qual/gcse/maths_cp_project_gce.php
Changes to GCSE Maths
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Why is GCSE Maths changing?
In 2004 the Smith Report identified ‘a crisis in the teaching and
learning of Mathematics in England’ and found that the current
GCSE Maths curriculum and qualifications framework:
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fails to meet the mathematical needs of learners
fails to fulfill the expectations of higher education and employers
fails to motivate sufficient numbers of young people to continue with
Maths study post-16. AQA
 Main changes:
• Inclusion of functional elements
• More emphasis on selecting appropriate technique, problem
solving and communicating arguments
• Less scaffolding
• Double Maths GCSE: Methods in Mathematics; Applications in
Mathematics
Maths A Levels: A variable and changing
foundation for degree studies
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Diversity in units studied, especially with Further Maths
Base line is C1-C4; diagnostic testing
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Different styles of teaching and learning across schools
Independent problem solving skills need to be developed (any
substantive changes in schools will take many years to reach
undergraduate entry)
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Future changes likely to address, at least in principle, ‘problem
solving aspect’.
In reality unlikely to affect grades, if numbers taking A Level Maths to be
maintained, alongside diverse range of alternatives.
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Has a lack of ‘depth’ in Mathematics been compensated for by
other skills?
In the longer term do students who struggle with Maths content early on
in the course, perform worse overall, in terms of degree level or
subsequent progress.
Differences depending on type of school attended.