1. What are you attending to?
Do it now ….
( ) + ( ) + ( ) + ( ) + ( ) =
0.62 x x 3.8 = =
What are you attending to?
Seen in a Y5 lesson in Birmingham

2. Moving to Maths Mastery
Owen Gratton
Torquay Academy
Mathematics SLE.
NCETM Professional Development Accredited Lead
Dawn Dyer
Stoke Damerel Community College
Mathematics SLE.

3. Explain Overview of Mastery Teaching for Mastery
Planning your next steps

4. Why Maths Mastery?
High performing East and South-east Asian Countries/Regions
The intention is to provide all children with full access to the curriculum, enabling them to achieve confidence and competence – ‘mastery’ – in mathematics, rather than many failing to develop the maths skills they need for the future.
All student are successfully in math’s not some, or a few.

5. Key Principles from other countries
High expectations ALL students capable of achieving in mathematics
Large Majority of students Progress through curriculum at same Pace, differentiation through deep knowledge and individual content – NOT more content
Carefully designed variation building fluency and understanding of underlying mathematical concepts in tandem
Teachers use precise questioning in class to test conceptual and procedural knowledge, and assess pupils regularly to identify those requiring intervention so that all pupils keep up.

6. What does ‘Mastery’ look like
A mastery approach; a set of principles and beliefs.
A mastery curriculum.
Teaching for mastery: a set of pedagogic practices.
Achieving mastery of particular topics and areas of mathematics.
The essential idea behind mastery is that all children need a deep understanding of the mathematics they are learning.
A mastery approach; a set of principles and beliefs.
This includes a belief that all pupils are capable of understanding and doing mathematics, given sufficient time. Pupils are neither ‘born with the maths gene’ nor ‘just no good at maths.’ With good teaching, appropriate resources, effort and a ‘can do’ attitude all children can achieve in and enjoy mathematics.
2. A mastery curriculum
One set of mathematical concepts and big ideas for all. All pupils need access to these concepts and ideas and to the rich connections between them. There is no such thing as ‘special needs mathematics’ or ‘gifted and talented mathematics’. Mathematics is mathematics and the key ideas and building blocks are important for everyone.
3. Teaching for mastery: a set of pedagogic practices that keep the class working together on the same topic, whilst at the same time addressing the need for all pupils to master the curriculum. Challenge is provided through depth rather than acceleration into new content. More time is spent on teaching topics to allow for the development of depth. Carefully crafted lesson design provides a scaffolded, conceptual journey through the mathematics, engaging pupils in reasoning and the development of mathematical thinking.
4. Achieving mastery of particular topics and areas of mathematics.
Mastery is not just being able to memorise key facts and procedures and answer test questions accurately and quickly. It involves knowing ‘why’ as well as knowing ‘that’ and knowing ‘how.’ It means being able to use one’s knowledge appropriately, flexibly and creatively and to apply it in new and unfamiliar situations.

7. What do we mean by Mastery?
Mastery means that learning is sufficiently:
Embedded
Deep
Connected
Fluent
In order for it to be:
Sustained
Built upon
Connected to

8. Essence of Mastery All pupils can succeed.
Whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time.
Pupils master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind.
Early intervention to ensure pupils keep up (not catch up).
Lesson design focuses on small steps through a carefully sequenced learning journey.
Typical lesson content includes questioning, short tasks, explanation, demonstration, and discussion.
NCETM document released in June 2016
Clear elements of TfM approach

9. Essence of Mastery
Procedural fluency and conceptual understanding are developed in tandem through intelligent practice.
Significant time is spent developing deep knowledge of the key ideas needed to underpin future learning.
Structures and connections are emphasised.
Key facts are learnt to avoid cognitive overload and to enable pupils to focus on new concepts.

10. Is Teaching for Mastery just good teaching?
How does it differ from standard practice in UK Secondary Schools?
Standard practice?
What is their understanding of TfM?
Opportunity to brainstorm ideas – flipchart paper: pin up on wall?

11. 5 big ideas –Primary and Secondary NCETM
5 big ideas from Primary Mastery Specialist Programme
Are these relevant to Secondary?

