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Changes to Level 3 Mathematics in England
29 November 2016
Core Maths
Paul Glaister
Professor of Mathematics & Mathematics Education, University of Reading
CMSP / ALCAB / ALMAB / Ofqual / IMA / JMC (Chair)
Council for Mathematical Sciences: Driving the UK Economy (2016)
Council for Mathematical Sciences: Driving the UK Economy (2016)
Council for Mathematical Sciences: Driving the UK Economy (2016)
Council for Mathematical Sciences: Driving the UK Economy
The Royal Society: Vision for science and mathematics education for
2030
The Royal Society: Vision for science and mathematics education for
2030
British Academy: Count Us In –
Quantitative Skills for a New Generation (2015)
Improving standards: GCSE
• As part of the government’s plans to
ensure pupils can compete with the top
performers in the world and secure the
best jobs, a new grading system is being
introduced from 2017 at GCSE to replace
the A to U system with a new 9 to 1
scale.
• Under the new system, a good pass,
currently a C grade, will become a grade
5 under the new scale. The new good
pass is comparable to a high C or low B
under the current system.
Post-16 GCSE
• “The government intends to align the 16 to 19 maths and
English funding condition with the new GCSE good pass in
maths and English. A phased approach will be taken. For
students studying in academic years 2017 to 2018 and 2018 to
2019 the funding condition will be based on the new GCSE
grade 4.
• Beyond this, we intend to revise the funding condition to reflect
the new GCSE good pass (grade 5). The specific date from which
this will take effect will be confirmed closer to the time.”
Level 3 mathematics progress has been good
Sustained growth in
the number of
students progressing
to AS and A level
mathematics
2016 entries
Male
Female
Total
AS Mathematics
98735
64006
162741
AL Mathematics
56535
35628
92163
AS FM
19033
7709
26742
AL FM
11054
4203
15257
Post-16 Mathematics
What have A*-C GCSE maths
students achieved by age 18?
(2011 GCSE cohort)
A level FM
2%
Other L3
1%
A level maths
12%
“330,000 students start courses each
year which require advanced (postGCSE) maths, but over 200,000 of them
will not have studied beyond GCSE”
(ACME, Mathematical Needs, 2011)
AS maths
6%
No change
79%
“Many undergraduate students are
surprised at the amount of
mathematical content in their degree
programmes and some struggle to cope
with this content..”
(Higher Education Academy,
Mathematical Transitions, 2014)
Sources: DfE analysis of pupil-level data
Recent AS/A level numbers (England)
Recent A level grades vs GCSE (England)
Recent AS/A level numbers (England)
Qualifications: AS/A levels (from 2017)
Key aims:
• Better support transition to mathematical study at
university.
Key changes:
A level mathematics
• Specified in more detail to clarify requirements.
•
100% prescribed, giving universities confidence about the
mathematics that undergraduates have studied.
•
Compulsory applied content in statistics and mechanics and
removal of decision mathematics.
Diverse destinations of A level maths students
•
A emphasis on mathematical argument, language and
proof; mathematical problem-solving and modelling; use of
large data sets in statistics.
A level further mathematics
• Common pure core - 50% of overall content, allowing scope
for options.
AS/A level Maths and Further Maths (from 2017)
Overarching themes:
Students to demonstrate the following overarching knowledge and skills:
• Mathematical argument, language and proof;
• Mathematical problem solving;
• Mathematical modelling.
Must be applied, along with associated mathematical thinking and understanding,
across the whole of the detailed content.
Aims and objectives:
Must encourage students to:
• understand mathematics and mathematical processes in a way that promotes confidence,
fosters enjoyment and provides a strong foundation for progress to further study;
• use their mathematical knowledge to make logical and reasoned decisions in solving
problems both within pure mathematics and in a variety of contexts, and communicate the
mathematical rationale for these decisions clearly;
• and others see: Mathematics and Further Mathematics
AS/A level Maths and Further Maths (from 2017)
Key aims:
• introduce calculus and its applications;
• emphasise how mathematical ideas are interconnected;
• show how mathematics can be applied to model situations mathematically;
• make sense of data;
• understand the physical world;
• solve problems in a variety of contexts;
• prepare students for further study and employment in a wide range of disciplines.
