1. A case study in using Singapore textbooks to support teaching for mastery.
Liz Robbins – Sheringham Primary School
Jack Corson – Nelson Primary School 1

2. 2 experiences:
On this side of the room, imagine you were a child who always sat on the red table for Maths. You know you’re not very good at Maths, as you always sit with an adult and your teacher makes sure you use the cubes etc. You know that your teacher will always give you something different to do, as the work the rest of the class does is just too difficult for you.
On this side of the room, imagine you were a child who always sat at the green table. You’re generally expected to get on with your work without adult help and without using the cubes etc. You know you’re pretty good at Maths as you can remember how to do things and get nearly all the questions right. You like to do lots of similar questions when you’re confident that you’re going to get them right. You don’t get stuck very often and you don’t like it when it does happen.
In our schools, your experiences would be rather different:
On this side of the room, imagine you are that same child. You get to work with lots of different pupils in your class. You are always doing the same work as everyone else, although sometimes it takes a little longer. Your teacher gives you lots of problems to work on together and you have to find lots of different ways to get to the answer. It’s been nice when you’ve found a way that your partner didn’t think of!
On this side of the room, imagine you are also the same child as before. You get to work with lots of different pupils in your class. You are always doing the same work as everyone else, although sometimes you have to do something extra. Your teacher gives you lots of problems to work on together and you have to find lots of different ways to get to the answer. It’s been a little strange when someone else finds a way that you didn’t think of, but you’re beginning to realise there’s no one ‘right’ way. Your teacher is always asking you to explain your ideas which you found difficult at first, but the cubes etc. have helped you to show your ideas more easily. In fact, you’ve started to spot your own mistakes before your teacher does, because using the cubes etc. means you understand what is realistic.

4. Large Primary Schools in the Borough of Newham
Trialled Maths – No Problem! Text books
Participated in the NCETM
NCP2 Textbook trial – trialling MNP textbooks in one year 1 class
Decided to trial MNP textbooks independently – across three year 1 classes and three year 3 classes
Will use Maths – No Problem Textbooks in Years 1-6 in 2015/16
An emphasis on a mastery approach – not merely a scheme to follow
An emphasis on CPD for our staff

5. Singapore background

6. “…being mathematical with and in front of the children…”

8. Are you convinced that… ?
Metacognition
Our responses as teachers can either promote children’s tendency to depend on external cues or a tendency to self reflect and correct independently
Well done! That’s right!
How do you… ?
Do you agree with… ?
Are you sure… ?
The answer is not important at the moment…
Are you convinced that… ?
Is there another way… ?

9. Visualisation
Our questioning and modelling as teachers can either promote children’s tendency to passively imitate or to learn to imagine a world of mathematical possibilities
Can you picture in your mind …
Can you imagine…
Can you see with the eyes in your mind…
Pavin says we can move the 3 to the 7 to make 10. Do you agree? Can you see with the eyes in your mind the 7 and the 3 making 10?

10. Generalisation What do you notice? What’s the same? What’s different?
Making and breaking rules
Is it always true that…?
Is it sometimes/always/never true that… ?

11. Number Sense
How does the scaffolding in this encourage the development of number sense?
What experiences do children need to have had in order to develop a deeply embedded number sense?

12. Number Sense

13. Number Sense

14. Communication If we cannot explain it, we cannot use it in class!
Silence within a mathematics classroom is suspicious!

15. Have you watched any cookery programs on TV?

16. Paradigm Shift a cumulative curriculum vs a spiral curriculum

17. Y1 overview

18. Y2 overview

19. Y3 overview

20. Paradigm Shift a cumulative curriculum vs a spiral curriculum a focus on concepts and interconnected ideas vs isolated objectives

21. Multiple Success Criteria and Representations

22. Same activities – same questions
Paradigm Shift a cumulative curriculum vs a spiral curriculum a focus on concepts and interconnected ideas vs isolated objectives the whole class working together vs differentiation by content
Same activities – same questions

