Bucks, Berks and Oxon Maths Hub Launch Charlie Stripp Director, NCETM

There are huge changes taking place in maths education

New National Curriculum: ambitious New Maths GCSEs: more demanding New post-16 Core Maths qualifications Maths to age 18 for those who do not achieve GCSE by age 16 New A levels from 2016

Direction of policy There is a wide consensus, supported by OECD evidence, that a population that is able to use mathematics effectively brings significant economic benefit to the country, hence the current political interest in maths education

Direction of policy 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

Maths Hubs Idea initiated by the NCETM Regional hubs to provide specialist, school-led support to improve maths education Coordinated by the NCETM to provide national expertise and leadership Cross-phase, collaborative, joined up

Lead School: Providing the mathematical and partnership leadership Maths Lead Julia Brown Hub Administrator Victoria Plunket Senior Leader with a strategic role Sharon Cromie School Other Institution Lead School: Providing the mathematical and partnership leadership Strategic partners: Working with the lead school to provide strategic leadership for the hubs Operational partners: Further local leadership and specialist expertise to support whole area

Maths Hubs: School/college improvement Determined support for all schools/colleges to improve: the teaching of mathematics the leadership of mathematics the school’s mathematics curriculum

Maths Hubs: National Collaborative projects NCP1: China-England maths education research and innovation project NCP2: Singapore textbooks NCP3: Raising participation in maths education post-16, linking with the CMSP and FMSP

Maths Hubs Shanghai teacher exchange The England-China Maths Education Innovation and Research Project Transformational impact Drawing on international expertise Generating and informed by evidence Local leadership but with national collaboration Exemplary maths education

Maths Hubs Local projects Supporting national priorities to improve maths education Meeting local need

‘Mastery’ teaching in mathematics

A way to improve maths education at all levels Promoting mastery: Not a gimmick, an evidence-based change of approach Cultural change: success in maths (and just about anything else) comes primarily from effort, not from ‘being clever’ Intelligent practice to develop deep understanding is the key to success We can learn from Shanghai and Singapore

3 forms of knowledge I know that I know how I know why

Mastery A belief that pupils can and will achieve Development of deep structural knowledge Carefully chosen examples supporting the opportunity to make connections Keeping the class working together Quick intervention Longer time on key topics

Deep Conceptual Learning ‘It is essential to enquire into the origins of the applications of the methods so they will not be forgotten for a long time’ ‘It is difficult to see the logic and method behind complicated problems. Simple problems are hereby given and elucidated. Once these are understood, problems, however difficult, will become clear’ (Yang Hui 1274)

The Answer is only the beginning……….. The teacher presents a maths problem And then asks: What is the answer? Describe the method/procedure you used Why does the method work, what relationships are involved, what generalities or rules can we glean?

Practice makes perfect! Is doing a large number of exercises compatible with deep learning? It depends on the nature of the practice – Intelligent practice provides opportunity for The development of procedural fluency and conceptual understanding in tandem - Variation theory

Procedural Variation – where successive problems link to the previous problem Examples are linked and support the notion of intelligent practice

Procedural Variation ‘In designing these exercises, the teacher is advised to avoid mechanical repetition and to create an appropriate path for practising the thinking process with increasing creativity’ (Gu, 1991).

Variation supports intelligent practice

Notice the progression from the first example to the final one?

Conceptual Variation Where the concept is represented in different ways to expose and connect different aspects of the concept. This supports depth of understanding and Mastery

The Singapore Bar Model: Representing Ratio Stella and Tom share football stickers in the ratio of 1 to 3. Altogether they have 48 Stickers. How many does Tom have? Stella 12 48 Flexibility of thinking Tom 12 12 12 How many more stickers does Tom have than Stella?

Grape Raisin A confusing problem A grape is 80% water. of the water is removed by drying, turning it into a raisin. What is the percentage of water in the raisin? Grape Raisin 20 80 20 20

Simultaneous equations with the Singapore bar 88 children at a party. 1/3 of the boys pair with 2/5 of the girls for a 3 legged race. How many boys at the party? Boys 11 pieces, so 8 children for each piece, so 48 boys Girls

A teaser You have 7 dice You roll them all at the same time What is more likely: they all show the same number? they all show different numbers?