Core content:
• variety of mathematical concepts, methods and techniques – pure mathematics and applied,
with overlap and interplay between them;
• need for better problem-solving skills: change in emphasis to problem solving, interpretation
and testing understanding;
• drive assessment with less structured questions that test understanding and help to develop
strategies for solving problems either in a purely mathematical or in an applications context.
AS/A level Maths and Further Maths (from 2017)
Statistics:
• primary focus not routine calculations of summary statistical measures;
• use of real, large data sets should permeate the teaching, learning and assessment
• more emphasis upon understanding, interpretation of data and making inferences from data;
• use of large pre-released data sets is suggested;
Mechanics:
• two-way process between pure and mechanics;
• emphasis upon understanding, interpretation and problem solving should pervade the
teaching and assessment of mechanics;
• natural linkages with pure these should be exploited;
• emphasis on mathematical modelling.
ACME report – ‘Mathematical Needs: Mathematics in the
workplace and in higher education’, 2011
▪
Quantitative demands of almost all university courses are increasing,
particularly in statistics.
▪
330,000 HE entrants would benefit from recent experience of studying
some mathematics (including statistics) at a level beyond GCSE, but fewer
than 125,000 have done so.
▪ The recent increase in the numbers of those studying A-levels will not
solve higher education's need for more mathematically competent
students.
▪ For many students aspiring to higher education, a variety of mathematics
courses beyond GCSE is needed.
HEA report - ‘Mathematical Transitions’, 2014
▪ The number of students entering the disciplines with an A or ASlevel in Mathematics has increased in recent years but has probably
reached a limit.
▪ Many students arrive at university with unrealistic expectations of
the mathematical and statistical demands of their subjects.
▪
Lack of confidence and anxiety about Mathematics/Statistics are
problems for many students.
Reports
• Reports
‘Core Maths’ Qualifications
Core Maths qualifications should:
▪ consolidate and build on students’ mathematical understanding and
develop further mathematical understanding and skills in the
application of maths to authentic problems, thereby offering
progression from GCSE mathematics.
▪
provide a sound basis for the mathematical demands that students
will face at university and within employment across a broad range of
academic, professional and technical fields.
‘Core Maths’ Qualifications launch
▪ Strong maths skills are an essential part of our plan for education and
are also vitally important to our economy.
▪
Core Maths teaches pupils how to use and apply maths in real situations,
and will help address a 16 to 18 ‘maths gap’ whereby students who
achieve a good maths grade at GCSE currently drop the subject and start
to lose their confidence and skills.
▪
Thanks to these new high-quality courses more pupils will be able to
continue their study of maths, ensuring more young people leave
education properly prepared for the demands of university, work and
life in modern Britain.
‘Core Maths’ Qualifications
Core Maths qualifications will:
1. Deepen competence in the selection and use of mathematical
methods and techniques.
2. Develop confidence in representing and analysing authentic
situations mathematically and in applying mathematics to address
related questions and issues.
