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Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology, and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education, therefore, provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

1.
Haringey

Session 1

Supporting fluency and

reasoning through rich

tasks

8 October 2014

Lynne McClure

Director, NRICH project

© University of Cambridge

Session 1

Supporting fluency and

reasoning through rich

tasks

8 October 2014

Lynne McClure

Director, NRICH project

© University of Cambridge

2.
National Curriculum

Become fluent in the fundamentals of

mathematics, including through varied and

frequent practice with increasingly complex

problems over time, so that pupils develop

conceptual understanding and the ability to

recall and apply knowledge rapidly and

accurately.

© University of Cambridge

Become fluent in the fundamentals of

mathematics, including through varied and

frequent practice with increasingly complex

problems over time, so that pupils develop

conceptual understanding and the ability to

recall and apply knowledge rapidly and

accurately.

© University of Cambridge

3.
National Curriculum

Reason mathematically by following a line of

enquiry, conjecturing relationships and

generalisations, and developing an

argument, justification or proof using

mathematical language

© University of Cambridge

Reason mathematically by following a line of

enquiry, conjecturing relationships and

generalisations, and developing an

argument, justification or proof using

mathematical language

© University of Cambridge

4.
Reach 100

Choose four different digits from 1−9 and

put one in each box. For example:

This gives four two-digit

numbers: 52,19, 51, 29

In this case their sum is 151.

Can you find four different digits that give

four two-digit numbers which add to a total

of 100?

© University of Cambridge

Choose four different digits from 1−9 and

put one in each box. For example:

This gives four two-digit

numbers: 52,19, 51, 29

In this case their sum is 151.

Can you find four different digits that give

four two-digit numbers which add to a total

of 100?

© University of Cambridge

5.
• What is the mathematical

knowledge that is needed?

• Who would this be for?

• What is the ‘value added’ for higher

attaining children/struggling children.

5

© University of Cambridge

knowledge that is needed?

• Who would this be for?

• What is the ‘value added’ for higher

attaining children/struggling children.

5

© University of Cambridge

6.
Strike It Out

6 + 4 = 10

10 take away 9 makes 1

1 add 17 is 18

Competitive aim – stop your partner

from going

Collaborative aim – cross off as many

as possible

6

© University of Cambridge

6 + 4 = 10

10 take away 9 makes 1

1 add 17 is 18

Competitive aim – stop your partner

from going

Collaborative aim – cross off as many

as possible

6

© University of Cambridge

7.
• What is the mathematical knowledge

that is needed to play?

• Who would this game be for?

• What is the ‘value added’ for able

children/struggling children of playing

the game?

• How could you adapt this game to use

it in your classroom?

7

© University of Cambridge

that is needed to play?

• Who would this game be for?

• What is the ‘value added’ for able

children/struggling children of playing

the game?

• How could you adapt this game to use

it in your classroom?

7

© University of Cambridge

8.
How do these rich tasks contribute to

fluency?

reasoning?

© University of Cambridge

fluency?

reasoning?

© University of Cambridge

9.
An efficient strategy is one that the student

can carry out easily, keeping track of sub-

problems and making use of intermediate

results to solve the problem.

© University of Cambridge

can carry out easily, keeping track of sub-

problems and making use of intermediate

results to solve the problem.

© University of Cambridge

10.
depends on careful recording, the

knowledge of basic number combinations

and other important number relationships,

and checking results.

© University of Cambridge

knowledge of basic number combinations

and other important number relationships,

and checking results.

© University of Cambridge

11.
requires the knowledge of more than one

approach and being able to choose

appropriately between them

(Russell, 2000

© University of Cambridge

approach and being able to choose

appropriately between them

(Russell, 2000

© University of Cambridge

12.
Procedural &

conceptual fluency

Automaticity with recall

© University of Cambridge

conceptual fluency

Automaticity with recall

© University of Cambridge

13.
Fluency

Procedural without conceptual Conceptual without procedural

Computation without meaning Computation which is slow, effortful

and frustrating

Inability to adapt skills to unfamiliar Inability to focus on the bigger picture

contexts when solving problems

Difficulty reconstructing forgotten Difficulty progressing to new or more

knowledge or skills complex ideas

© University of Cambridge

Procedural without conceptual Conceptual without procedural

Computation without meaning Computation which is slow, effortful

and frustrating

Inability to adapt skills to unfamiliar Inability to focus on the bigger picture

contexts when solving problems

Difficulty reconstructing forgotten Difficulty progressing to new or more

knowledge or skills complex ideas

© University of Cambridge

14.
Using the same rules is it possible to cross all

the numbers off?

