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About this guide:
The Higher Education Academy STEM Subject Centres for
Bioscience, Engineering, Information and Computer Sciences,
Materials, Maths, Stats & OR Network and Physical Sciences
commissioned this guide to be written by Mathematics in
Education and Industry (MEI)
...
The STEM centres consist of:
The Engineering Subject Centre:
www
...
ac
...
mathstore
...
uk
Physical Sciences:
www
...
ac
...
bioscience
...
ac
...
materials
...
uk
Subject Centre for Information and Computer Sciences:
www
...
heacademy
...
uk/
Copyright
The STEM Subject Centres own the copyright to this guide
so that they may use excerpts from it or update and modify
as appropriate
...
In any future version of this document it should be
acknowledged that MEI produced the original
...
ac
...
engsc
...
uk
– a guide for Academic Members of Staff –
Authors’ biographies
Stephen Lee (Lead Author), MEI Data Analyst / Web Manager
Email: Stephen
...
org
...
His thesis focussed upon Mathematics at the transition from School/College to
University
...
In 2008 he authored an
undergraduate textbook on introductory mathematics
...
browne@mei
...
uk
Richard Browne was a secondary mathematics teacher in Inner London for 12 years before joining SEAC,
one of the Qualifications and Curriculum Development Agency’s (QCDA) predecessor bodies, in 1989
...
Richard
works as part of the Engineering Professors’ Council Maths Task Group
...
Stella Dudzic, MEI Programme Leader (Curriculum)
Email: Stella
...
org
...
She has taught mathematics
in secondary schools for 22 years and was a head of faculty before taking up her current post with MEI
in 2006
...
She drafts many of MEI’s position papers on
developments in mathematics education
...
stripp@mei
...
uk
Charlie Stripp is well known for his pioneering work for MEI promoting Further Mathematics during the
last 10 years
...
A former teacher, Charlie has experience in almost all
aspects of mathematics education: examinations, textbooks, on-line learning, masterclasses and CPD
...
ISBN 978-1-907632-07-5 (print)
ISBN 978-1-907632-08-2 (online)
Printed on stock sourced from a sustainable forest
...
b) Copyright in the report resides with the publishers, the Higher Education
Academy STEM Subject Centres, from whom permission to reproduce
all or part of the report should be obtained
...
Understanding the UK Mathematics
Curriculum Pre-Higher Education
– a guide for academic members of staff –
Understanding the UK Mathematics Curriculum Pre-Higher Education
Contents
1
...
3
1
...
3
1
...
3
2
...
4
2
...
4
2
...
4
2
...
5
3
...
5
3
...
6
3
...
1 Overview
...
1
...
6
3
...
3 International General Certificate of Secondary Education
...
2 Advanced Subsidiary and Advanced Levels
...
2
...
7
3
...
2 Subject knowledge and skills
...
3 Advanced Extension Award and Sixth Term Examination Paper
...
4 Free Standing Mathematics Qualifications
...
4
...
11
3
...
11
3
...
11
3
...
1 International Baccalaureate
...
6
...
12
3
...
3 Access courses
...
6
...
12
3
...
12
4
...
13
4
...
14
4
...
14
4
...
1 Documents/information
...
2
...
15
5
...
17
5
...
17
5
...
18
5
...
19
5
...
1What mathematics do students study in A level Mathematics courses?
...
4 Important dates for Mathematics (authored by Roger Porkess)
...
Background
1
...
A considerable number of pre-higher education mathematics qualifications are available
within the UK and, for those working within the higher education (HE) sector, it is not
always clear what mathematics content, methods and processes students will have studied
(or indeed can be expected to know and understand) as they commence their universitylevel programmes
...
This outlines what students with given prior qualifications in mathematics are likely
to know and be able to do and is written for those within the HE sector
...
1
...
This includes an introduction to the main qualifications, a brief historical review of
major developments and an overview of what and how entrants have studied prior to
starting higher education
...
Information about qualifications is
given in short sections; if the user wishes to refer to a particular qualification it should be
straightforward to identify the relevant section of the chapter
...
