WHY?

Because…

What if…?

How might…?

I think that…

WHY?

Mathematically Speaking

WHY?

Because…

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How might…?

I think that…

WHY?

Workshop Foci

• APP S & L

• Brookfield lesson study

• Pedagogy of talk in maths

• Activities to enhance maths talk

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

S and L Guidelines

• Speaking and listening skills inherent in Using and Applying; Problem solving, Reasoning and Communicating

• Using and Applying – responses from P levels onwards, EYFS; NC PoS

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

What is Using & Applying Mathematics?

• Solving Problems• Representing - analyse, do, record,

check, confirm• Enquiring - plan, decide, organise,

interpret, reason, justify• Reasoning - create, deduce, apply,

explore, predict, hypothesise, test• Communicating - explain methods

and solutions, choices, decisions, reasoning

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

KS1 PoS

Communicating• Use the correct language, symbols and vocabulary associated with

number and data• Communicate in spoken, pictorial and written form, at first using

informal language and recording, then mathematical language and symbols

Reasoning• present results in an organised way• understand a general statement and investigate whether particular

cases match it• Explain their methods and reasoning when solving problems

involving number and data

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

KS2 Pos

Communicating• Organise work and refine ways of recording• Use notion diagrams and symbols correctly within a given problem• present and interpret solutions in the context of the problem• communicate mathematically, including the use of precise

mathematical language

Reasoning• understand and investigate general statements [for example, 'there

are four prime numbers less than 10', 'wrist size is half neck size']• search for pattern in their results; develop logical thinking and

explain their reasoning.

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

NC: Skills

These are the skills that children need to learn to make progress:

a. generate and explore ideas and strategies, pursue lines of mathematical enquiry and apply logic and reasoning to mathematical problems

b. make and test generalisations, identify patterns and recognise equivalences and relationships

c. develop, select and apply a range of mental, written and ICT based methods and models to estimate, calculate, classify, quantify, order and compare

d. communicate ideas and justify arguments using mathematical symbols, diagrams, images and language

e. interpret findings, evaluate methods and check outcomes

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

Speaking and Listening, Using and Applying, and APP

WHY?

Because…

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How might…?

I think that…

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Lesson Study Using APP S & L

What we did• Met as a trio to decide objectives, class,

teacher and focused teaching technique• Chose activities and planned lesson• Taught lesson, with two observers (3

children chosen)• Pupil conferencing, reflection, evaluation

WHY?

Because…

What if…?

How might…?

I think that…

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The lesson

• Based on contextualised problems

• Emphasis on shared ideas using a prop for turn taking

• Mini plenaries for discussion, reflection and progression (collating strategies)

• Class discussion regarding supportive sharing of strategies through turn taking

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

The Pupil Conferencing

• Less able Mathematician – felt empowered by the opportunity to be heard

• All children felt more like a team – “…from a liquid to a solid …now definitely a rock”

• Valued the supportive nature of sharing strategies

WHY?

Because…

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How might…?

I think that…

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Reflections

• Sharing and building on others’ strategies as a skill, would need explicit teaching

• Using a prop for turn taking: a powerful tool• Support the empowerment of LA in Maths by giving

enough time for thoughts, and space to share ideas• Further enhanced by having more time

WHY?

Because…

What if…?

How might…?

I think that…

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Talk for Learning

Developing Meaningful Maths Dialogue

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

Pick a domino

WHY?

Because…

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How might…?

I think that…

WHY?

Domino Trick

1. Take a domino tile

2. Pick a side of the tile,multiply number by 2

3. Add 3

4. Multiply the result by 5

5. Add the other side to the result

6. Ask for the result

7. Subtract (3 x 5) from the result

8. You have now both numbers in the tile.

WHY?

Because…

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How might…?

I think that…

WHY?

Williams Report 2008

“Talking mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics, novel and important though that may be for the young learner. It should extend to high-quality discussion that develops children’s logic, reasoning and deduction skills, and underpins all mathematical learning activity. The ultimate goal is to develop mathematical understanding – comprehension of mathematical ideas and applications.”

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

Effective features of talk (EPPI)

• Going beyond ‘Initiate, Response, Feedback’

• Focusing attention on mathematics rather than ‘getting the answer right’

• Working collaboratively with pupils• Transformative listening• Scaffolding• Enhancing pupils’ self-knowledge about

using dialogue as a learning experience• Encouraging high quality pupil dialogue• Inclusive teaching

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

More likely than probable

Select one of the statementsThe statement you have chosen may be

either correct or incorrect. Discuss it between you: you have to decide whether it is right or wrong.

If you think it is correct then you should explain how you know.

If you think it is incorrect then you should explain what is wrong with it and give an example to show it is wrong.

WHY?

Because…

What if…?

How might…?

I think that…

WHY?

Odd or even?

Take a numberSquare it

Subtract the original numberWhat do you find out about the answer?

Why?Refine your explanation until it is as clear and

concise as you can make it.

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Because…

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How might…?

I think that…

WHY?

Discussion

How will you develop the characteristics of effective dialogue in your school?

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Because…

What if…?

How might…?

I think that…

WHY?

Key MessagesEffective dialogue:

• Provides regular opportunities for all children and adults to talk about mathematics in order

– to challenge mathematical ideas – to refine thinking– to confirm understanding

• Involves listening and responding to one another’s ideas to build on and secure learning

• Develops and shares models of how mathematical language can be used accurately

• Links to and between practical, written and all other forms of mathematical communication

• Is an integral part of effective mathematics learning