How do you know?

14

© University of Cambridge

the numbers off?

How do you know?

14

© University of Cambridge

15.
Two types of reasoning

Inductive reasoning

• Can be incorrect

• Can’t be used to ‘prove’

Deductive reasoning

• Follows rules of logic

• Can be used to prove

© University of Cambridge

Inductive reasoning

• Can be incorrect

• Can’t be used to ‘prove’

Deductive reasoning

• Follows rules of logic

• Can be used to prove

© University of Cambridge

16.
In a problem:

• Reasoning is necessary when:

• The route through the problem is not clear

• There are some conflicts in what you are given

or know

• There are some things you don’t know

• Theres no structure to what you’re given

• There are different possible solutions

• All of which require mental work….

© University of Cambridge

• Reasoning is necessary when:

• The route through the problem is not clear

• There are some conflicts in what you are given

or know

• There are some things you don’t know

• Theres no structure to what you’re given

• There are different possible solutions

• All of which require mental work….

© University of Cambridge

17.
Reasoning is…

• A critical skill to knowing and doing maths

• Enabling – it allows children to make use of all

the other mathematical skills – it’s the glue that

helps maths to make sense.

© University of Cambridge

• A critical skill to knowing and doing maths

• Enabling – it allows children to make use of all

the other mathematical skills – it’s the glue that

helps maths to make sense.

© University of Cambridge

18.
Structuring

children’s reasoning

• Questioning: closed v open

• Listening

• Acknowledging

• Improving

• Modelling KS1: good 'because' statements,

short chains

• KS2: logic, convincing

© University of Cambridge

children’s reasoning

• Questioning: closed v open

• Listening

• Acknowledging

• Improving

• Modelling KS1: good 'because' statements,

short chains

• KS2: logic, convincing

© University of Cambridge

19.
Session 2

Problem solving

© University of Cambridge

Problem solving

© University of Cambridge

20.
National Curriculum

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

© University of Cambridge

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

© University of Cambridge

21.
Historically

• learning the content v problem solving

• theory versus practice, reason versus

experience, acquiring knowledge versus

applying knowledge.

• problems seen as vehicles for practicing

applications ie computation procedures are

acquired first and then applied

• problem-based learning

© University of Cambridge

• learning the content v problem solving

• theory versus practice, reason versus

experience, acquiring knowledge versus

applying knowledge.

• problems seen as vehicles for practicing

applications ie computation procedures are

acquired first and then applied

• problem-based learning

© University of Cambridge

22.
Dominoes

• Dominoes – have a play….

• Have you got a full set?

• How do you know?

• Can you arrange them in some way to

convince yourself/others that you have/

haven’t got full set?

© University of Cambridge

• Dominoes – have a play….

• Have you got a full set?

• How do you know?

• Can you arrange them in some way to

convince yourself/others that you have/

haven’t got full set?

© University of Cambridge

23.
• What number knowledge/skills did you

use?

• What mathematical processes did you

use?

• What ‘soft skills’ did you use?

© University of Cambridge

use?

• What mathematical processes did you

use?

• What ‘soft skills’ did you use?

© University of Cambridge

24.
Amy has a box containing ordinary

domino pieces but she does not think it is

a complete set. She has 24 dominoes in

her box and there are 125 spots on them

altogether. Which of her domino pieces

are missing?

© University of Cambridge

domino pieces but she does not think it is

a complete set. She has 24 dominoes in

her box and there are 125 spots on them

altogether. Which of her domino pieces

are missing?

© University of Cambridge

25.
• What number knowledge/skills did you

use?

• What mathematical processes did you

use?

• What ‘soft skills’ did you use?

© University of Cambridge

use?

• What mathematical processes did you

use?

• What ‘soft skills’ did you use?

© University of Cambridge

26.
Order of events

• Free play –Montessori ‘work’

• Closed activity: structure of the

apparatus

• Task which uses that knowledge

• Multistep

• With or without apparatus

Ruthven’s

Exploration

Codification

Consolidation

© University of Cambridge

• Free play –Montessori ‘work’

• Closed activity: structure of the

apparatus

• Task which uses that knowledge

• Multistep

• With or without apparatus

Ruthven’s

Exploration

Codification

Consolidation

© University of Cambridge

27.
Dominoes v houses

Sort – have you got them all?

How do you know?

