In the last meeting we discussed mental mathematics have you explored this in your school
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In the last meeting we discussed: Mental mathematics Have you explored this in your school?. Subject Leader. Summer 2009. Agenda. Speaking and Listening in Mathematics The Learning Environment. Speaking and Listening. Aims for session.

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In the last meeting we discussed: Mental mathematics Have you explored this in your school?

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In the last meeting we discussed:

Mental mathematics

Have you explored this in

your school?

Subject Leader

Summer 2009


  • Speaking and Listening in Mathematics

  • The Learning Environment


Aims for session

  • To reflect on the use of talk in the mathematics lesson in the context of the Williams Review

  • To become familiar with recent research into different characteristics of effective talk in the classroom

  • To consider how these characteristics might be developed to enhance children’s mathematical understanding

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 ofmathematical ideas and applications.’

Talk for learning

Children need to:

  • Develop mathematical thinking and reasoning

  • Use mathematical vocabulary

  • Have opportunities to communicate effectively in a collaborative group

  • Be able to be independent and take their own lines of enquiry through group discussions and debates

Describe this group of numbers

12, 2, 6, 18, 9, 3, 4, 1, 2

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


Enhancing pupils’ self-knowledge about using dialogue as a learning experience

Encouraging high quality pupil dialogue

Inclusive teaching

Assessment opportunities

Using planned opportunities for focussed talk, dialogue and discussion teachers develop an understanding of children’s thought processes and ideas.

Three characteristics of talk in more depth

  • Going beyond ‘Initiate, Response, Feedback’ (IRF)

  • Encouraging high quality pupil dialogue

  • Scaffolding

1. Going beyond IRF

  • What can you work out? (From the information given)

  • If you know that, what else do you know?

  • Can you tell me what your thinking is?

  • Shall we test that?

  • Does it work?

  • Do you still think that is …..?

  • Do you agree that ………….?

  • Why is that bit important?

  • So, what must it be?

2. High quality pupil dialogue

‘Teachers can respond in an encouraging manner to pupils’ contributions. There is a need for teachers to be accepting towards pupils’ contributions, to encourage pupils to develop their contributions further and indeed, to allow the direction of a lesson to follow the pupil’s contribution.

Being accepting towards pupils’ contributions may enhance the quality of the discourse, but may also create a tension for the teacher in wanting to direct pupils’ attention towards mathematically acceptable strategies.’ (Kyriacou, C. Issitt, J. 2008)

3. Scaffolding

Tom collects stamps.

One day he counted his stamps.

He said “When I count the stamps by two I have one left over.When I count the stamps by three, I have one left over.When I count by five I have none left over.”

How many stamps has Tom got?

Problem puppets

The puppet can:

  • Read / explain the problem, initially to the children and ask for their help

  • Generate ideas and make silly ‘mistakes’ that the children must correct

  • Model strategies and encourage checking


‘Some teachers go beyond the typical use of IRF which involves asking pupils to answer closed questions and then giving them some evaluative feedback. Some teachers use more open-ended question and follow-up questions, and asking pupils to explain the method they had used.’ (Kyriacou, C. Issitt, J. 2008)


Questions can be classified as those that:

  • Prompt– to direct teaching and inform learning

    e.g. What is the question asking you to do?

  • Probe– to assess learning and inform planning and

    teaching e.g. How can you find the answer?

  • Promote– to extend thinking and redirect learning and teaching e.g. Why? What if…? What next?

Questioning can be improved by ensuring a balance between closed questions and open questions that demand more complex and higher order thinking.

Examples of open-ended questions that genuinely invite children to think include:

  • 'What do you think ...?'

  • 'How do you know ...?'

  • 'Why do you think that ...?'

  • 'Do you have a reason ...?'

  • 'How can you be sure ...?'

  • 'Is this always so ...?'

  • 'Is there another way/reason/idea ...?'

  • 'What if ...? / What if ... does not ...?'

  • 'Where is there another example of this ...?'

  • 'What do you think happens next?’   

Whole class teaching

  • Children spend enough time listening to teachers’ explanation and working to develop their understanding, and teachers move them on when appropriate.

  • Teachers ensure all children participate actively in whole class activity, such as through using mini whiteboards or partner discussions

  • When offering answers or accounts, the teacher expects children to give explanations of their reasoning as well as their methods. Children are challenged if their explanations do not reflect their ability

Guided group work

  • Teacher to be the role model by using the appropriate mathematical language within an explanation to strengthen children’s use of associated language.

  • Children to have the opportunity to talk / discuss in a small group and in pairs. Teacher able to construct the group to extend the use of language.