23. Paradigm Shift a cumulative curriculum vs a spiral curriculum a focus on concepts and interconnected ideas vs isolated objectives the whole class working together vs differentiation by content depth vs acceleration ‘working on’ vs ‘working through’

26. Paradigm Shift a cumulative curriculum vs a spiral curriculum a focus on concepts and interconnected ideas vs isolated objectives the whole class working together vs differentiation by content depth vs acceleration ‘working on’ vs ‘working through’ intelligent practice/variation theory vs mechanical repetition

27. Intelligent Practice/Variation Theory

28. Paradigm Shift a cumulative curriculum vs a spiral curriculum a focus on concepts and interconnected ideas vs isolated objectives the whole class working together vs differentiation by content depth vs acceleration ‘working on’ vs ‘working through’ intelligent practice/variation theory vs mechanical repetition An expectation that all children can achieve vs labelling children according to ‘ability’

30. Textbook and workbook materials
What is there?
Video academy
Online teacher guide

32. Textbook and workbook materials
What is there?
Video academy
Online teacher guide
Textbooks
Anchor task
Targeted strategies
Guided practice
Some consolidation activities
Workbooks
Questions for every lesson
Unit reviews
Mid-year and end-of-year reviews

33. Textbook and workbook materials
How does it help?
More effective use of time
Less time spent preparing worksheets and resources
More time spent thinking about mathematical concepts
Children engagement
Whole-school consistency and continuity
Subject knowledge

35. Subject knowledge Appropriate pitch Carefully chosen questions
Pre-empt misconceptions
Progressive
Intelligent practice leading to mastery (i.e. application in a variety of contexts)
Opportunities for challenge through depth and reasoning
Carefully chosen and scaffolded recording formats
Guides towards practical resources and visual models

36. Conceptual Variation

37. Subject knowledge Appropriate pitch Carefully chosen questions
Pre-empt misconceptions
Progressive
Intelligent practice leading to mastery (i.e. application in a variety of contexts)
Opportunities for challenge through depth and reasoning
Carefully chosen and scaffolded recording formats
Guides towards practical resources and visual models

38. Workbook examples – Year 1

39. Workbook examples – Year 2

40. Workbook examples – Year 3

41. Subject knowledge Appropriate pitch Carefully chosen questions
Pre-empt misconceptions
Progressive
Intelligent practice leading to mastery (i.e. application in a variety of contexts)
Opportunities for challenge through depth and reasoning
Carefully chosen and scaffolded recording formats
Guides towards practical resources and visual models

42. Summary reflections – pros and cons
Strengths
Weaknesses
Content aligned with new curriculum – appropriate pitch
Embedded opportunities for problem-solving and reasoning
Emphasis on visual models
Explicit strategies to be taught
Engaging for pupils
Carefully considered progression
Consistency throughout school life
Subject knowledge developed
Meets wider aims of high pupil expectations and confidence
Pre-designed tests
Potential to be lazy
Purpose or intention of tasks/strategies not always clear
Lack of provision to extend pupils; tendency for teachers to only consider an extension activity, not how to extend in rest of lesson
Assumes that teachers are aware of earlier strategies so not always explicit
Children’s understanding of the task can be a barrier; contexts change frequently, so children must get used to switching
Reading expectations in Y1 above our children’s actual ability
Some errors
Use of hands-on resources inconsistent with 2016 national tests where no resources are allowed
Summary
Materials insufficient on their own
A ‘mastery’ approach is not easily adopted
On balance, the content delivered is better than it would have been previously

43. Teacher & pupil reflections
“Once resources are easily accessible, lessons run really smoothly.”
“It’s a complete change and you have to have an open mind to see the benefit.”
“It really works for assessment, even though the tasks are the same.”
“I’ve discovered methods I never knew existed.”

44. Teacher & pupil reflections
“Maths is more fun than it was before.” (Year 3 high attainer)
“It’s better cos we do more difficult stuff and I like the booklet.” (Year 3 low attainer)
“I like Maths now because we do more Maths work and I can write in the booklet.” (Year 1 middle attainer)