Tasks using that knowledge

Guess the dominoes/ houses

© University of Cambridge

Sort – have you got them all?

How do you know?

Tasks using that knowledge

Guess the dominoes/ houses

© University of Cambridge

28.
Rich tasks….

• combine fluency, problem solving and

mathematical reasoning

• are accessible

• promote success through supporting

thinking at different levels of challenge (low

threshold - high ceiling tasks)

• encourage collaboration and discussion

• use intriguing contexts or intriguing maths

© University of Cambridge

• combine fluency, problem solving and

mathematical reasoning

• are accessible

• promote success through supporting

thinking at different levels of challenge (low

threshold - high ceiling tasks)

• encourage collaboration and discussion

• use intriguing contexts or intriguing maths

© University of Cambridge

29.
• allow for:

• learners to pose their own problems,

• different methods and different responses

• identification of elegant or efficient solutions,

• creativity and imaginative application of

knowledge.

• have the potential for revealing patterns or

lead to generalisations or unexpected

results,

• have the potential to reveal underlying

principles or make connections between

areas of mathematics

(adapted from Jenny Piggott, NRICH)

© University of Cambridge

• learners to pose their own problems,

• different methods and different responses

• identification of elegant or efficient solutions,

• creativity and imaginative application of

knowledge.

• have the potential for revealing patterns or

lead to generalisations or unexpected

results,

• have the potential to reveal underlying

principles or make connections between

areas of mathematics

(adapted from Jenny Piggott, NRICH)

© University of Cambridge

30.
Tasks

• Non-routine

• Accessible

• Challenging

• Curriculum linked

• Rich tasks/LTHC tasks

Implications for your teaching?

© University of Cambridge

• Non-routine

• Accessible

• Challenging

• Curriculum linked

• Rich tasks/LTHC tasks

Implications for your teaching?

© University of Cambridge

31.
Valuing mathematical

thinking

• Process as well as end product

• Talk as well as recording

• Questioning as well as answering

• …………

© University of Cambridge

thinking

• Process as well as end product

• Talk as well as recording

• Questioning as well as answering

• …………

© University of Cambridge

32.
Purposeful activity

Give the pupils something to do,

not something to learn;

and if the doing is of such a nature

as to demand thinking;

learning naturally results.

John Dewey

© University of Cambridge

Give the pupils something to do,

not something to learn;

and if the doing is of such a nature

as to demand thinking;

learning naturally results.

John Dewey

© University of Cambridge

33.
Session 4

Games are more than fillers

© University of Cambridge

Games are more than fillers

© University of Cambridge

34.
Dotty

4 6

Green wins!

© University of Cambridge

4 6

Green wins!

© University of Cambridge

35.
• What is the mathematical knowledge that

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

36.
Board Block

© University of Cambridge

© University of Cambridge

37.
• What is the mathematical knowledge that

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

38.
Four Go

© University of Cambridge

© University of Cambridge

39.
• What is the mathematical knowledge that

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

40.
Nice and nasty

© University of Cambridge

© University of Cambridge

41.
• What is the mathematical knowledge that

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

is needed to play?

• Who would this game be for?

• What is the value added of playing the

game?

• Could you adapt it to use it in your

classroom?

• Contribute to F, R, PS?

© University of Cambridge

42.
© University of Cambridge

43.
“If I ran a school, I’d give all the average

grades to the ones who gave me all the right

answers, for being good parrots. I’d give the

top grades to those who made lots of

mistakes and told me about them and then

told me what they had learned from them.”

Buckminster Fuller, Inventor

© University of Cambridge

grades to the ones who gave me all the right

answers, for being good parrots. I’d give the

top grades to those who made lots of

mistakes and told me about them and then

told me what they had learned from them.”

Buckminster Fuller, Inventor

© University of Cambridge

44.
• What were these children’s views of

maths?

• Would you get the same answers?

© University of Cambridge

maths?

• Would you get the same answers?

© University of Cambridge

45.
Session 3

Maths Working Group

© University of Cambridge

Maths Working Group

© University of Cambridge

46.
Purpose of study

Mathematics is a creative and highly inter-

connected discipline that has been developed over

centuries, providing the solution to some of

history’s most intriguing problems. It is essential to

everyday life, critical to science, technology and

engineering, and necessary for financial literacy

and most forms of employment. A high-quality

mathematics education therefore provides a

foundation for understanding the world, the ability

to reason mathematically, an appreciation of the

beauty and power of mathematics, and a sense of

enjoyment and curiosity about the subject.

