1. Mastery in Mathematics
Written by Mike Askew
Reviewed by Steve Lomax

2. Outcomes for the session
Develop key professional knowledge about what a teaching for mastery approach might involve
Reflect on your school’s current position on teaching for mastery
Consider what it means to teach for depth rather
than breadth
Examine strategies for meeting individual needs
Plan next steps

3. Introducing mastery WATCH: Mastery in Mathematics
Note: you can find this film in Training Toolkit: Mastery in Mathematics

4. Key points
Major emphases:
Keeping classes and year groups more together as they progress through the mathematics curriculum
An emphasis on fluency, reasoning and problem solving across all mathematics lessons
The importance of the concrete, pictorial and abstract for all ages and levels of attainment: CPA in all years supports access for all

5. National Curriculum for Mathematics
The National Curriculum for Mathematics aims to ensure that all children:
become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that they develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. 1
Extracts from Department for Education materials are © Crown Copyright, and are reproduced under the terms of the Open Government Licence.
1 Department for Education (July 2013) The National Curriculum in England: Framework document. © Crown Copyright 2013.

6. National Curriculum for mathematics
Expectations:
Majority of pupils will move through the programmes of study at broadly the same pace.
When to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage.
Offer rich and sophisticated problems before any acceleration through new content.
Consolidate understanding through additional practice, if not yet sufficiently fluent.1
Extracts from Department for Education materials are © Crown Copyright, and are reproduced under the terms of the Open Government Licence.
1 Department for Education (July 2013) The National Curriculum in England: Framework document. © Crown Copyright 2013.

7. Recognising mastery
‘A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.’
Helen Drury from Mastering Mathematics: Teaching to transform achievement (Oxford University Press 2014, page 9)

8. What about setting? Primary schools: Secondary schools:
Many primary schools have moved away both from setting between classes and grouping by attainment within classes.
Secondary schools:
Some secondary schools that have adopted a mastery approach have moved to a hybrid approach where only the top and bottom set are streamed, and all the others are non-streamed.-streamed approach

9. Reflection task Working with a partner or small group, discuss:
What do you think accounts for differences in pupils’ attainment in mathematics?
What do you understand by the phrase ‘growth mindset’?

10. Some people are just naturally smart and better at maths Growth:
Two mindsets
Fixed:
Some people are just naturally smart and better at maths
Growth:
Everyone can get smarter and do better at maths

11. Teaching for depth

12. Reflections on the task
Working with a partner or small group, discuss:
Did the ‘Teaching for Depth’ task involve fluency? Problem solving? Reasoning?
How could you adapt the task for different levels of attainment? What would make it more challenging? What would make it easier?

13. Keeping all pupils involved
Plan for sound learning
Develop a supportive community of learners
Enable access to the mathematics within lessons
Support those who need it
Go deeper rather than further

14. Planning for sound learning
Fewer topics
Greater depth
Intelligent practice
Not moving on too quickly

15. Reflection Task
Working with a partner or in a small group, discuss to what extent our current practices:
support keeping pupils together as they progress through the mathematics curriculum?
emphasise fluency, reasoning and problem solving across all mathematics lessons?
promote the use of the concrete, pictorial and abstract for all ages and levels of attainment?

16. Going deeper Two ways to promote depth:
Open-ended tasks where pupils can make some choice
Matched tasks where pupils choose between them

17. Open-ended tasks Fill in the blanks: ___ is 6 more than ___
____ is ____ plus 9
7 is ____ minus _____
Go deeper: Create three different answers
for each.

18. Open-ended tasks Fill in the blanks: ____ is 3/5 of ____
8 is _____ (fraction) of _____
_____ is _____ (fraction) of 24
Go deeper: Create three different answers
for each.

19. Odd one out Which is the odd one out?
Choose whether to work with set A or B. A:
B: 4 x ÷ 4 18 ÷ 2
Go deeper: Give a reason for why each one could be the odd one out.

20. Community of learners
Low threshold, high ceiling tasks to engage everyone
Honour getting stuck
Mistakes as opportunities for learning
Accept and build on pupils’ solution methods
Pupils listen to and engage with each other’s solutions

21. Enable access to mathematics Concrete Pictorial Abstract
These are not stages to work through.
They provide a repertoire of ways of representing mathematics.

22. Variation Variation is not the same as variety
Variation requires close attention to what is changed and what is kept constant
Example ‘spaces’ are constructed around a key idea

23. Variation
Fill in the blanks. Work down the columns
6 > 4
199 _ 45
502 _ 2667
60 _ 40
1.99 _ 4.5
5.02 _ 2.667
60 _ 400
19.9 _ 4.5
0.502 _ 2.667

24. Lesson design based in variation
Key point
Difficult point
Critical point

25. Variation
Fill in the blanks. Work down the columns
6 > 4
199 _ 45
502 _ 2667
60 _ 40
1.99 _ 4.5
5.02 _ 2.667
60 _ 400
19.9 _ 4.5
0.502 _ 2.667
What might be the key point?
What might be the difficult point?
What might be the critical point?

26. Support for pupils Pre-teaching Post-lesson support
What might be the advantages of each of these interventions?
What might be some disadvantages?

27. Case study
WATCH: Video case study of pre-teaching at Grazebrook Primary School
Note: you can find this film in Training Toolkit: Mastery in Mathematics
What are the main points that stand out for you?
Note: you can find this film in xxx

28. Reflection task Working with a partner or small group, discuss:
In the video, the teachers talk about language at the centre of their planning. Why make this a key focus?
They also talk about the importance of flexible grouping. How does this fit with your grouping practices?
The importance of timely feedback on pupil learning is also raised. What forms of feedback do you use?

29. Mathematical talk
Talk brings meaning to the concrete, pictorial and abstract
Encouraging learners to give answers in complete sentences helps to develop understanding
Listening is as important as speaking

30. Reflection task Working with a partner or small group, discuss:
What do we currently do to help all pupils meet age-related curriculum expectations?
What might we need to begin to do to support mastery for all?

31. Developing planning Working with a partner:
Choose a topic that you will soon be teaching. Discuss what, within that topic are the:
Key point
Difficult point
Critical point
eflection task – based on above video
Either adapt some of the tasks in your plans so they address some or all of these ideas, or develop a new task that addresses one or more of these points.

32. Moving forward Working as a group:
Identify three or four things that you would like to see happening in your mathematics teaching in three months time.
Identify what needs to be in place for your vision of the future to come about.