This is broken down into two
parts, the first giving links to specific references raised in the previous chapter, and the
second part on additional links to other documents (useful for gaining a more detailed
understanding) and to relevant organisations (where information and updates can be
found)
...
Overall this guide will give an overview of the key qualifications and offers links to
further information that should aid the reader to gain an understanding of pre-university
mathematics qualifications
...
Setting the scene: pre-higher education qualifications and
study
2
...
At the heart of this strategy are three main routes to higher education:
apprenticeships, diplomas and general qualifications, including the General Certificate of
Secondary Education (GCSE) and the General Certificate of Education, Advanced Level
(GCE A Level)
...
For A Levels, students work at Advanced Subsidiary (AS) Level
in their first year and at ‘A2’ Level in their second year
...
Apprenticeships combine paid work with on-the-job training, qualifications and
progression
...
Diplomas offer a blend of classroom work and practical experience
...
All diploma lines of
learning permit learners to include other mathematics qualifications
...
5
...
This guide will clarify the
content, style of assessment and probable learning outcomes that may be expected in
a number of general qualifications in mathematics: these are GCSE, A Level and Free
Standing Mathematics Qualifications (FSMQ)
...
2 Brief historical review of major developments
General qualifications in mathematics have developed in the context of widespread
recent changes in expectations for learners
...
The replacement of the General Certificate of Education, Ordinary Level (GCE O
Level) by GCSE in 1988 may be seen as the start of a process by which these ‘school
leaving’ qualifications could more closely reflect what the majority of 16 year olds know,
understand and can do
...
Similarly, the introduction of subject cores for A Level examinations in 1983, the
acknowledgement in 1996 that the AS standard should be pitched according to what is
likely to be achieved a year before taking A Level and the rise of modular assessment
at A Level since 1990 have all played significant parts in making A Level Mathematics
examinations much more accessible than they were between 1951 and 1983
...
This produced a bimodal
distribution which did not match candidates’ mathematical knowledge
...
3 Where and how will entrants have studied pre-higher education?
It is important to be clear that those entering degree courses come from a wide range of
backgrounds and bring with them a wide range of experiences
...
This information guide is made with particular reference to those entering onto a degree
from a UK background (i
...
not overseas)
...
7) the major breakdown
of categories of places of learning is in terms of age range, type and whether it is statefunded or independent (fee paying)
...
Age ranges for secondary study could
involve 11-18, 14-19 or 16-19
...
A learner may have been at the same place of study since the age of 11,
or may have been at an establishment for only one or two years to complete their prehigher education studies
...
Having detailed the above, it is very difficult to definitively describe the way students will
have been taught in all of these different establishments
...
What is apparent, though, is that learners will enter HE with different
experiences and respond to the relative changes that university-level study will bring in
different ways
...
3
...
However,
the content of qualification specifications cannot be assumed to be an accurate measure
of what students will actually know and understand when they start higher education
...
Several universities have used diagnostic tests to determine the mathematical knowledge,
understanding and fluency of new undergraduates, and how they relate to students’
qualifications at the start of their HE courses
...
They are regulated by the Office of the Qualifications and Examinations
Regulator (Ofqual)
...
GCSE and A
level qualifications are also taken by students in Wales and Northern Ireland, though the
A Guide for Academic Members of Staff
5
Understanding the UK Mathematics Curriculum Pre-Higher Education
arrangements for administration are different
...
The large majority of students entering HE have taken GCSE and A Level qualifications,
but several other qualifications are also used as routes into HE
...
1 General Certificate of Secondary Education
3
...
1 Overview
Students in state schools have to follow the National Curriculum until age 16
...
Some GCSEs follow a modular
structure, with students taking some examinations in year 10 (age 15) and the rest in
year 11 (age 16)
...
The content of GCSE Mathematics is the same for all awarding
bodies, though it can be divided in different ways for modular courses
...
Many students do not do any more mathematics after GCSE
...
GCSE Mathematics is available at either Foundation Tier or Higher Tier
...
Students who narrowly miss grade C at Higher Tier may be awarded grade D
...
Grade C was not available at
Foundation Tier until 2008
...
Students entering GCSE Mathematics at Foundation Tier will not have studied as much
mathematics as students taking Higher Tier
...
3
...
