Core Maths

Paul Glaister Professor of Mathematics & Mathematics Education, University of Reading

CMSP / ALCAB / ALMAB / Ofqual / IMA / JMC (Chair)

Changes to Level 3 Mathematics in England 29 November 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 (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.”

Sustained growth in the number of students progressing to AS and A level mathematics

Level 3 mathematics progress has been good

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

Sources: DfE analysis of pupil-level data

No change 79%

AS maths 6%

A level maths 12%

A level FM 2%

Other L3 1%

What have A*-C GCSE maths students achieved by age 18?

(2011 GCSE cohort) “330,000 students start courses each year which require advanced (post-GCSE) maths, but over 200,000 of them will not have studied beyond GCSE”

(ACME, Mathematical Needs, 2011)

“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)

Post-16 Mathematics

Recent AS/A level numbers (England)

Recent A level grades vs GCSE (England)

Recent AS/A level numbers (England)

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.

• 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.

Diverse destinations of A level maths students

Qualifications: AS/A levels (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.

AS/A level Maths and Further Maths (from 2017)

▪ 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.

ACME report – ‘Mathematical Needs: Mathematics in the workplace and in higher education’, 2011

▪ The number of students entering the disciplines with an A or AS-level 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.

HEA report - ‘Mathematical Transitions’, 2014

• Reports

Reports

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

▪ 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 launch

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’ Qualifications

▪ 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

▪ 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’ Qualifications

• 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 topics

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

September 2014 ▪ 153 Early Adopter Teaching

Projects ▪ ~3,000 students

September 2016 ▪ ~ 500 centres teaching Core

Maths ▪ ~10,000+ students

Core Maths numbers

Core Maths by sector

Type of institution

Number teaching Core Maths

Total number of institutions

Percentage coverage

2014-15 2015-16 2016-17 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

AS and A level mathematics

Core Maths

keeps options open for a wide range of university courses is essential for entry to many degree courses including most STEM and medicine, economics and architecture supports the mathematical elements of other A-level subjects introduces new ideas, applications and techniques such as - proof, calculus, modelling offers more rapid progression for higher achieving students in mathematics

helps students maintain and further develop valuable mathematical skills for university and employment helps with the mathematical elements of other level 3 courses, including humanities and social sciences builds valuable skills through an emphasis on mathematical problem solving in real life contexts provides an option which is suitable for all students with a good pass at GCSE

Core Maths/AS and A level

▪ 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

Core Maths and universities

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.

University Endorsement

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 advice for 16-19 study programmes (Jan 2016)

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

DfE 16-19 accountability measures

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

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.

HM Treasury Budget - March 2016: Smith review

Thank you

Paul Glaister

p.glaister@reading.ac.uk

Changes to Level 3 Mathematics in England 29 November 2016