© University of Cambridge

Mathematics is a creative and highly inter-

connected discipline that has been developed over

centuries, providing the solution to some of

history’s most intriguing problems. It is essential to

everyday life, critical to science, technology and

engineering, and necessary for financial literacy

and most forms of employment. A high-quality

mathematics education therefore provides a

foundation for understanding the world, the ability

to reason mathematically, an appreciation of the

beauty and power of mathematics, and a sense of

enjoyment and curiosity about the subject.

© University of Cambridge

47.
Purpose of study

Mathematics is a creative and highly inter-

connected discipline that has been developed over

centuries, providing the solution to some of

history’s most intriguing problems. It is essential to

everyday life, critical to science, technology and

engineering, and necessary for financial literacy

and most forms of employment. A high-quality

mathematics education therefore provides a

foundation for understanding the world, the ability

to reason mathematically, an appreciation of the

beauty and power of mathematics, and a sense of

enjoyment and curiosity about the subject.

© University of Cambridge

Mathematics is a creative and highly inter-

connected discipline that has been developed over

centuries, providing the solution to some of

history’s most intriguing problems. It is essential to

everyday life, critical to science, technology and

engineering, and necessary for financial literacy

and most forms of employment. A high-quality

mathematics education therefore provides a

foundation for understanding the world, the ability

to reason mathematically, an appreciation of the

beauty and power of mathematics, and a sense of

enjoyment and curiosity about the subject.

© University of Cambridge

48.
• interconnected subject in which pupils need

to be able to move fluently between

representations of mathematical ideas.

• make rich connections across mathematical

ideas to develop fluency, mathematical

reasoning and competence in solving

increasingly sophisticated problems

• apply their mathematical knowledge to

science and other subjects.

© University of Cambridge

to be able to move fluently between

representations of mathematical ideas.

• make rich connections across mathematical

ideas to develop fluency, mathematical

reasoning and competence in solving

increasingly sophisticated problems

• apply their mathematical knowledge to

science and other subjects.

© University of Cambridge

49.
• interconnected subject in which pupils need

to be able to move fluently between

representations of mathematical ideas.

• make rich connections across mathematical

ideas to develop fluency, mathematical

reasoning and competence in solving

increasingly sophisticated problems

• apply their mathematical knowledge to

science and other subjects.

© University of Cambridge

to be able to move fluently between

representations of mathematical ideas.

• make rich connections across mathematical

ideas to develop fluency, mathematical

reasoning and competence in solving

increasingly sophisticated problems

• apply their mathematical knowledge to

science and other subjects.

© University of Cambridge

50.
The new National Curriculum

What’s important to teachers?

© University of Cambridge

What’s important to teachers?

© University of Cambridge

51.
Aims

• All equally important

• First two feed into third

© University of Cambridge

• All equally important

• First two feed into third

© University of Cambridge

52.
Big ideas

• Fluency

• Reasoning

• Problem solving

• Arithmetic/calculation (fractions)

• Multiplicative/proportional reasoning

• Pre-algebra/algebra

• Connections within and without

• No probability at KS1/2

• Reduced data handling at 1/2/3

© University of Cambridge

• Fluency

• Reasoning

• Problem solving

• Arithmetic/calculation (fractions)

• Multiplicative/proportional reasoning

• Pre-algebra/algebra

• Connections within and without

• No probability at KS1/2

• Reduced data handling at 1/2/3

© University of Cambridge

53.
Year 6

Pupils should be taught to: • Pupils should be introduced to

•use simple formulae the use of symbols and letters to

•generate and describe represent variables and

linear number sequences unknowns in mathematical

situations that they already

•express missing number understand, such as:

problems algebraically • missing numbers, lengths,

•find pairs of numbers that coordinates and angles,

satisfy an equation with two • formulae in mathematics and

unknowns science

•enumerate all possibilities of • equivalent expressions (for

combinations of two example, a + b = b + a)

variables. • generalisations of number

patterns

• number puzzles (for example,

what two numbers can add up

to). © University of Cambridge

Pupils should be taught to: • Pupils should be introduced to

•use simple formulae the use of symbols and letters to

•generate and describe represent variables and

linear number sequences unknowns in mathematical

situations that they already

•express missing number understand, such as:

problems algebraically • missing numbers, lengths,

•find pairs of numbers that coordinates and angles,

satisfy an equation with two • formulae in mathematics and

unknowns science

•enumerate all possibilities of • equivalent expressions (for

combinations of two example, a + b = b + a)

