1. head teachers, senior leaders & mathematics mastery school leads

2. Introduce yourself to a person on your table who is not from your school.
Introduce this person to the rest of your table.
Name, role, and three facts.

3. Pioneer partner schools
Manchester (1)
Birmingham (4)
Suffolk (6)
London (20)
Portsmouth (1)
Essex (2)
Reading (2)
Peterborough (1)
Northants (1)
Kent (1)
Sussex (2)
“Mathematics Mastery looks like it has all of the attributes that we are seeking to transform mathematical learning and success in our school.”

4. A belief and a frustration
ARK Schools wanted a new maths curriculum to ensure that their aspirations for every child’s mathematics success becomes reality, through significantly raising standards.
Success in mathematics for every child
Close the attainment gap

5. Best practice – national and international
The connections
Best practice – national and international
Research findings and evidence
ARK
Schools
Mathematics Mastery

6. Curricular principles
Fewer topics in greater depth
Mastery for all pupils
Number sense and place value come first
Problem solving is central

7. Feedback from
Problem solving and investigations give pupils the opportunity to demonstrate an in-depth understanding of the topic.
The use of manipulatives and the focus upon explaining promotes mathematical understanding.
They are the kind of tasks you would create if you could spend a significant amount of time thinking about the best way to approach teaching concepts to students.
Since teaching in a mastery style, I have really had to think about my questioning which has improved my subject knowledge.

8. Agenda 10.00am What's really possible? 11:15am Break
11:15am Break
11.30am What does ‘mastery’ look like in the classroom?
12.30pm Lunch
1.00pm Mastery in your school
2:45pm Action planning
3:30pm Questions and answers
4:00 Close

9. Why are we here?
Why have you and your school chosen to join the Mathematics Mastery community?
What do you want/need to know by the end of today?

10. Why are we here?
“We know that no child is limited by their background and that by working hard all children can become excellent mathematicians. ”

11. Research shows:
The gap at age 10 between our strongest and weakest maths performers is one of the widest in TIMSS - with fewer of our pupils overall reaching the very highest levels
The 10% not reaching the expected level at age 7 becomes 20% by age 11 and, in 2012, almost 40% did not gain grade C at GCSE
Girls are less likely than boys to study maths beyond 16 and less confident about their ability overall
Lower income pupils are falling behind in maths

12. International Trends 2009 PISA
Nationally, what are we doing well? What are we not doing so well?

13. Maths is not a measuring tool
“Mathematics education should be so much more than just passing exams and Mathematics Mastery will help us achieve this. We want every child to not just pass GCSE mathematics but pass with top grades and to leave our school with a love of mathematics. ”

14. Our shared vision
Every school leaver to achieve a strong foundation in mathematics, with no child left behind
A significant proportion of pupils to be in a position to choose to study A-level and degree level science, technology, engineering and mathematics-related subjects
What is necessary to make this vision a reality?

15. Who are our students and what are they capable of?
“Many of our students come from disadvantaged backgrounds and arrive at secondary school not fully equipped mathematically and so there is a necessity to close the attainment gap.”
“We have a key stage two score on entry that is below the national average. This means that in order for our young people to achieve A and A* grades at GCSE mathematics we have to work harder for them and develop a mathematics curriculum that is beyond outstanding.”

16. A/A* B C
Above expectations
Meeting expectations
Below expectations

17. Maths achievement in your school
What is your expectation of your students’ achievement in mathematics?
Who will study maths-related subjects at degree level?
Who will study A-level maths? How will they do?
How will students achieve at 16?
Consider your new intake of Year 7 students.

18. Collaborative Community
“One of the most exciting things about the programme is the idea that we will be able to talk to colleagues in different schools about what we are doing. We would hope to learn from others and to share the ideas we have that we find work well. ”

19. Shared curriculum framework Online Collaborative cluster workshops
Task banks
Assessments
Training
Videos
Blogs
Collaborative
cluster
workshops
Mathematics
Mastery
Lesson
observation
tools
In-school
development
visits
Launch
training
Teachers
Leaders

20. Our approach
You say:
“The mathematics team is firmly committed to a problem solving approach which will equip our students for later life.”
Conceptual understanding
Mathematical
problem
solving
Language and communication
Mathematical thinking

21. Our approach: problem solving
What does it mean to teach through problem solving?
What does it mean to teach for problem solving?

22. Problem solving – you say:
“Our evidence shows that students are performing markedly worse on problem solving questions in GCSE exams in comparison to procedural questions.”
“We promote problem solving within the mathematics department through our use of starters and as part of the differentiated extension tasks. However, deeper problem solving occurs more in the higher sets. Mathematics Mastery will enable us to bring the culture of problem solving in the mixed ability, lower sets and intervention sets.”

