1. RNLC ASSESSMENT NETWORK CONFERENCE ‘Principles not Products’ 10 th June 2016 Pete Griffin, Assistant Director (Maths Hubs)

2. The (new) curriculum needs a new form of assessment The research for the review of the National Curriculum showed that it should focus on “fewer things in greater depth”, and secure learning which persists, rather than relentless, “over-rapid progression” Depth and sustainability is what assessment should focus on (Living in a Levels-Free World, by Tim Oates published by DfE)

3. What do we mean by ‘mastery’? The essential idea behind ‘mastery’ is that all children need a deep understanding of the mathematics they are learning so that future mathematical learning is built on solid foundations which do not need to be re-taught; From ‘Assessing Mastery’ - introduction

4. Four ways in which the term mastery is being used : 1.A mastery approach; a set of principles and beliefs 2.A mastery curriculum 3.Teaching for mastery; a set of pedagogic practices 4.Achieving mastery of particular topics and areas of mathematics From ‘Assessing Mastery’ - Introduction

5. 3. Teaching for mastery; a set of pedagogic practices that keep the class working together on the same topic, whilst at the same time addressing the need for all pupils to master the curriculum. Challenge is provided through depth rather than acceleration into new content. More time is spent on teaching topics to allow for the development of depth. Carefully crafted lesson design provides a scaffolded, conceptual journey through the mathematics, engaging pupils in reasoning and the development of mathematical thinking. From ‘Assessing Mastery’ - Introduction

6. 4. Achieving mastery of particular topics and areas of mathematics. Mastery is not just being able to memorise key facts and procedures and answer test questions accurately and quickly. It involves knowing ‘why’ as well as knowing ‘that’ and knowing ‘how.’ It means being able to use one’s knowledge appropriately, flexibly and creatively and to apply it in new and unfamiliar situations. From ‘Assessing Mastery’ - Introduction

7. Mastery Mastery means that learning is sufficiently: Embedded Deep Connected Fluent In order for it to be: Sustained Built upon Connected to

8. A pupil really understands a mathematical concept, idea or technique if he or she can: describe it in his or her own words; represent it in a variety of ways (e.g. using concrete materials, pictures and symbols – the CPA approach) explain it to someone else; make up his or her own examples (and non- examples) of it; see connections between it and other facts or ideas; recognise it in new situations and contexts; make use of it in various ways, including in new situations. From ‘Assessing Mastery’ – Introduction. Adapted from a list in ‘How Children Fail’, John Holt, 1964.

9. The aims of the mathematics curriculum The National Curriculum for mathematics aims to ensure all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions All 3 of these aims relate to depth and sustainability – i.e. mastery

10. The aims of the mathematics curriculum The National Curriculum for mathematics aims to ensure all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

11. Fluency Fluency demands more of learners than memorisation of a single procedure or collection of facts. It encompasses a mixture of efficiency, accuracy and flexibility. Quick and efficient recall of facts and procedures is important in order for learners’ to keep track of sub problems, think strategically and solve problems. Fluency also demands the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections and to choose from a whole toolkit of methods, strategies and approaches.

12. What is the area of this triangle? 10 cm 3 cm Area of triangle = half of the base × height Area of triangle = ½ b × h Why?

13. What is the area of this triangle? Area of triangle = half of the (base × height) Area of triangle = ½ (b × h)

14. What is the area of this triangle? 10 cm 3 cm Why?

40. What is the area of this triangle? 10 cm 3 cm Area of triangle = half of the base × perpendicular height Area of triangle = ½ b × h

41. Sally knows all her tables up to 12 x 12 When asked what 13 x 4 is she looks blank. Does she have fluency and understanding? What does it really mean to know your tables?

43. 8 16 24 zero 8one 8two 8sThree 8s 32 40 48 56 64 72 80 Four 8s Five8sSix 8sSeven 8s Eight 8sNine8s Ten 8s 16 24 32 40 48 56 64 72 8 2 16 8 3 24 8 4 32 8 5 40 8 6 48 8 7 56 8 8 64 8 9 72

44. 1 spider has 8 legs. 2 spiders have ( ) legs. 3 spiders have ( ) legs. 4 spiders have ( ) legs. 5 spiders have ( ) legs. 6 spiders have ( ) legs. 7 spiders have ( ) legs. 8 spiders have ( ) legs. 9 spiders have ( ) legs. 16 24 32 40 48 56 64 72

45. 38 24 83 What can you see?

46. 5×8= 40 8×5= 40 (cm) 8 is the length. 5 means lots of the length.

47. There are 5 rows. In each row there are 8 children. How many children altogether? 5×8 = 40 8×5 = 40 What is the answer to the question?

48. An octopus has 8 legs. How many legs do 6 have? 8×6 = 48 6×8 = 48 What is the answer to the question?

49. 4 × 4 = 5 × 4 = 9 × 4 = 4 × 8 = 5 × 8= 9 × 8 = 162036 3240 72

50. 3 x 8 + 7 = 8 x 7 + 5 = 8 x 8 – 3 = 16 = ( ) x 8 24 = ( ) x 8 72 = 8 x ( ) 5 x 8 = 6 x 8 = 0 x 8 = Challenge: Write your own multiplication sentences using the symbols =,

51. 8 x 7 + 5 = 56 + 5 4 1 60 + 1 = 61 3 x 8 + 7 = 24 + 7 6 1 30 + 1 = 31 Whisper the rule to yourself.

53. Intelligent Practice

54. The Year 1 Class January 2016: The children are all working only with numbers to 10 Standards low? Requires improvement?

55. 3 + 2 = 6 + = 8 + 7 = 9 9 = + 7 7 - = 4 6 = - 7

56. The aims of the mathematics curriculum The National Curriculum for mathematics aims to ensure all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

57. Assessment From Fractions Year 3

58. Think: Which line is longer? First: Second: Teach, learn, confuse 1 3 1 2

60. Solve the following  + 17 = 15 + 24 99 –  = 90 – 59 48 × 2.5 =  × 10 3 ÷ 4 = 15 ÷ 

61. Structural Arithmetic From Multiplication and Division Year 2 Take a minute to look at this example from the materials.

62. Structural Arithmetic Examples of practice development

63. The aims of the mathematics curriculum The National Curriculum for mathematics aims to ensure all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non- routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

64. Problem solving: teaching problem solving teaching through problem solving

65. From Geometry Year 3

66. Using the bar model a b c

67. There are 32 children in the class. There are 3 times as many boys as girls. How many girls? G BB B 32 GBB B

68. A computer game was reduced in a sale by 20% and it now costs £48. What was the original price? 20% ? £48

69. http://nrich.maths. org/7233

70. National Curriculum Assessment Materials: https://www.ncetm. org.uk/resources/4 6689 https://www.ncetm. org.uk/resources/4 6689

71. Ongoing assessment as an integral part of teaching The questions, tasks, and activities that are offered in the materials are intended to be a useful vehicle for assessing whether pupils have mastered the mathematics taught. However, the best forms of ongoing, formative assessment arise from well- structured classroom activities involving interaction and dialogue (between teacher and pupils, and between pupils themselves). From ‘Assessing Mastery’ - Introduction

72. Ongoing assessment as an integral part of teaching The tasks and activities need not necessarily be offered to pupils in written form. They may be presented orally, using equipment and/or as part of a group activity. The encouragement of discussion, debate and the sharing of ideas and strategies will often add to both the quality of the assessment information gained and the richness of the teaching and learning situation. From ‘Assessing Mastery’ - Introduction