subject-specific residential courses for able post-16 students life-changing raise aspirations,...
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Subject-specific residential courses for able post-16 students • Life-changing• Raise aspirations, self-confidence, study skills, knowledge,
attainment• 99.5% ‘good’ or ‘excellent’ ratings, 85%+ excellent• Students from throughout the UK, 50%+ less advantaged
Mathematics: Chaos or Clear Cut?• Programme• Sample projects for presentations
Inspiring Excellence Programme
Mathematics: Chaos or Clear Cut?Monday - Introduction to Course; To Infinity and Beyond; Primes and Factors; Mathematical Relays
Tuesday - Black and Blue Balls and Blooming Big Numbers; Number Theory and the Science of Secrecy; Introduction to Projects; Shaping Your Future; Erorr Correction; Public Key Cryptography; Film: Enigma
Wednesday - Visit to National Codes Centre, Bletchley Park; Fractals and Chaos; Graph Theory for Beginners; The Ups and Downs of Juggling
Thursday - The Four Colour Theorem; Presentation Workshop; Enigma Variations; Where Should I Park My Spaceship?; Combinatorics and How to Rig an Election; Preparation for Presentations
Friday - Relativity and Reckless Railwaymen; Biomechanics and the Abominable Snowman; Presentations
Advisory Service support to schools and colleges – the handbook
Inspiring Excellence Programme
• Keep teacher talk down to a maximum of 20 minutes out of every hour
• Utilise group work, controlling who works with who, eg a group of high-flyers together; a mixed ability group with most able tasked with explaining the process to others
• Build in regular 2-3 minute slots for learners to explain any new ideas to each other and assess each other’s understanding
• Front load ‘homework’ – link lessons to learners’ study out of lessons by setting preparation work and utilising it in the lesson
• Utilise projects to foster extended groupwork and presentation skills• Real world applications• History of Maths?
Brightening up Maths classes
A four-year pathway for able disadvantaged students age 14 – 19 (Years 10 to 13) to make sure they maximise their potential, ie high attainment and access to a leading university.• Residential courses• University masterclasses• Learning mentors• Online hub• Support for families• University undergraduate e-mentors• Work with schools to support everyday classroom teaching
Starting point – to develop a passion for learning
The Scholars Programme
1. Think of a number between I and 102. Multiply by 93. Add the two digits in your answer together4. Subtract 55. Convert your answer to a letter eg 1 = A, 2 = B6. Think of a European country beginning with that letter7. Take the second letter of that country8. Think of an animal beginning with that letter9. Think of the colour of that animal10. And stand up if…
Brightening up Maths classes
5 + 5 + 5 = 550Add one straight line to correct this sum
5 + 5 + 5 = 550 or 5 + 5 + 5 = 550
545 + 5 = 550 or 5 + 5 + 5 ≠ 550
Brightening up Maths classes
Mathematics Matters#MathsMatters
Charlie Stripp Director, NCETM
What the future might look like for mathematics teaching in the UK, the main direction of policy and the core priorities, including why it is so important to build a cohort of strong practitioners in the subject.
Policy direction and curriculum changes in mathematics
Direction of policy
• There is a wide consensus that a population that is able to use mathematics effectively brings economic benefit to the country
• Policies aim to:– Improve educational achievement in mathematics– Increase participation in learning mathematics post-16– Increase public understanding of the benefits of learning
mathematics– Develop school-led professional development of teachers through
‘Teaching Schools’
Background: An International Perspective
• TIMSS PISA
• Is the UK an Outlier?
• Ofqual study of senior secondary assessment
What’s happening
• A move to school-led/market-led professional development• New National Curriculum• Raising of the leaving age• The Wolf review• New GCSEs• New A levels• New level 3 ‘Core Maths’ qualifications
School-led/market-led professional development
• Funding that was going to local authorities to provide CPD is now going directly to schools
• The government, through the National College for Teaching and Leadership (NCTL), has established a network of ‘Teaching Schools’, with responsibility to lead professional development within their school alliances, developing school-to-school support
School-led/market-led professional development
• ‘Academy chains’ are becoming established to provide school improvement services, including CPD
• Schools can also purchase CPD through other training providers• To help develop capacity in schools and training providers, the
NCETM is training 800 Mathematics Professional Development Leads to provide mathematics CPD at primary and secondary level
New National Curriculum
• The Myth: The Curriculum is largely focused on rote learning and practice
The government wishes to continue to emphasise fluency, but this should not be understood to mean “rote learning without understanding”.....conceptual understanding is clearly important and ..any emphasis on practice needs to be a part of achieving that understanding.
