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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

In the last meeting we discussed:

Mental mathematics

Have you explored this in

your school?


Subject leader

Subject Leader

Summer 2009


Agenda
Agenda

  • Speaking and Listening in Mathematics

  • The Learning Environment


Speaking and listening

SpeakingandListening


Aims for session
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
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
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
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


Assessment opportunities
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
Three characteristics of talk in more depth

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

  • Encouraging high quality pupil dialogue

  • Scaffolding


1 going beyond irf
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
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
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
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


Questioning
Questioning

‘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)


Questioning

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
Whole class teaching closed questions and open questions that demand more complex and higher order thinking.

  • 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
Guided group work closed questions and open questions that demand more complex and higher order thinking.

  • 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
Problem solving closed questions and open questions that demand more complex and higher order thinking.


Classroom tips at a glance
Classroom tips at a glance closed questions and open questions that demand more complex and higher order thinking.

  • 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



Observation
Observation closed questions and open questions that demand more complex and higher order thinking.


Key messages for effective dialogue
Key Messages for closed questions and open questions that demand more complex and higher order thinking.effective 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


Task closed questions and open questions that demand more complex and higher order thinking.

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


Itp spreadsheets

ITP / Spreadsheets closed questions and open questions that demand more complex and higher order thinking.


Carroll diagram
Carroll Diagram closed questions and open questions that demand more complex and higher order thinking.


The learning environment

The closed questions and open questions that demand more complex and higher order thinking.Learning Environment


Aims for session1
Aims for session closed questions and open questions that demand more complex and higher order thinking.

  • 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 environment1
The Learning environment closed questions and open questions that demand more complex and higher order thinking.

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

The Children’s Plan


The child’s environment closed questions and open questions that demand more complex and higher order thinking.

Society

Wider Community

Family

Classroom/setting

School

Group



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 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.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
Learning Walk 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.

Is there evidence of Mathematics?


The physical environment has a significant influence on learning
The physical environment has a 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.significant 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
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


Organisation
Organisation pupils’ learning?

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

  • Layout

  • Display

  • Resources

  • Organisation of materials

  • ICT equipment



Learning objectives
Learning objectives pupils’ learning?

  • 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
Curricular targets pupils’ learning?

  • Key Mathematics targets displayed

    • School target

    • Class target

    • Group target

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


Promote key vocabulary
Promote key vocabulary pupils’ learning?

  • 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
Displays / Learning walls pupils’ learning?


Display boards
Display Boards pupils’ learning?

  • 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
Towards an independent classroom pupils’ learning?

  • 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
Working Walls / Learning Walls pupils’ learning?

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 pupils’ learning?

Visual Stimuli

Check lists

Good examples

Prompts

Success Criteria

Displays Working walls Learning walls

Resources easily accessible

Vocabulary

Counters, number lines,100 squares & rulers

Maths mats

Books

Open questions


Working walls
Working walls pupils’ learning?

  • Interactive

  • Open activities

  • Next steps to learning

  • Independent

  • Enriching mathematics



Use windows . . . pupils’ learning?


tables . . . pupils’ learning?


prompt sheets . . . pupils’ learning?


or doors! pupils’ learning?


Here is a number what might the question have been 121
Here is a number what might pupils’ learning?the question have been?121


Here is a chart
Here is a chart pupils’ learning?

What might the title be?

Could you write a question about

this chart for your friends to answer


Here is a calculation. pupils’ learning?

Can you write a

word problem for it?

43 – 17 = 26


The outdoor classroom
The outdoor classroom pupils’ learning?

  • Using the outdoors

  • Enriching the mathematics curriculum by giving it purpose


Positive affirmations
Positive affirmations pupils’ learning?

  • Displayed and referred to regularly

  • Teacher fosters positive attitudes and behaviours

  • Successes are celebrated


Conclusion
Conclusion pupils’ learning?

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


Task pupils’ learning?

  • 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
Happy Holidays pupils’ learning?

Next meeting


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