3. Build skills in mathematical thinking, reasoning and communication.
Core Maths
▪ Core Maths ≡ AS
▪ Core Maths has the same UCAS points as an AS
▪
Graded: A-E
▪
2 year course taken across years 12 and 13
▪
Some will take as 1 year course in year 12 or 13
▪ First teaching 2014
▪ Targeted at the 250,000 not taking any mathematics post-16
‘Core Maths’ Qualifications
▪ Mathematical Studies (AQA)
▪ Using and Applying Mathematics (City & Guilds)
▪ Mathematics in Context (Pearson/Edexcel)
▪ Mathematics for Work and Life (eduqas/WJEC)
▪ Quantitative Reasoning/Quantitative Problem Solving (OCR/MEI)
▪
ALL BRANDED Core Maths
Core Maths topics
•
Analysis of data
•
Maths for finance
•
Estimation
•
Critical analysis of given data and models (including spreadsheets and
tabular data)
•
The normal distribution
•
Probabilities
•
Correlation and regression
•
Critical path analysis
•
Graphical methods
•
Rates of change
•
Exponential functions
•
(STATISTICAL) PROBLEM SOLVING
•
MODELLING
Core Maths question
Core Maths question
Core Maths question
Core Maths question
Core Maths question
Core Maths question
Core Maths question
Core Maths website
www.core-maths.org
Core Maths numbers
September 2014
September 2016
▪
153 Early Adopter Teaching
Projects
▪
~ 500 centres teaching Core
Maths
▪
~3,000 students
▪
~10,000+ students
Core Maths by sector
Type of
institution
Number teaching Core
Maths
2014-15 2015-16
2016-17
Total
number of
institutions
Percentage coverage
2014-15 2015-16 2016-17
Schools with
sixth forms
77
245
362
2104
4%
12%
17%
Sixth Form
Colleges
14
33
47
95
15%
35%
49%
FE Colleges
54
68
85
225
24%
30%
38%
Studio
schools/UTC
3
15
24
52
6%
29%
46%
Total
148
361
518*
2476
6%
15%
21%
*Figures
based on centres known as of October 2016
Core Maths/AS and A level
AS and A level mathematics
Core Maths
keeps options open for a wide range of
university courses
helps students maintain and further develop
valuable mathematical skills for university and
employment
is essential for entry to many degree courses
including most STEM and medicine, economics helps with the mathematical elements of
and architecture
other level 3 courses, including humanities
and social sciences
supports the mathematical elements of other
A-level subjects
builds valuable skills through an emphasis on
mathematical problem solving in real life
introduces new ideas, applications and
contexts
techniques such as - proof, calculus, modelling
provides an option which is suitable for all
offers more rapid progression for higher
students with a good pass at GCSE
achieving students in mathematics
Core Maths and universities
▪
Nick Gibb, Minister for Schools (DfE) and Jo Johnson Minister for Universities
and Science (BIS) wrote to VCs in September 2015:
• ‘provide information on the new Core Maths qualifications’
• ‘want to give more young people the opportunity to acquire the
mathematical knowledge to succeed’
• ‘universities have a particular role to play in building demand for these
qualifications among students and parents by signalling their value for
higher education’
• ‘extremely helpful if you would consider how the value of CM can be
signalled to prospective undergraduates’
Core Maths and universities
▪
BIS/DfE letter accompanied by my briefing paper: more details on CM and
its relevance to higher education
▪ BIS referred VCs to my engagement with universities:
• “PG would very much welcome the opportunity to give institution-wide
briefings on CM to senior staff and staff responsible for admissions in
universities”
• “all universities are encouraged to take up this opportunity to find out
more about CM, its relevance to higher education, and to discuss any
aspects of CM”
▪
Briefed 16 Russell Group universities and 19 others
University Endorsement
The University of Bath
▪ welcomes the introduction of Core Mathematics qualifications to
▪
allow students the opportunity to develop their mathematical
and statistical problem-solving, evaluation and data-analysis
skills beyond GCSE.
Many of the degree schemes at Bath value these skills, even
where there is no formal requirement for attainment of a
Mathematics qualification beyond GCSE level, and highlight this
in their published selection criteria. Successful completion of a
Core Mathematics qualification would therefore be appropriate
evidence of mathematical skills and would contribute towards
receipt of an offer for these courses.
University Endorsement
▪ For degree courses in Architecture, Biosciences, Biomedical
▪
Science, Business and Management degrees, Chemistry,
Education with Psychology, International Development with
Economics, Pharmacology, Pharmacy, Physical Activity and
Health, Politics and International Relations, Psychology,
Sociology, Social Policy, Social Science and Sports Science degrees
a Core Mathematics qualification would therefore be viewed as a
positive enhancement for selection decisions if a candidate was
not taking A-level Mathematics.