2 Subject knowledge and skills
Students who have not gone beyond the content of Foundation Tier GCSE will not have
met some topics which students taking Higher Tier will have encountered
...
A Guide for Academic Members of Staff
Understanding the UK Mathematics Curriculum Pre-Higher Education
Students who have been entered for Higher Tier Mathematics and achieved grade B or C
will have an incomplete understanding of items from the list above and are likely to find
algebra difficult
...
3
...
3 International General Certificate of Secondary Education
The International General Certificate of Secondary Education (iGCSE) was originally
designed for international schools but is now taken by students in some independent
schools in the UK
...
The standard and content are similar
to GCSE but students may have studied some additional topics, such as an introduction to
calculus or matrices
...
2 Advanced Subsidiary and Advanced Levels
3
...
1 Overview
The information below refers to Advanced Subsidiary and A Levels taken after the year
2000
...
AS Level Mathematics, Further Mathematics and Statistics each consist of three modules
(also called ‘units’)
...
Students who have A Level will also have studied the AS content,
but as they may not have requested the certification for the AS separately it might not
appear on their certificate
...
The raw marks on each module are converted to Uniform Marks (UMS) to allow for
slight differences in difficulty of examinations from year to year: the overall grade is
decided by the total uniform mark gained on all modules
...
All modules are available in June with some also available
in January
...
(Note the MEI specification is administered through the Awarding Body
OCR
...
AS Mathematics consists of the compulsory modules C1 and C2 and an applied module,
which could be in mechanics, statistics or decision mathematics
...
The two applied modules in A Level Mathematics can be from the same area of applied
mathematics or from different areas
...
The content of applied modules varies between
different exam awarding bodies
...
This document also details what students
who achieve grade A, C or E can typically do (this only gives a general idea as grades are
based on total marks achieved rather than on these criteria, so strengths in some areas
may balance out relative weaknesses in others)
...
A Guide for Academic Members of Staff
7
Understanding the UK Mathematics Curriculum Pre-Higher Education
Figure 1
(Figure 1 notes – AM is Additional Mathematics, FAM is Foundations of Advanced Mathematics, NM
is Numerical Methods, NC is Numerical Computation, FP is Further Pure Mathematics, C is Core
Mathematics, DE is Differential Equations, M is Mechanics, S is Statistics, D is Decision Mathematics, DC
is Decision Mathematics Computation
...
They may stop their study of
mathematics at this point or go on to complete the full A Level in a further year
...
Other
students take AS in year 13 (age 18) when their future plans are clearer
...
They
take three further modules for AS, including one compulsory module, Further Pure 1
...
Students taking A Level Mathematics and A Level Further
Mathematics will take 12 different modules and students taking A Level Mathematics and
AS Level Further Mathematics will take 9 modules
...
Applied modules are in suites for the
three strands of applications: mechanics, statistics and decision mathematics
...
Similarly, for modules in statistics most awarding bodies only have
two decision mathematics modules available
...
The remaining modules make up the
Further Mathematics qualification
...
The rules for aggregation and certification can be seen in (3)
...
2
...
3
...
2 Subject knowledge and skills
The vast majority of A Level students will be taught in schools and colleges and so will not
be used to studying mathematics independently
...
Past papers and specimen papers can be found on awarding bodies’ websites
and will give an idea of what students are expected to be able to do
...
A document giving an overview
of the content studied in mathematics A Levels can be seen in (4)
...
3
...
From summer 2010 grade A* will be available for the full
A Level (but not for AS)
...
For A Level Further
Mathematics, a total of at least 270 (out of 300) is needed on the best three A2 modules
...
A small number of students take AS or A Level Pure Mathematics
...
It cannot be taken with Mathematics or Further Mathematics
AS or A Level
...
This is a separate qualification from
Mathematics and Further Mathematics and the modules in it focus more on the use of
statistics, whereas the statistics modules in the mathematics suite are more mathematical
...
Students who have completed their mathematical studies a year or more before starting
higher education may need some support with revision to regain the fluency they had
when they sat their examinations
...
3 Advanced Extension Award and Sixth Term Examination Paper
The Advanced Extension Award (AEA) is based on A Level Mathematics core content and
is designed to challenge the most able students
...
