Making Effective Use of the Renewed Framework for Mathematics Day 3

1. Making Effective Use of the Renewed Framework for MathematicsDay 3 123

2. Aims • Supporting colleagues in developing a shared view of what is successful learning in mathematics • Supporting colleagues in developing an approach to planning that will enable all children to learn successfully • Supporting colleagues in enabling underperforming children to become successful learners

3. SESSIONS ‘Quality first’ learning opportunities Supporting underperforming pupils Leading improvement and next steps 10.30-10.45 Coffee 12.15-1.00 Lunch 2.30-2.45 Tea Programme

4. ‘’Quality first’ learning opportunities Wave 3 Additional highly personalised interventions Wave 2 Additional interventions to enable children to work at age related expectations or above Wave 1 Inclusive quality first teaching for all 3.11

5. Phases of planning a unit in mathematics Practise and consolidate

6. Planning a teaching and learning cycle • Is there a context which will facilitate learning and develop the connections between the objectives? • What prior learning will need to be activated? • What is the new teaching? • How will the children practise and consolidate this new learning? • How will the learning be applied, extended and secured by all? • How will the learning be reviewed by the children and the teacher?

7. How did the different approach to planning impact on the learning in your classroom?

8. How did the teaching and learning strategies differ at different phases of the learning cycle?

9. Successful teaching…Successful learning Two commonly accepted ways of understanding teaching and learning are: • transmission teaching/acquisition learning • participation teaching/constructive learning

10. Transmission teaching, acquisition learning Some facts are arbitrary: • the units we use to measure length are centimetres, metres and kilometres Some facts are useful to learn by rote: • 3 x 7 = 21, 100 cm = 1m Some skills need clear demonstrations: • how to use a protractor

11. Jar A contains 25 marbles Jar B contains 75 marbles Each jar’s contents is poured into a third jar How many marbles are in the jar? Jar A contains 1 litre of water at 25oC Jar B contains 1 litre of water at 75oC Each jar’s contents is poured into a third jar What is the temperature of the water in the jar?

12. Participation teaching, constructive learning New knowledge needs to connect with established knowledge: • I can choose the appropriate unit to measure Known facts can be used to derive unknown facts: • 3 x 7 = 21, 6 x 0.7 = 4.2, doubling and halving can be used to derive multiplication facts – derive 6 x 7 = 42 from 3 x 7 = 21 Knowledge can be applied in a variety of contexts: • Fractions can be used to solve problems involving shape, involving numbers and can be used to order numbers

13. Quality first teaching and learning • What does it look like? • What are the key elements? • How does it fulfil the needs of all children? • How do we know? • How can the Renewed Framework support this?

15. Monitor-Evaluate-Action plan

16. The Data Handling Cycle

17. Task: “Practice improves estimation skills” True or false? What’s the evidence?

18. Specify the Problem Brainstorm What? How? Who? Practice improves estimation skills Evaluation Was your hypothesis right? Improvements - & how? Does it raise another problem? Plan Collect Data Who? How? When? Why? Where will the data come from? What skills will you use – Why? Interpret and discuss data Summary of all your results Process and Represent the Data What? How? Why?

19. Phases of planning a unit in mathematics Practise and consolidate

20. ‘Eight out of ten cats prefer Whiskas’ How do they know?!

21. Personalising learning and teaching through: • matching high quality teaching to the different and developing abilities of pupils • regular monitoring of progress, and rapid response at the point at which pupils begin to fall behind • dialogue between teachers and pupils, encouraging them to explore their ideas through talk … and to reflect on what they have learnt 2020 Vision - Report of the Teaching and Learning in 2020 Review Group

22. Personalising learning and teaching through: • collaborative relationships which encourage and enable all pupils to participate • judicious use of whole class teaching, as well as paired and group work • using more open ended tasks with pupils 2020 Vision - Report of the Teaching and Learning in 2020 Review Group

23. Personalised learning is … …learner-centred and knowledge-centred … • learners are active and curious • create their own hypotheses and ask their own questions • coach one another • set goals for themselves • experiment with ideas for taking risks, knowing that mistakes and being ’stuck’ are part of learning

24. Supporting Underperforming Pupils 123

25. How were the needs of all learners actively addressed in the lesson?

27. Successful learning… successful teaching? Discussion groups: • What are the characteristics of children who are successful at mathematics? • What are the characteristics of children who struggle to learn mathematics?