Stefano Pozzi, DfE, Mathematics in School, May 2013
New National Curriculum
• Aims: – Fluency– Mathematical Reasoning– Problem Solving
• What is mathematical fluency? Conceptual understanding + procedural knowledge
‘Efficiency, Accuracy, Flexibility’ (Russell, 2000)
New National Curriculum
• The new NC Programmes of Study for KS 1-3 have been published – KS4 is out for consultation
• The new NC PoS list what should be taught, but do not suggest how it should be taught – the emphasis on schools and teachers to interpret and implement the curriculum
• Primary mathematics content is very ambitious• The NCETM is publishing extensive guidance to support primary
teachers in implementing the new mathematics NC
New National CurriculumKS3 has been identified as a particular area of concern – TIMSS data, research from King’s College (ICCAMS study) and Ofsted:
– ‘Learning and progress were strongest in the EYFS and Years 5 and 6 with around three quarters of lessons good or outstanding. They were least effective in Key Stage 3, where only 38% of lessons were good or better and 12% were inadequate.
– Teaching was strongest in the Early Years Foundation Stage and upper Key Stage 2 and markedly weakest in Key Stage 3.’
Ofsted ‘Made to Measure’, 2012
New National Curriculum• The new PoS at KS3 has a strong focus on ‘Ratio, proportion and
rates of change’ – Multiplicative Reasoning
• The NCETM is running a project with schools on improving the teaching and learning of ‘Multiplicative Reasoning’ at KS3
Wolf review and the raising of the leaving age
• New requirement that all those continuing in education beyond 16 who have not gained a C or higher in GCSE Maths must continue to work towards it
• This is around 250 000 young people each year• There are huge workforce implications for schools and colleges• The NCETM has developed a ‘Post-16 GCSE Enhancement
Programme’ and is training 60 professional development leads to use the programme to train FE teachers of numeracy and functional skills mathematics to teach GCSE Mathematics
New Mathematics GCSEs
• Much content from the KS3 PoS is explicit in the new GCSE content• Particular focus on ‘Ratio, proportion and rates of change–
‘Multiplicative Reasoning’ • Clear emphasis on the NC aims• Double-counted in accountability measures• Structure(?) and grading
New Mathematics GCSEs
• There is some extra content (introductions to vectors and to conditional probability)
• The main increases arise from – making a large amount of KS3 work more explicit, – a greater focus on reasoning and problem solving in the
Assessment Objectives– the need to know more mathematical formulae
New Mathematics GCSEs
"The new mathematics GCSE will be more demanding and we anticipate that schools will want to increase the time spent teaching mathematics”
Michael Gove, November 2013
(The DfE cites Singapore and Australia, who teach an average of 143 and 138 hours of maths per year, respectively – UK is 116 hours per year)
New A levels in Mathematics and Further Mathematics
• Numbers of students taking A level Mathematics and Further Mathematics have risen strongly in recent years
• The Further Mathematics Support Programme has done much to support these increases and the DfE has just confirmed a further 3 years’ funding for the FMSP
• New Mathematics A levels will be introduced for first teaching from September 2016 (a year later than most other A levels)
• The structure of the Mathematics A levels will change from a modular structure to a more linear one
New level 3 ‘Core Maths’ qualifications
• Low UK participation in post-16 Maths• ‘Gap’ in maths qualifications beyond GCSE for non-specialists
‘Issue 3: Different levels of demand within mathematics – The number of different mathematics assessments at a variety of levels available to students in many education systems was also in contrast to A level Mathematics. Is there a need for A level Mathematics to have further lower-level options in addition to AS?’