AEAs in other subjects exist but are being
withdrawn - the Mathematics AEA will continue until at least 2012
...
Grades available are Distinction and Merit
...
A Guide for Academic Members of Staff
9
Understanding the UK Mathematics Curriculum Pre-Higher Education
The Sixth Term Examination Paper (STEP) is a university admissions test originally used
only for entrance to Cambridge but it is now also used by some other universities
...
There are three
mathematics papers (I, II and III) and candidates usually take two of them
...
However,
candidates are not expected to learn extra content for the examination
...
No calculator is
allowed
...
Grades available
are S (Outstanding), 1 (Very Good), 2 (Good), 3 (Satisfactory) and U (Unclassified)
...
Students who are successful in AEA or STEP will have a high level of ability to think for
themselves, persist with a problem and present structured mathematical arguments
...
4 Free Standing Mathematics Qualifications
FSMQs were first developed in the late 1990s
...
g
...
Uptake of the original FSMQs was not high and only AQA now offer them in their original
form
...
OCR offers two FSMQs
...
Foundations of Advanced Mathematics (FAM) is a level 2 qualification that is designed to
help bridge the gap between GCSE and AS Mathematics for students with a C/B grade in
Mathematics GCSE
...
It is comparable in difficulty to AS
Mathematics
...
The OCR qualifications are more likely to be used to
demonstrate achievement of a milestone in a learner’s mathematical development
...
Level 3 units are awarded Universities and Colleges Admissions Service (UCAS) points
...
Candidates must produce a
coursework portfolio worth 50% of the credit and sit a written examination for the
remaining credit
...
Students who have achieved success in these qualifications are likely to share the broad
capabilities of students achieving other mathematics qualifications at Levels 1, 2 and 3,
see (5)
...
Students who have achieved
success with OCR Additional Mathematics are likely to have shown an excellent grasp
of basic advanced topics, which should be valued all the more highly if the qualification
was taken pre-16
...
10
A Guide for Academic Members of Staff
Understanding the UK Mathematics Curriculum Pre-Higher Education
3
...
1 AS Use of Mathematics
Students who take level 3 FSMQs with AQA have an opportunity to use these as part of
an AS qualification called AS Use of Mathematics
...
A full A Level in Use of Mathematics is currently being piloted by AQA
...
5 Diplomas
These qualifications for 14 to 19 year olds offer a blend of classroom work and practical
experience
...
5 A Levels
...
Note that there is also a slightly smaller version of the diploma
(the progression diploma) and a slightly larger version (the extended diploma)
...
Diplomas consist of three curriculum parts:
• principal learning, the learning related to the title of the particular diploma
• generic learning, which consists of functional skills and a project
• additional specialist learning (ASL), which may be chosen freely from an extensive
catalogue
From September 2009 a consortia of schools and colleges will offer diplomas in ten
lines of learning, currently planned to increase to 17 by 2011
...
This unit is called ‘Mathematical Techniques and Applications
for Engineers’
...
Many experts have suggested that the
Mathematical Techniques and Applications for Engineers unit is significantly larger than a
single unit of A Level Mathematics
...
This is the size of an A Level, so learners who have completed level 3 diplomas could
include A Level Mathematics as part of their diploma
...
Its title is ‘Mathematics for Engineering’ and it is rated at 180 guided learning hours,
the same size as an AS qualification, but the unit does have a considerable amount of
material, appearing to be larger than a typical AS in mathematics
...
6 Other qualifications
3
...
1 International Baccalaureate
The International Baccalaureate (IB) Diploma Programme is recognised as a challenging
two-year course for students aged 16-19
...
The course consists of a core (made up of three separate parts) and six subject groups,
from which students select six subjects
...
Four courses are available in mathematics: mathematics studies, mathematics or further
mathematics at standard level, and mathematics at higher level
...
All students who study the IB are required to study one of the mathematics qualifications
...
3
...
2 Pre-U
The Pre-U is a recent qualification which began for first teaching in 2008, with first
certification due to take place in summer 2010
...
Students study at least three Principal Cambridge Pre-U subjects from a choice of 26,
see (9)
...