For applications to Natural Sciences where students are not
taking options in Physics or Mathematics then an A grade in the
Core Mathematics qualification would be an acceptable
alternative to A level Mathematics.
University Endorsement
▪ For degree courses where there is a specified GCSE grade in
▪
Mathematics, then attainment of a C grade or better in Core
Mathematics could serve as an alternate way to meet the GCSE
requirement.
Please note that for degree courses where an A-level in
Mathematics (or equivalent) is a specified requirement, a Core
Mathematics qualification would not be a substitute
qualification.
University Endorsement
▪
▪
▪
LSE recognises that the skills and experience gained by students
who choose to undertake the Core Maths Qualification may be
very useful as preparation for the study of social sciences at
undergraduate level.
Whilst we do not include the grades gained from Core Maths in
our standard offers, and there is no requirement to do one,
successful completion of the Core Maths qualification can help
you demonstrate your readiness to study the rigorously academic
undergraduate programmes at LSE.
Applicants to LSE are expected to have at least a grade B (or a
grade 5 under the new grading system) in GCSE mathematics. We
would be likely to consider a pass in Core Maths to be an
alternative way to meet this requirement.
DfE advice for 16-19 study programmes (Jan 2016)
Core Maths
▪
In most other advanced economies, the study of maths is the norm for
students within their 16 to 19 education. Students who have already
achieved GCSE A*-C should be encouraged to study maths at level 3 in
the light of the value placed on this by employers and HE institutions.
▪ Awarding organisations have introduced new ‘core maths’
qualifications at level 3 which will build on GCSE study. The focus of
these is on problem solving, reasoning and the practical application of
mathematics and statistics. These new qualifications have been
designed with the support and help of employers and universities and
suit students with a range of pass grades at GCSE maths.
DfE 16-19 accountability measures
Level 3 Mathematics
▪
The government has set the ambition that by 2020 the vast majority of
young people continue to study maths to age 18. For students who
have already gained a good pass at GCSE, we will introduce an
additional measure (in 2017) showing the percentage who achieve an
approved level 3 maths qualification, which includes new Core Maths
qualifications to be introduced for first teaching in September 2015.
DfE 16-19 accountability measures
Attainment of an approved level 3 maths qualification
▪
▪
▪
Our ambition is for the overwhelming majority of young people in
England to study maths to age 18 by 2020.
New, high-quality ‘Core Maths’ qualifications will provide an option to
continue the study of maths for those students with at least a grade C
at GCSE, but who do not wish to take A level or AS level maths.
The measure will show the percentage of students who achieved GCSE
maths (at A*-C) at the end of key stage 4, who have gone on to achieve
an approved level 3 Core Maths qualification, maths AS or A Level, or
an International Baccalaureate level 3 maths certificate
HM Treasury Budget - March 2016
Investing in the next generation – Education
▪
“We are going to look at teaching maths to 18 for all pupils.
Providing great schooling is the single most important thing we
can do to help any child from a disadvantaged background
succeed.”
▪ “It’s also the single most important thing we can do to boost the
long-term productivity of our economy, because our nation’s
productivity is no more and no less than the combined talents and
efforts of the people of these islands.”
HM Treasury Budget - March 2016: Smith review
Investing in the next generation – Education
▪
“The government will ask Professor Sir Adrian Smith to review the
case for how to improve the study of maths from 16 to 18, to
ensure the future workforce is skilled and competitive, including
looking at the case and feasibility for more or all students
continuing to study maths to 18, in the longer-term. The review
will report during 2016.”
▪ The government has not announced that maths will be
compulsory post-16. The review will consider the case and
feasibility for this.
Changes to Level 3 Mathematics in England
29 November 2016
Thank you
Paul Glaister
[email protected]