23. Mastery for all Represent Mathematical problem solving Communicate
Generalise

24. Potential barrier 1: language and communication
Represent
Mathematical
problem
solving
Communicate
Generalise

25. Mastering mathematical language
Mathematics Mastery lessons provide opportunities for pupils to communicate and develop mathematical language through:
Sharing essential vocabulary at the beginning of every lesson and insisting on its use throughout
Modelling clear sentence structures using mathematical language
Insisting on correct use of language – “I know what you’re trying to say” as start not end
Talk Tasks
Continuous questioning in all segments which give a further opportunity to assess understanding through pupil explanations

26. Potential barrier 2: reasoning
Represent
Mathematical
problem
solving
Communicate
Generalise

27. Mastering mathematical thinking
“Mathematics can be terrific fun; knowing that you can enjoy it is psychologically and intellectually empowering.” (Watson, 2006)
We believe that pupils should:
Explore, wonder, question and conjecture
Compare, classify, sort
Experiment, play with possibilities, modify an aspect and see what happens
Make theories and predictions and act purposefully to see what happens, generalise

28. Mathematical thinking – you say
“By focusing on fewer topics whilst increasing their skills as independent learners (which fits fantastically with our whole school policy of collaborative learning) we will increase the confidence of a large majority of our students in their key mathematical skills.”

29. Potential barrier 3: conceptual understanding
Represent
Mathematical
problem
solving
Communicate
Generalise

30. What are manipulatives?
Bead strings
Language and communication
Mathematical thinking
Conceptual understanding
Mathematical
problem
solving
Bar models
Dienes blocks
100 grids
Fraction towers
Number lines
Cuisenaire rods
Shapes
Multilink cubes

31. Let’s do some maths... Problem solving using bar models!
Pupils draw a visual representation of a word problem.
Taught early on in the programme, using concrete and pictorial representations, in the context of the four operations.
Pupils are then expected to use models for fractions, decimals, percentages, algebra, pie charts....

32. Solving problems with unknowns
John gives his brother three marbles.
Now his brother has three times as many marbles as John.
Altogether they now have sixteen marbles.
How many marbles did John have at the start? ? 3
John 16
John’s brother
Ben scored 1,866
Abe scored 2,177

33. Conceptual understanding – you say
“It is essential that all of our teachers aim for all our students to clearly understand a mathematical concept rather than simply learning the process.”
“Our aim is to teach for understanding, but realistically this is not happening in all classes all the time.”
“I feel that the use of concrete manipulatives and a constant focus on problem solving will mean that students are much more able to understand mathematical concepts.”

34. Lesson structure Do Now New learning Talk task Develop learning
Independent task
Plenary
Ofsted outstanding:
Planning is astute
Time is used very well
Every opportunity is used to successfully develop crucial skills (inc. literacy and numeracy)
Lessons proceed without interruption
Appropriate independent learning tasks are set
Pupils are resilient, confident and independent
Well judged and often imaginative teaching strategies are used

35. with problem solving at the heart
You don’t achieve mastery by climbing...you achieve mastery through DEPTH
Mathematical Thinking
Understanding
Language
Representing
Explaining
Connecting
Generalising
Comparing
Modifying
Justifying
CPA
Curriculum
with problem solving at the heart

36. Maths learning in your school
What is consistent across the department?
What happens in every lesson?
What does ‘students’ work’ look like?
How are students supported to:
use language to reason and communicate with accuracy?
represent mathematical concepts and techniques?
make connections within mathematics?
make connections beyond mathematics?
think mathematically and solve problems?

37. Using data and evidence
Fine grain detailed data analysis on a question level and by national curriculum sub-levels are essential to ensuring that every student is successful
The big picture is what’s important – the focus should be on the best way to teach the students, and the best way to teach the concept or technique, with their long term success in mind

38. ‘Big picture’ data can tell us…
1) What the essential concepts and techniques are for students to succeed at A-level and beyond.
2) What the essential concepts and techniques are for students who might otherwise fall behind.
3) That these are the same!
4) The ‘habits of mind’ that students need to succeed
a) in maths
b) in applying their maths

39. Classroom data
In lessons: student responses, student engagement
Work scrutiny
Student voice
Student tracking
Case studies – progress of students in challenging circumstances
Views of parents
Discussion with staff and senior leaders

40. Work scrutiny

41. Classroom data can tell us…
Which students are at risk of underachieving
Which concepts and techniques need re-teaching/teaching differently next time round
Which students need additional challenge
Which pedagogic approaches were particularly effective

42. ‘Exam’ data tells us…
Areas where the classroom evidence might be misleading
How students might perform in high stakes external exams

43. Assessment
Pre- and post-module assessments Termly holistic assessments

44. Expectations

45. Attainment at end of term
What does success look like?
Year 7 Term
Evidence of success
Attainment at end of term
Autumn
Spring
Summer

46. Fewer topics, greater depth
“Our students have a brief knowledge of a large range of topics but their foundation skills crumble as we approach more complex topics.”
“By focusing on fewer topics whilst increasing their skills as independent learners (which fits fantastically with our whole school policy of collaborative learning) we will increase the confidence of a large majority of our students in their key mathematical skills.”
“We want to close the achievement gap across all year groups so that it is not necessary to put all of our resources and effort into just the Y11 groups each year and so that maths can be truly understood and embraced by all year groups prior to their GCSE year.”