Mathematics and Further Mathematics are individual subjects in this list of 26
...
It is too early to tell what a student will ‘look’ like having studied such a qualification and
it is unknown how much take up there will be, but it is expected to be low
...
3
...
3 Access courses
Access to Higher Education courses are specifically designed for people who left
school without traditional qualifications but who would like to take a degree level
course
...
It may be advisable for institutions to review
students entering with such qualifications on an individual basis to determine their prior
mathematical experience
...
6
...
Although it is perhaps usual for a learner on such a course to progress onto a subsequent
course at the institution at which they had studied their Foundation course, this need not
necessarily be the case
...
3
...
However, most students sit examinations with the
awarding body, the Welsh Joint Education Committee (WJEC)
...
The regulatory body is the Department for Children, Education, Lifelong
Learning and Skills (DCELLS)
...
A Level Further Mathematics numbers
are still comparatively low at 250 in 2009 (up from 140 in 2004)
...
In Scotland, at age 16 students take Standard Grade examinations (roughly equivalent to
the English GCSEs), at age 17 they take Highers (equivalent to AS Levels) and then at 18
Advanced Highers (equivalent to A Levels)
...
Grades for Standard Grades are on a scale from 1 to 7, where 7 is the lowest and
awarded if the course was completed but the examination not passed
...
Each level has two papers, one which allows a calculator and one which
does not
...
There are also two Intermediate courses, Intermediate 1 and Intermediate 2, which can
be studied instead of Standard Grades, or taken alongside Highers
...
Their structure is similar to that of Highers (i
...
a one-year course split into
units)
...
There is only one examining body in Scotland, the Scottish Qualifications Authority (SQA)
...
The Course will consolidate and extend the candidates’ existing mathematical skills,
knowledge and understanding in a way that recognises problem solving as an essential
skill and that will allow them to integrate their knowledge of different areas of the
subject
...
However, the uptake for this is relatively low, with around 300 students studying it each
year, see (14)
...
In
2009 approximately 2750 students studied A Level Mathematics, up from 2300 in 2004
but, again, relatively few study A Level Further Mathematics - 150 in 2009 (up from 140
in 2004)
...
A Guide for Academic Members of Staff
13
Understanding the UK Mathematics Curriculum Pre-Higher Education
4
...
Links to relevant sources of information are given here
...
4
...
qcda
...
uk/key-stages-3-and-4/
subjects/key-stage-4/mathematics/index
...
ofqual
...
uk/files/2002-12-gce-maths-subject-criteria
...
jcq
...
uk/attachments/published/1047/GCE%20Maths%20Rules%20-%20guidance%20
for%20centres
...
mei
...
uk/files/Maths_
Alevel_Content_09
...
qcda
...
uk/libraryAssets/media/
qca_05_2242_level_descriptors
...
direct
...
uk/diplomas
(7) Full specification for IB mathematics at higher level can be seen at: http://www
...
umd
...
sl
...
(8) Full specification for IB further mathematics at standard level can be seen at: http://
www
...
umd
...
fut
...
(9) Information on the subjects available in the Pre-U can be seen at: http://www
...
org
...
cie
...
uk/qualifications/academic/
uppersec/preu
(11) Access courses website, see http://www
...
ac
...
wbq
...
uk/about-us
(13) Detail of Scottish Intermediate and Higher qualifications, see http://www
...
org
...
jsp?p_applic=CCC&p_
service=Content
...
sqa
...
uk/sqa/2468
...
2 Additional references
4
...
1 Documents/information
BTEC and OCR Nationals http://www
...
com/quals/nat/Pages/default
...
com/level-3
...
dg
...
pipex
...
shtml
(A report of the Committee of Inquiry into the teaching of Mathematics in Schools)
Evaluation of participation in A level mathematics: Final report, QCA (2007) http://www
...
gov
...
aspx
Guide to qualifications: http://www
...
gov
...
htm
Ideas from Mathematics Education - An Introduction for Mathematicians
...
ISBN 978-0-9555914-3-3 http://www
...
ac
...