variables. • generalisations of number

patterns

• number puzzles (for example,

what two numbers can add up

to). © University of Cambridge

54.
Year 6

Pupils should be taught to: • Pupils should be introduced to

•use simple formulae the use of symbols and letters to

•generate and describe represent variables and

linear number sequences unknowns in mathematical

situations that they already

•express missing number

understand, such as:

problems algebraically • missing numbers, lengths,

•find pairs of numbers that coordinates and angles,

satisfy an equation with two • formulae in mathematics and

unknowns science

•enumerate all possibilities of • equivalent expressions (for

combinations of two example, a + b = b + a)

variables. • generalisations of number

patterns

• number puzzles (for example,

what two numbers can add up

to). © University of Cambridge

Pupils should be taught to: • Pupils should be introduced to

•use simple formulae the use of symbols and letters to

•generate and describe represent variables and

linear number sequences unknowns in mathematical

situations that they already

•express missing number

understand, such as:

problems algebraically • missing numbers, lengths,

•find pairs of numbers that coordinates and angles,

satisfy an equation with two • formulae in mathematics and

unknowns science

•enumerate all possibilities of • equivalent expressions (for

combinations of two example, a + b = b + a)

variables. • generalisations of number

patterns

• number puzzles (for example,

what two numbers can add up

to). © University of Cambridge

55.
© University of Cambridge

56.
10 + 10 + 8 + 8

6+6+4+4

25 + 25 + 23 + 23

s + s + (s-2) +( s-2)

= 4s - 4

© University of Cambridge

6+6+4+4

25 + 25 + 23 + 23

s + s + (s-2) +( s-2)

= 4s - 4

© University of Cambridge

57.
10 + 9 + 8 + 9

6+5+4+5

25 + 24 + 23 + 24

s + s-1 + (s-2) +( s-1)

= 4s- 4

© University of Cambridge

6+5+4+5

25 + 24 + 23 + 24

s + s-1 + (s-2) +( s-1)

= 4s- 4

© University of Cambridge

58.
9 + 9 + 9+ 9

5+5+5+5

24 + 24 + 24 + 24

(s-1) + (s-1) + (s-1) +(s-1)

= 4s- 4

© University of Cambridge

5+5+5+5

24 + 24 + 24 + 24

(s-1) + (s-1) + (s-1) +(s-1)

= 4s- 4

© University of Cambridge

59.
10 + 10 + 10 + 10 – 4

6+6+6+6-4

25 + 25 + 25 + 25 - 4

= 4s- 4

© University of Cambridge

6+6+6+6-4

25 + 25 + 25 + 25 - 4

= 4s- 4

© University of Cambridge

60.
s + s + (s-2) +( s-2)

= 4s - 4

s + s-1 + (s-2) +( s-1)

= 4s- 4

(s-1) + (s-1) +( s-1) + (s-1)

= 4s- 4

= 4s- 4

© University of Cambridge

= 4s - 4

s + s-1 + (s-2) +( s-1)

= 4s- 4

(s-1) + (s-1) +( s-1) + (s-1)

= 4s- 4

= 4s- 4

© University of Cambridge

61.
102 - 82

62 - 4 2

182 - 162

s2 - (s-2)2

s2 - (s-2)2 = s2 - (s2 - 4s +4)

= s2 - s2 +4s – 4

= 4s - 4

© University of Cambridge

62 - 4 2

182 - 162

s2 - (s-2)2

s2 - (s-2)2 = s2 - (s2 - 4s +4)

= s2 - s2 +4s – 4

= 4s - 4

© University of Cambridge

62.
The expectation is that the majority of pupils will move

through the programmes of study at broadly the same

pace. However, decisions about when to progress should

always be based on the security of pupils’ understanding

and their readiness to progress to the next stage. Pupils

who grasp concepts rapidly should be challenged through

being offered rich and sophisticated problems before any

acceleration through new content. Those who are not

sufficiently fluent with earlier material should consolidate

their understanding, including through additional practice,

before moving on.

Opportunities?

© University of Cambridge

through the programmes of study at broadly the same

pace. However, decisions about when to progress should

always be based on the security of pupils’ understanding

and their readiness to progress to the next stage. Pupils

who grasp concepts rapidly should be challenged through

being offered rich and sophisticated problems before any

acceleration through new content. Those who are not

sufficiently fluent with earlier material should consolidate

their understanding, including through additional practice,

before moving on.

Opportunities?