  • Teacher to expect the use of mathematical vocabulary when the children are discussing in pairs or group and to intervene to support this.

Problem solving

Classroom tips at a glance

  • Model good and bad examples of mathematical talking situations and ask the children to discuss them

  • Allow time for paired discussion prior to group and whole class discussions

  • Take a ‘back seat’ when groups are working or join a group as a non expert

  • Change the grouping of the children

  • Use ‘game type’ rules to help children work together

  • Use one set of materials/resources per group

  • Display key vocabulary and encourage children to refer to when talking within the group


Key Messages foreffective 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


How can you promote the profile of mathematical dialogue within your school?

ITP / Spreadsheets

Carroll Diagram

TheLearning Environment

Aims for session

  • To have an agreed shared understanding of the nature, purpose and importance of an effective learning classroom environment

  • The classroom environment improves the quality of learning and teaching

The Learning environment

‘ Children need the right environment to be able to be able to learn and thrive’

The Children’s Plan

The child’s environment


Wider Community





Do you think ‘good’ mathematics takes place in this classroom?

Where the learning environment is well organised and used flexibly to support a range of different interactive teaching and learning approaches, personalised learning can be considerably enhanced. The school classroom, and the organisation of resources within it, can have a very significant impact on the quality of children’s learning.

Where the learning environment is well organised and used flexibly to support a range of different interactive teaching and learning approaches, personalised learning can be considerably enhanced. The school classroom, and the organisation of resources within it, can have a very significant impact on the quality of children’s learning.

Learning Walk

Is there evidence of Mathematics?

The physical environment has asignificant influence on learning.

  • Clear messages

  • Value learning

  • Supportive of independent learning

Is the learning environment arranged and organised to promote learning and children’s attainment?

How can the classroom be used to effectively support pupils’ learning?

  • Use of visual prompts and interactive resources

  • Promoting key vocabulary

  • Sharing objectives and reviewing learning

  • Supporting curricular targets


What elements of your learning environment promote the learning and support all learners in Mathematics?

  • Layout

  • Display

  • Resources

  • Organisation of materials

  • ICT equipment

  • What are the most successful elements?

  • What would you change and why?

Learning objectives

  • Shared and discussed with children

  • Key questions used throughout the lesson.

  • Prompts available to support children’s talk and thinking

  • Curriculum displays to include statements and questions to highlight key learning points

Curricular targets

  • Key Mathematics targets displayed

    • School target

    • Class target

    • Group target

  • Visual prompts, questions and resources to support key curricular target focus

Promote key vocabulary

  • Key words / technical vocabulary displayed for a variety of curriculum areas

  • Vocabulary referred to and used within teaching

  • Definition of words discussed in lessons

  • Collection of words phrases to support key writing forms

    • Aide memoires

Displays / Learning walls

Display Boards

  • Sharing good practice

  • How do we make display boards more useful, manageable, interactive, accessible, effective?

  • Sharing good practice in your school – learning walks, meeting venues.

  • Why Bother?

Towards an independent classroom

  • How do we support the development of independence?

  • What is an independent learner?

  • How do you encourage independence where children are working in groups or individually?

  • What supports independence in the classroom?

  • How is this supported in the wider community?

Working Walls / Learning Walls

What is a ‘working wall’?

What do we want, need, like to see on a Classroom wall or in a Classroom to really support and help children learn? ... and help us teach?

Interactive challenges

Visual Stimuli

Check lists

Good examples


Success Criteria

Displays Working walls Learning walls

Resources easily accessible


Counters, number lines,100 squares & rulers

Maths mats


Open questions

Working walls

  • Interactive

  • Open activities

  • Next steps to learning

  • Independent

  • Enriching mathematics

But, there is NO space on my walls!

Use windows . . .

tables . . .

prompt sheets . . .

or doors!

Here is a number what mightthe question have been?121

Here is a chart

What might the title be?

Could you write a question about

this chart for your friends to answer

Here is a calculation.

Can you write a

word problem for it?

43 – 17 = 26

The outdoor classroom

  • Using the outdoors

  • Enriching the mathematics curriculum by giving it purpose

Positive affirmations

  • Displayed and referred to regularly

  • Teacher fosters positive attitudes and behaviours

  • Successes are celebrated


To have an engaging, rich, informative and challenging learning environment


  • Identify and implement one change you could make immediately to make the environment more supportive of learning.

  • Consider further changes to be made.

  • Monitor the impact of the changes made by walking round each classroom for one staff meeting.

Happy Holidays

Next meeting

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