28. Children who are successful at learning in mathematics We need to plan learning that may: • add breadth (for example enrichment through a broader range of content, tasks and resources). • increase depth (for example extension through complexity). • accelerate the pace of learning by tracking forward to future objectives within or across key stage

29. Children who struggle to learn mathematics We need to plan learning that will: • be aligned to age appropriate objectives • use a range of learning and teaching styles • accommodate children’s individual needs and differences • include challenge and high expectations for all

30. Do your underperforming children have similar characteristics to the children who struggle or do they have different characteristics?

31. Supporting children with difficulties How can we understand and begin to identify where children are having difficulties? One starting point is to categorise types of misunderstanding to help identify possible ways of addressing them: • Language • Conceptual • Procedural

32. Language Our system is irregular until 60! • Eleven “ “ onety-one • Twelve “ “ onety-two… • Sixteen “ “ onety-six… • Twenty “ “ twoty • Thirty “ “ threety • Fourty sounds OK but is incorrectly spelt • Fifty should be fivety

33. The variety of mathematical language 7,8 and 15 • 7 add 8 is 15 • 15 take away 8 is 7 • 8 added to 7 gives a total of 15 • 8 is 7 less than 15 • 15 is 8 morethan 7 • 8 more than 7 is 15 • The difference between 7 & 15 is 8 • 15 take away 8 leaves 7 • 8 plus 7 is 15 • 15 minus 7 is 8 • 15 is 7 added to 8 • 8 less than 15 is 7 • 7 and 8 make 15 • 15 subtract 8 is • When I count on 8 from 7 I get 15 • If you take 8 from 15, 7 is left • I count back 7 from 15 to get to 8

34. Conceptual Why might children: • not identify the following shapes as rectangles • calculate 24% of 525 by finding one twenty-fourth of 525 • put these decimal numbers in this order: 73.5, 73.32, 73.64

35. Procedural • A shepherd has 14 sheep and 9 goats altogether. How old is the shepherd? • If Henry the 8th had 6 wives, how many wives did Henry the 4th have? • To multiply by 10 you add a 0.

36. Supporting underperforming children • mathematical difficulties are highly susceptible to intervention • intervention should be as early as possible, partly because mathematical difficulties can affect performance in other areas of the curriculum, and partly to prevent the development of negative attitudes to and anxiety about mathematics

37. Supporting underperforming children • interventions should focus on the particular components of mathematics with which the child has difficulty rather than follow a set ‘programme’ • interventions using peer support, ICT or TA support work best when they are managed by a skilled teacher who orchestrates and retains overall responsibility for the child’s learning Dowker, A, (2004) What works for children with mathematical difficulties. London: DfES Research Report 554.

38. An enquiring classroom creates a culture of learning when both adults and children’s questions are valued and genuine dialogue is promoted From Excellence and enjoyment: learning and teachingin the primary years (DfES 0518-2004G)

39. Year 4 Block A unit 1 Objective • Partition, round and order four-digit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and > (e.g. –3 > –5,–1 < +1) • Assessment for learning • What is the biggest whole number that you can makewith these four digits: 3, 0, 6, 5? What is the smallest whole number that you can make with the digits? • Look at this number sentence:  +  = 1249. What could the missing numbers be?

40. Year 4 Pair - Share • Pairs Decide : – what is the biggest whole number you can make with the digits? –what is the smallest whole number you can make with the digits?

41. Year 4 Pair - Share • Share - share with the other pair why you think you are correct

42. Snowballing Pair Pair Group/class

43. Ground rules for dialogue • Making eye contact with the speaker • Everyone taking a turn • One person speaking at a time • Speaking in a clear voice • Using vocabulary • Being clear about what you mean • Responding to the other speaker • Making a longer contribution than just one or two words • Using facial expressions and gestures

44. Talk prompts It can’t be that because I think Why do you think that?

45. Talk Cards Select one prompt How might you use these with pairs or groups? Have them on view as prompts? Choose one each?

46. Talk prompts • What is the largest odd number you can make? • What is the smallest odd number you can create?

47. Roles in the group • Leader – organises the group, encourages all to participate • Scribe – notes main points of discussion • Reporter- works with the scribe to organise their ideas, summing up etc • Mentor – helps group members carry out the task, explaining and organising • Observer – makes notes on how the group works and shares it with group

48. Task • Can your group create instructions to work out the largest even number from your four digits • Can you write it so that it works for any four digits • Can another group follow your guidance?

49. Personalising learning and teaching through: • collaborative relationships which encourage and enable all pupils to participate • judicious use of whole class teaching, as well as paired and group work • using more open ended tasks with pupils 2020 Vision - Report of the Teaching and Learning in 2020 Review Group

50. Leading improvement and next steps 123