International Baccalaureate http://www
...
org/who/ and http://www
...
org/diploma/
curriculum/
iGCSE: http://www
...
org
...
m-a
...
uk/resources/TheChangingShapeOfTheCurriculum
...
ofsted
...
uk/Ofstedhome/Publications-and-research/Documents-by-type/Thematic-reports/Mathematicsunderstanding-the-score/(language)/eng-GB
Maths careers website: www
...
org
...
ac
...
Scottish Standard Grades: http://www
...
gov
...
htm
STEP: http://www
...
cambridgeassessment
...
uk/adt/step
Vocational qualifications: http://www
...
gov
...
2
...
The first is of organisations which serve
to provide additional information on mathematics and/or education (note that not
all have previously been mentioned explicitly in this guide, but are included here for
completeness); the second is of relevant Higher Education Academy (HEA) Subject
Centres
...
•
•
•
•
•
ACME www
...
org
AQA http://web
...
org
...
atm
...
uk/
CCEA http://www
...
org
...
asp
BIS http://www
...
gov
...
dcsf
...
uk/
Edexcel http://www
...
com/quals/gce/gce08/maths/Pages/default
...
jcq
...
uk
MA http://www
...
org
...
jsp
MEI www
...
org
...
ocr
...
uk/qualifications/subjects/mathematics/index
...
ofqual
...
uk
Ofsted www
...
gov
...
qcda
...
uk
SQA http://www
...
org
...
scqf
...
uk/
A complete list of HEA Subject Centres is available at:
http://www
...
ac
...
bioscience
...
ac
...
engsc
...
uk/
Information and Computer Sciences (Subject Centre) http://www
...
heacademy
...
uk
Materials Education (UK Centre) http://www
...
ac
...
mathstore
...
uk/
Physical Sciences (Centre) http://www
...
ac
...
Appendices
5
...
2 A Level Mathematics Numbers 1989 – 2009 (Source JCQ)
Year
Mathematics*
entries
(FM excl)
FM* entries
Total
Mathematics
entries
(FM incl)
FM as % of
Mathematics
Total
A Level
entries
Mathematics
as % of total
entries
(FM incl)
1989
84 744
661 591
12
...
7
1991
74 972
699 041
10
...
9
1993
66 340
734 081
9
...
9
1995
62 188
725 992
8
...
1
1997
68 880
777 710
8
...
9
1999
69 945
783 692
8
...
7
2001
66 247
748 866
8
...
7
2003
50 602
5315
55 917
10
...
5
2004
52 788
5720
58 508
10
...
6
2005
52 897
5933
58 830
11
...
5
2006
55 982
7270
63 252
13
...
9
2007
60 093
7872
67 965
13
...
4
2008
64 593
9091
73 684
14
...
9
2009
72 475
10 473
82 948
14
...
8
* Note that prior to 2003 JCQ did not report Mathematics and Further Mathematics numbers separately
...
3 Overview of content in mathematics A Levels
5
...
1What mathematics do students study in A level Mathematics courses?
Since the structure of A level Mathematics (and Further Mathematics) was changed in
September 2004, students with only a single A level in Mathematics will have studied only
two applied modules (in addition to the four core modules, Core 1 to Core 4, which
cover the compulsory ‘pure’ content of the A level)
...
meidistance
...
uk/pdf/revised_gce_maths_criteria_20040105
...
Possible combinations of modules studied for A level Mathematics are:
Core 1, Core 2, Core 3, Core 4
+ one of the combinations of two applied modules shown below
Statistics 1
Mechanics 1
Decision 1
Statistics 1
Decision 1
Mechanics 1
Mechanics 1
Decision 1
Statistics 1
Statistics 2
Decision 2
Mechanics 2
There are no prescribed applied modules that are required to be studied, hence students
could study any one of these combinations in order to gain an A level in Mathematics
...
However, there are differences between the content of such modules for
the different A level specifications (and additionally a few other applied modules may be
available from specific boards, e
...
Numerical Methods by MEI)
...
This highlights the worth of the further mathematics
qualification for those students who wish to study for mathematics-related degrees
at university
...
furthermaths
...
uk to find out more about Further
Mathematics
...
For more information,
please see www
...
org
...
If you have any queries, please contact:
Charlie Stripp (Charlie
...
org
...