Ofqual: International Comparisions in Senior Secondary Assessment, 2012
New level 3 ‘Core Maths’ qualifications
• At present:– 36 per cent of students do not achieve a grade C or better at GCSE;– 37 per cent achieve a grade C or better at GCSE but cease studying
maths
• 330,000 students start courses at Higher Education that require some element of post-16 mathematics, yet only 125,000 study mathematics from 16-18 [Advisory Committee on Mathematics Education, ‘Mathematical Needs’, 2011’].
New level 3 ‘Core Maths’ qualifications
• Students who gained a GCSE (specific grades) at Key Stage 4 who did not continue with maths during their 16-18 education (2011/2012 data):
– GCSE grade A/A* 29% 29,726– GCSE B 67% 67,555– GCSE C 76% 120,064
• Overall 60 per cent of students with a C or above at GCSE do not continue with maths. (217,300 out of a total of 360,100 with a grade C or above at Key Stage 4 in 2010).
The current position: 16-19 year olds in full-time education
New level 3 ‘Core Maths’ qualifications
• Core Maths qualifications will be designed to be suitable for students studying a range of post-16 programmes, including academic and vocational studies
• Core maths qualifications will not be compulsory but it is hoped that study of maths to be seen increasingly as the norm for students within their 16-18 education
New level 3 ‘Core Maths’ qualifications
• The DfE has just announced a ‘Core Maths Support Programme’, to work with schools and colleges to establish effective ways to support the new qualifications
• New qualifications are being developed by the awarding bodies – expected to be 2/3 the size of an AS and studied over 2 years
Post-16 Mathematics Pathways
• For those who have not achieved a grade C or above in GCSE Mathematics: A programme working towards this goal
• For those with GCSE grade C or above in GCSE Mathematics who do not intend to specialise in a mathematical discipline: Core Maths
• For those with GCSE grade C or above intend to specialise in a mathematical discipline, or who particularly enjoy maths: AS/A level Mathematics and, possibly AS/A level Further Mathematics
A vision for the future of mathematics teaching and how we might get there
A vision for the future
All teachers of mathematics• have strong subject knowledge, appropriate to the level at which they
teach• have strong pedagogical knowledge, appropriate to the level at which
they teach (including use of technology)• can put their knowledge to good effect in their teaching• enjoy the status of highly skilled professionals, playing a vital role in
society
A vision for the future
All teachers of mathematics• have access to high-quality CPD• develop and share their expertise throughout their careers• work within a career structure that rewards good subject teaching• are inspired by mathematics and able to inspire others with
mathematics
How do we get there?
• Social attitudes towards mathematics must change as its vital importance to society is better understood
• Structures should be developed that allow schools, colleges, universities, subject associations and other providers of mathematics CPD to collaborate in regional hubs with the aim of improving mathematics education, coordinated nationally to share knowledge and good practice
• It should be a requirement for every primary school to employ a suitably qualified mathematics specialist teacher to lead mathematics teaching throughout the school
How do we get there?
• Providing CPD should be an integral part of the work of successful, experienced teachers of mathematics, conferring increased status and financial reward
• A requirement to take part in CPD should be built into every teacher’s contract, including time which must be spent on CPD (equivalent to at least half-a-day per week [a day a week for the first two years])
• Core funding for CPD should be ring-fenced and set at an appropriate level
• It should be a requirement that all mathematics CPD is quality-assured through a universal standard
This vision for mathematics teaching could enable the governments’ key aims for mathematics education to be met; improving educational achievement in mathematics, increasing participation in mathematics education post-16 and improving public attitudes towards mathematics.
Trends in AS and A level Mathematics numbers
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
AS MathsA level Maths
Trends in AS and A level Further Mathematics numbers
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
2,500
5,000
7,500
10,000
12,500
15,000
17,500
20,000
22,500
25,000
AS Further MathsA level Further Maths
‘Maths Education Strategic Hub’ (MESH)
Common purpose:Excellence in
mathematics education
Lead Teaching School
Alliance (TSA)
Another TSA
UniversityMaths
Education Department
UniversityMaths faculty
Subject assoc. branch reps
LA maths advisers
Further Maths Support
Programme Area
Co-ordinator
Employer-Local links
Leading Further
Education College
Another TSA