© University of Cambridge

63.
The programmes of study for mathematics are set

out year-by-year for Key Stages 1 and 2. Schools

are, however, only required to teach the relevant

programme of study by the end of the key stage.

Within each key stage, schools therefore have the

flexibility to introduce content earlier or later than

set out in the programme of study.

Opportunity?

© University of Cambridge

out year-by-year for Key Stages 1 and 2. Schools

are, however, only required to teach the relevant

programme of study by the end of the key stage.

Within each key stage, schools therefore have the

flexibility to introduce content earlier or later than

set out in the programme of study.

Opportunity?

© University of Cambridge

64.
IWADWADWAGWAG

If we always do what we’ve always done

we’ll always get what we always got…..

© University of Cambridge

If we always do what we’ve always done

we’ll always get what we always got…..

© University of Cambridge

65.
Session 3

National Collaborative Projects

a.Mastery pedagogy for primary mathematics 1 – China-

England research and innovation project

b.Mastery pedagogy for primary mathematics 2 – Use of

high quality textbooks (linked to Singapore) to support

teacher professional development and deep conceptual

and procedural knowledge for pupils

© University of Cambridge

National Collaborative Projects

a.Mastery pedagogy for primary mathematics 1 – China-

England research and innovation project

b.Mastery pedagogy for primary mathematics 2 – Use of

high quality textbooks (linked to Singapore) to support

teacher professional development and deep conceptual

and procedural knowledge for pupils

© University of Cambridge

66.
1. Increasing supply of specialist teachers of mathematics

(including primary, secondary convertors, Post-16) (SO1a)

2. Developing specialist subject knowledge of teachers of

mathematics (all phases and including particular areas)

3. Developing pedagogical knowledge of teachers of

mathematics (especially understanding of mastery

pedagogy and Shanghai & Singapore pedagogy) (SO1c)

4. Improving quality of mathematics teaching practice

(including the move from good to outstanding) (SO1d)

5. Supporting teachers to address new curriculum and

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(including primary, secondary convertors, Post-16) (SO1a)

2. Developing specialist subject knowledge of teachers of

mathematics (all phases and including particular areas)

3. Developing pedagogical knowledge of teachers of

mathematics (especially understanding of mastery

pedagogy and Shanghai & Singapore pedagogy) (SO1c)

4. Improving quality of mathematics teaching practice

(including the move from good to outstanding) (SO1d)

5. Supporting teachers to address new curriculum and

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67.
6. Improving quality of curriculum resources and activities (especially

to support mastery teaching) (SO3b)

8. Improving supply and developing specialist leadership knowledge

of mathematics subject leaders (SO2a/b)

9. Improving quality of and access to mathematics enrichment

experiences (SO3c)

10. Increased progress and achievement in primary and secondary

(including sustained progress through transition phases) (PO1a/b)

11. Reducing the gap in achievement between disadvantaged pupils

and others (PO4c)

14. Developing confidence (can-do attitude) and resilience in learning

mathematics (PO3a)

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to support mastery teaching) (SO3b)

8. Improving supply and developing specialist leadership knowledge

of mathematics subject leaders (SO2a/b)

9. Improving quality of and access to mathematics enrichment

experiences (SO3c)

10. Increased progress and achievement in primary and secondary

(including sustained progress through transition phases) (PO1a/b)

11. Reducing the gap in achievement between disadvantaged pupils

and others (PO4c)

14. Developing confidence (can-do attitude) and resilience in learning

mathematics (PO3a)

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68.
Key Findings

Successful schools

• Hands on crucial in FS and KS1

• ‘Traditional’ methods need to be underpinned by place

value, mental methods fluency, facts

• Inverse operations important

• Confidence fluency and versatility nurtured through

problem solving and investigations

• Clear coherent calculation policy

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Successful schools

• Hands on crucial in FS and KS1

• ‘Traditional’ methods need to be underpinned by place

value, mental methods fluency, facts

• Inverse operations important

• Confidence fluency and versatility nurtured through

problem solving and investigations

• Clear coherent calculation policy

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69.
Key findings

Made to Measure

• Inconsistency within schools

• Need to increase emphasis on problem solving

• Teachers to be enabled to choose approaches that foster

deeper understanding

• Checking understanding and reacting immediately

• Attention on most and least able

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Made to Measure

• Inconsistency within schools

• Need to increase emphasis on problem solving

• Teachers to be enabled to choose approaches that foster

deeper understanding

• Checking understanding and reacting immediately

• Attention on most and least able

© University of Cambridge