Lee@mei
...
uk)
...
Some students, particularly those who have not studied Further Mathematics, may
not have had the opportunity to have studied certain applied modules, e
...
M2, D2
to name but two, during their time in the sixth form
...
A Guide for Academic Members of Staff
21
Understanding the UK Mathematics Curriculum Pre-Higher Education
MECHANICS
Motion Graphs
Displacement-time,
distance-time, velocity time
Interpreting the graphs
Using differentiation and
integration
Constant Acceleration and
“SUVAT” Equations
Introduction to the variables
Using the variables
Standard properties
Use in solving equations
Projectiles
Finding the maximum height,
range and path of a projectile
Centre of Mass
Uniform bodies (symmetry)
Composite bodies
Centres of mass when
suspended
Variable Acceleration
Newton's Laws Applied
Along a line
Vectors and Newton’s Laws
in 2 Dimensions
Resolving forces into
components
Motion on a slope (excluding
and including friction)
Collisions
Coefficient of restitution
Conservation of linear
momentum
Impulse
Calculations involving a loss of
energy
Equilibrium of a Rigid Body
Moment about a point
Coplanar forces
Toppling/sliding
Using differentiation in 1 and
2-D
Using integration in 1 and 2-D
Uniform Motion in a Circle
Angular speed
Acceleration
Horizontal circle, conical
pendulum
Motion in a horizontal plane
Motion in a vertical plane
Pulleys
Connected bodies
Energy, Work and Power
Work done
GPE, KE
Conservation of energy
Power (force does work)
© MEI 2009
22
A Guide for Academic Members of Staff
Understanding the UK Mathematics Curriculum Pre-Higher Education
STATISTICS
Correlation and Regression
Product moment correlation
Spearman coefficient rank
correlation
Independent and dependant
variables
Least squares regression
Scatter diagrams
The Binomial Distribution and
Probability
Probability based on selecting
or arranging
Probability based on binomial
distribution
Expected value of a binomial
distribution
Expected frequencies from a
series of trials
Exploring Data
Types of data
Stem and Leaf diagrams
Measures of central tendency
and of spread
Linear coding
Skewness and outliers
Data Presentation
Bar charts, pie charts
Vertical line graphs,
histograms
Cumulative frequency
Discrete Random Variables
Expectation and variance of
discrete random variables
Formulae extensions E(aX+b)
Probability
Measuring, estimating and
expectation
Combined probability
Two trials
Conditional probability
Simple applications of laws
Hypothesis Testing
Establishing the null and
alternate hypothesis
Conducting the test and
interpreting the results
Use of the binomial or normal
distribution
Type 1 and type 2 errors
Normal Distribution
Properties (including use of
tables)
Mean and variance
Cumulative distribution
function
Continuous random variables
(probability density function
and mean/variance)
As an approximation
to binomial or Poisson
distributions
t-distribution
Chi-squared
Introduction
Conditions
Poisson Distribution
Properties (including use of
tables)
Mean and variance
Use as an approximation to
binomial distribution
Sampling/Estimation
Randomness in choosing
Sample means and standard
errors
Unbiased estimates of
population means
Use of central limit theorem
Confidence intervals
© MEI 2009
A Guide for Academic Members of Staff
23
Understanding the UK Mathematics Curriculum Pre-Higher Education
DECISION
Graphs
Graphs
Networks
Prim
Kruskal
Dijkstra
TSP
Route inspection
Network flows
Critical Path Analysis
Activity networks
Cascade charts
Game Theory
Game theory
Using simplex
Algorithms
Communicating
Sorting
Packing
Efficiency and complexity
Discrete Random Variables
LP graphical
LP simplex
Two stage simplex
Simulation
Monte Carlo methods
Uniformly distributed random
variables
Non-uniformly distributed
random variables
Simulation models
Logic and Boolean Algebra
Optimisation
Matchings
Hungarian algorithm
Transportation problem
Dynamic programming
Logical propositions and truth
tables
Laws of Boolean algebra
Combinatorial circuits and
switching circuits
© MEI 2009
24
A Guide for Academic Members of Staff
Understanding the UK Mathematics Curriculum Pre-Higher Education
5
...