12. Education Fad? Curriculum becomes muddled Poor CPD for teachers
Not embedded

13. MASTERY 2
Teaching for Mastery

14. Variation v’s Variety What’s the difference?
What are the implications for maths teachers?
Us talking

15. Variation versus variety
‘Pick and mix’
Most practice exercises contain variety
Variation
Careful choice of WHAT to vary
Careful choice of what the variation will draw attention to
2011, Mike Askew, Transforming Primary Mathematics

16. If variety is the spice of life then variation is the key to mastery

17. Variation … an introduction

18. What are these questions
examples
of?

19. What are these questions
examples of ?

20. What are you attending to?=
0.62 x x 3.8 =
( ) + ( ) + ( ) + ( ) + ( ) =
What are you attending to?
Seen in a Y5 lesson in Birmingham

21. 0.62 x x 3.8 =
( ) + ( ) + ( ) + ( ) + ( ) = 5 =

22. The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features.

23. Conceptual and procedural variation
Standard variation
Positive variation
Non-standard variation
Conceptual Variation
Negative variation
Variation to scaffold mathematical thinking
Procedural Variation
Variation as a support for problem solving
Trilogy with variation

24. Conceptual Variation Drawing attention to what is to be learnt –
the object of the learning, the essence of
the concept.
Leading to generalisation

25. Conceptual and procedural variation
Standard variation
Positive variation
Non-standard variation
Conceptual Variation
Negative variation
Find the length of the missing side: 5 13 5 13 13 5

26. Conceptual: Negative variation
True or False 4 9 5 10 = 6 8 16 = 3 3 5 10 = 3 7 6 14 =

27. True or False +1 4 9 5 10 = +1

28. True or False ×2 ？ 6 3 5 10 = ×2

29. True or False ÷2 ×2 12 6 8 3 = 16 ×2

30. True or False
× 2 3 7 6 14 = ×2

31. Conceptual: Negative variation5 13 a x B C c b A
a2 + b2 = c2
Do you agree?
x = 132
x = 169
x2 = 144
x = 12

32. Conceptual: Negative variation5 13 x B C A
x2 = (5 + 13)2
Do you agree?
x2 = 182
x2 = 324
x = 18

33. Variation can start small

34. Task Common Resources Review
What aspects of variation can you find in your task?
What changes can be made to improve the resource?
Task

35. Conceptual and procedural variation
Standard variation
Positive variation
Non-standard variation
Conceptual Variation
Negative variation
Procedural Variation
Variation to scaffold mathematical thinking
Trilogy with variation
Variation as a support for problem solving

36. Procedural Variation Provides the opportunity
for practice (intelligent rather than mechanical);
to focus on relationships, not just the procedure;
to make connections between problems;
to use one problem to work out the next;
to create other examples of their own.

37. Procedural variation 2016 KS2 National Curriculum Tests
Questions from Reasoning Papers

38. Procedural variation

39. Procedural variation
Choose the correct answer:

40. Procedural variation
Solve the equation:

41. Conceptual and procedural variation
T1 – Pupils solve in many different ways;
T2 – Teacher highlights one particular solution which is generally applicable to other problems
T3 – Teachers change the conditions of the first problem to generate other problems
Conceptual and procedural variation
Standard variation
Positive variation
Non-standard variation
Conceptual Variation
Negative variation
Variation to scaffold mathematical thinking
Procedural Variation
Variation as a support for problem solving
Trilogy with variation

42. Providing Textbook Supports for Teaching Math Akihiko Takahashi

43. Different methods
Providing Textbook Supports for Teaching Math Akihiko Takahashi

45. Purpose of variation
Supports deep learning by providing rich experience rather than superficial contact
Provides the necessary consolidation (in familiar and unfamiliar situations) to embed and sustain learning
Focuses on conceptual relationships and make connections between ideas
Supports pupils’ ability to reason and to generalise

46. Conceptual and procedural variation
Standard variation
Positive variation
Non-standard variation
Conceptual Variation
Negative variation
Variation to scaffold mathematical thinking
Procedural Variation
Variation as a support for problem solving
Trilogy with variation

47. Key Ideas
The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features.
When giving examples of a mathematical concept, it is useful to add variation to emphasise:
What it is (as varied as possible);
What it is not.
When constructing a set of activities / questions it is important to consider what connects the examples; what mathematical structures are being highlighted?
Variation is not the same as variety – careful attention needs to be paid to what aspects are being varied (and what is not being varied) and for what purpose.

48. Next Steps Teacher Research Groups
Contact us to express interest for 2017/18 cohort

49. http://www.glowmathshub.com/resources.html More information
Thank you
More information
NCETM – Developing Mastery in Mathematics October 2014
White Rose Maths Hub
Mr Reddy Maths – Curriculum design
Mastery Learning – getting the foundations right