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

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

  2. Subject Leader Summer 2009

  3. Agenda • Speaking and Listening in Mathematics • The Learning Environment

  4. SpeakingandListening

  5. 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

  6. 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.’

  7. 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

  8. Describe this group of numbers 12, 2, 6, 18, 9, 3, 4, 1, 2

  9. 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

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

  11. Three characteristics of talk in more depth • Going beyond ‘Initiate, Response, Feedback’ (IRF) • Encouraging high quality pupil dialogue • Scaffolding

  12. 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?

  13. 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)

  14. 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?

  15. 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

  16. 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)

  17. 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?

  18. 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?’   

  19. 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

  20. 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.

  21. Problem solving

  22. 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

  23. 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

  24. Observation

  25. 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

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

  27. ITP / Spreadsheets

  28. Carroll Diagram

  29. TheLearning Environment

  30. 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

  31. The Learning environment ‘ Children need the right environment to be able to be able to learn and thrive’ The Children’s Plan

  32. The child’s environment Society Wider Community Family Classroom/setting School Group

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

  34. 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.

  35. 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.

  36. Learning Walk Is there evidence of Mathematics?

  37. The physical environment has asignificant influence on learning. • Clear messages • Value learning • Supportive of independent learning

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

  39. 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

  40. Organisation What elements of your learning environment promote the learning and support all learners in Mathematics? • Layout • Display • Resources • Organisation of materials • ICT equipment

  41. What are the most successful elements? • What would you change and why?

  42. 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

  43. Curricular targets • Key Mathematics targets displayed • School target • Class target • Group target • Visual prompts, questions and resources to support key curricular target focus