Several syllabuses (e
...
GAIM and MEI are lost)
New A Level syllabuses developed but put on
hold following the general election
1999
National Numeracy Strategy (primary schools)
New common cores at AS and A Level, now
known as subject cores
A Guide for Academic Members of Staff
25
Understanding the UK Mathematics Curriculum Pre-Higher Education
Year
Up to 16
16-19
1999
National Numeracy Strategy (primary schools)
New common cores at AS and A Level, now
known as subject cores
2000
First teaching of new syllabuses to conform with
Curriculum 2000
2000
Work starts on an MEI pilot programme to
foster Further Mathematics
2001
Key Stage 3 National Strategy Framework for
teaching mathematics to Years 7, 8 and 9
Very poor results at AS Level
Marked drop in retention rate for full A Level
Introduction of data handling coursework at
GCSE
2002
Large reduction in numbers taking A Level
mathematics
2003
New subject cores for AS and A Level
Mathematics
2004
The Smith Report: Making Mathematics Count
2004
The Tomlinson Report on 14-19 Curriculum and Qualifications Reform (mostly rejected)
2004
First teaching of new mathematics syllabuses,
now known as specifications, introduced to
overcome the problems caused by Curriculum
2000
2005
DfES rolls out the MEI Further Mathematics
programme as the Further Mathematics
Network (still run by MEI)
2006
First teaching of GCSE syllabuses that have
changed from 3-tier to 2-tier
2007
First teaching of GCSE Mathematics with no
coursework
2009
Key Stage 3 National Curriculum tests
discontinued
2009
Uptake starts to rise under the new
specifications
Uptake is the highest since 1989
The Further Mathematics Network is replaced
by the Further Mathematics Support Programme
(still run by MEI)
2010
New GCSE syllabuses to start
2010
Pilot of twin GCSEs to start
26
A Guide for Academic Members of Staff
Authors’ biographies
Stephen Lee (Lead Author), MEI Data Analyst / Web Manager
Email: Stephen
...
org
...
His thesis focussed upon Mathematics at the transition from School/College to
University
...
In 2008 he authored an
undergraduate textbook on introductory mathematics
...
browne@mei
...
uk
Richard Browne was a secondary mathematics teacher in Inner London for 12 years before joining SEAC,
one of the Qualifications and Curriculum Development Agency’s (QCDA) predecessor bodies, in 1989
...
Richard
works as part of the Engineering Professors’ Council Maths Task Group
...
Stella Dudzic, MEI Programme Leader (Curriculum)
Email: Stella
...
org
...
She has taught mathematics
in secondary schools for 22 years and was a head of faculty before taking up her current post with MEI
in 2006
...
She drafts many of MEI’s position papers on
developments in mathematics education
...
stripp@mei
...
uk
Charlie Stripp is well known for his pioneering work for MEI promoting Further Mathematics during the
last 10 years
...
A former teacher, Charlie has experience in almost all
aspects of mathematics education: examinations, textbooks, on-line learning, masterclasses and CPD
...
ISBN 978-1-907632-07-5 (print)
ISBN 978-1-907632-08-2 (online)
Printed on stock sourced from a sustainable forest
...
b) Copyright in the report resides with the publishers, the Higher Education
Academy STEM Subject Centres, from whom permission to reproduce
all or part of the report should be obtained
...
About this guide:
The Higher Education Academy STEM Subject Centres for
Bioscience, Engineering, Information and Computer Sciences,
Materials, Maths, Stats & OR Network and Physical Sciences
commissioned this guide to be written by Mathematics in
Education and Industry (MEI)
...
The STEM centres consist of:
The Engineering Subject Centre:
www
...
ac
...
mathstore
...
uk
Physical Sciences:
www
...
ac
...
bioscience
...
ac
...
materials
...
uk
Subject Centre for Information and Computer Sciences:
www
...
heacademy
...
uk/
Copyright
The STEM Subject Centres own the copyright to this guide
so that they may use excerpts from it or update and modify
as appropriate
...
In any future version of this document it should be
acknowledged that MEI produced the original
...
ac
...
engsc
...
uk
– a guide for Academic Members of Staff –