47. Knowledge, understanding and skills by week
Year 7
Knowledge, understanding and skills by week
Weeks
Half terms
Integer place value
Round and estimate
Add and subtract
Word problems
Decimal numbers
Decimal place value
Find perimeter
Multiple, LCM
Multiplication
Multiplication of decimals
Rectangle and triangle area
Factor, HCF
Division
Mean average
(Investigation)
Estimate measures
Read scales
Draw, measure and name angles
Angle types
Triangles
Quadrilaterals
Fractions as numbers, fractions as operators
Equivalent fractions
Compare and order fractions
Multiplicative relationships with fractions
Fraction of a quantity
Multiply and divide fractions
Order of operations
Symbolic notation
Substitute and simplify
Interpret pie charts
Convert fractions, decimals
and percentages
Percentage of a quantity
(Investigations)

48.  Place value Fractions, decimals and percentages
Half term 1
Number sense
Half term 2
Multiplication & division
Half term 3
Angle and line properties
Half term 4
Fractions
Half term 5
Algebraic representation
Half term 6
Percentages & pie charts 
Place value
Fractions, decimals and percentages
Addition and subtraction
Perimeter
Multiplication and division
Area
Using scales
Year 7
Angle and line properties
KEY
Half term topic
Big idea
Substantial new knowledge mastered
Calculating with fractions
Algebraic notation

49. Support and challenge Conceptual understanding Mathematical problem
solving
Language and communication
Mathematical thinking

50. Low threshold, high ceiling
Pupils compare the area and perimeter of rectangles.
Which is bigger? Which is smaller?
4cm
8cm
2cm
4cm
Can/does this task involve modifying? How could the teacher prompt this?
Can/does this task involve generalising? How could the teacher prompt this?

51. Summary What does Mastery mean?
Assumption is that what has been learnt really has been learnt – this doesn’t happen after one lesson however!
Achieving mastery through ‘less explicit’ repetition
Mastery occurs as a result of repetition through using skills continuously across genres
Taking time to explore, clarify, practice and apply, not memorise
Valuing concrete and pictorial, not rushing to the abstract

52. Supporting, monitoring and evaluating
What to look for in a lesson
evidence of C-P-A
use of language structures
great questioning
100% involvement
AfL

53. Looking at a lesson What is 0.27 plus 1.009?
It’s one point two seven nine. That means it has nine thousandths.
Good. How many tenths are there in 0.27?
There are two tenths, in 0.27 and two tenths in the answer.
Actually there are twelve tenths aren’t there?
Yes. There are. What is 1.27 plus 1.009?

54. Supporting, monitoring and evaluating
Conceptual understanding
Mathematical
problem
solving
Language and communication
Mathematical thinking

55. Looking at a lesson
I know you can already do this, but you need to show this using manipulatives.
But why, sir? We’re a top set.
It’s important. Show me which is bigger, 0.2 multiplied by £25 or 250% of £2.
How many different ways can you find of showing this.

56. Supporting, monitoring and evaluating
Conceptual understanding
Mathematical
problem
solving
Language and communication
Mathematical thinking

57. Looking at a lesson What is a fraction? It’s a number less than one.
Good. Any examples?
It’s like three quarters, the top number is divided by the bottom number.
Brilliant. Division. Anyone else?
It’s part of a whole.
Excellent!

58. Supporting, monitoring and evaluating
Conceptual understanding
Mathematical
problem
solving
Language and communication
Mathematical thinking

59. What are you looking for?
Do Now
New learning
Talk task
Develop learning
Independent task
Plenary

60. Ofsted: Made to measure (2011) Evidence from successful schools
Pupil collaboration and discussion of work
Mixture of group tasks, exploratory activities and independent tasks
Focus on concepts, not on teaching rules
All pupils tackled a wide variety of problems
Use of hands on resources and visual images
Consistent approaches and use of visual images and models
Importance of good teacher subject-knowledge and subject-specific skills
Collaborative discussion of tasks amongst teachers

61. Emily Hudsmith, Head of Maths
Do the maths
I can't stress enough how vital it is for teachers to complete the tasks before teaching them. By doing this I have found it far easier to anticipate what my students might do or where they may struggle (particularly with the open problems) so I can plan scaffolding carefully. On the occasions I haven't done this I have ended up having very 'teacher led' lessons which were not as effective.
Emily Hudsmith, Head of Maths
Charter Academy