1. Better mathematics conference Keynote: understanding ways forward Jane Jones HMI, National lead for Mathematics Autumn 2015

2. Aims of keynote session To be better informed about:  important weaknesses nationally in provision and outcomes in mathematics  key features of good practice and effective ways schools have overcome weaknesses. To sharpen your expertise in identifying:  key weaknesses in mathematics in your school  priorities to drive improvement. Better mathematics conference keynote 2015

3. Keynote content  National figures for attainment and progress in mathematics  Findings from our report, Mathematics: made to measure, and subsequent inspection evidence, highlighting good practice and key concerns nationally  Short activities to help convey main points (for example, about problem solving and conceptual understanding)  Opportunities for you to reflect on implications for your school and to prioritise areas for improvement During the session, please do not hesitate to speak about the activities to supporting HMI. If you have further questions, please note them down on paper and hand to HMI. Better mathematics conference keynote 2015

4. Keynote sections Achievement Teaching Curriculum Leadership and management Planning ways forward in your school The information booklet contains text from the principal slides, in particular the national findings and key concerns. Better mathematics conference keynote 2015

5. Achievement Better mathematics conference keynote 2015

6. Attainment Attainment has risen in secondary schools:  at GCSE grades A*-C; dipped in 2014, rose a bit in 2015  at AS/A level with a huge increase in uptake. In primary schools, attainment has:  risen in the EYFS, but with girls doing better than boys  stalled then recent rise at L2+ at KS1; declining trend at L3+  stalled then recent rise at L4+ at KS2; rise at L5+. Key concern 1.Although attainment is generally rising, pupils are not made to think hard enough for themselves. Pupils of all ages do too little problem solving and reasoning about mathematics. Better mathematics conference keynote 2015

7. A problem for you to solve The animals represent values. Which value could be found first, next and last, and why? Which value cannot be found second and why? Better mathematics conference keynote 2015

8. Problems and puzzles  Problems do not have to be set in real-life contexts.  Providing a range of puzzles and other problems helps pupils to reason strategically to:  find possible ways into solving a problem  sequence an unfolding solution to a problem  use recording to help their thinking about the next step.  It is particularly important that teachers and teaching assistants stress such reasoning, rather than just checking whether the final answer is correct.  All pupils need to learn how to solve problems – not just the high attainers or fastest workers.

9. Early Years Foundation Stage The Early Learning Goals introduced in Sept 2012 represent substantially higher expectations than previously. Problem solving is now an explicit part of each ELG. The percentage of children in 2014 reaching or exceeding the mathematics ELGs (2013 in brackets): As well as a gender gap, a large FSM gap is evident at age 5. Better mathematics conference keynote 2015 EYFS ELGsNumbers (%)SSM (%) National75 (69)79 (75) Girls Boys 78 (72) 71 (65) 83 (79) 76 (72) FSM Non-FSM 60 78 65 82

10. Progress ( 2014 figures; 2011 in brackets ) 89% ( 82% ) of pupils made the expected 2 levels of progress KS1  KS2 but:  74% of L2c reach L4 compared with 93% of L2b; ( 58% cf 86% in 2011 ).  65% ( 62% ) of pupils made the expected 3 levels of progress KS2  KS4 but:  48% of L4c reached grade C; ( 48% in 2011 )  only 26% of low attaining pupils made expected progress; ( 30% in 2011 )  over 40000 pupils who attained L5 at primary school got no better than grade C at GCSE; 3800+ got grade D or lower. Better mathematics conference keynote 2015

11. Gaps in attainment and progress (2014 in black; 2011 figures in brackets)  Overall, 8% of pupils did not reach L2 at age 7, 14% did not reach L4 at age 11, and 33% of the cohort did not reach grade C at GCSE; (cf 10%, 20% and 36% in 2011).  FSM pupils did much worse than their peers on attainment and progress, the gaps generally widening with key stage. The gaps are still there! AttainmentFSM (%)Non-FSM (%) KS1 L2+ L3+ 88 (81) 15 (9) 95 (92) 30 (23) KS2 L4+ L5+ 78 (67) 28 (19) 90 (83) 48 (38) GCSE C A*/A 49 (42) 7 (6) 73 (68) 21 (21) Expected progress FSM (%) Non-FSM (%) KS1-286 (75)91 (84) KS2-448 (45)71 (67) Better mathematics conference keynote 2015

12. Think for a moment … How well do your FSM pupils, and others supported by the Pupil Premium, achieve? To think about back at school … When do they start to lose ground? Better mathematics conference keynote 2015

13. Achievement – key concerns 2.The percentage of pupils meeting expected standard falls at successive key stages. Reaching the expected level in one key stage does not ensure meeting it at the next. This is often due to a focus on meeting thresholds rather than securing essential foundations for the next stage. 3.FSM pupils do far worse than their peers at all key stages, most markedly at Key Stage 4. 4.Low attainers are not helped soon enough to catch up, particularly in the EYFS and Key Stage 1. No improvement in the proportion making expected progress KS2  KS4. 5.High attainers not challenged enough from EYFS onwards. 6.Potential high attainers are being lost to AS/A level – the big uptake has come mainly from pupils with GCSE A*/A. Better mathematics conference keynote 2015

14. Achievement Highlight any of the national key concerns that are also a concern in your school. Better mathematics conference keynote 2015

15. Teaching Better mathematics conference keynote 2015

16. Teaching – Ofsted’s findings The best teaching develops conceptual understanding alongside pupils’ proficient recall of knowledge, their confidence in problem solving and ability to reason mathematically. In highly effective practice, teachers get ‘inside pupils’ heads’. They find out how pupils think by observing pupils closely, listening carefully to what they say, and asking questions to probe and extend their understanding, then adapting teaching accordingly. Too much teaching concentrates on the acquisition of disparate skills that enable pupils to pass tests and examinations but do not equip them for the next stage of education, work and life. Better mathematics conference keynote 2015

17. Two worksheets  The two worksheets in your information booklet were used as the basis of lessons in which the teachers introduced a written method for short division and Pythagoras’ Theorem. Select one of the worksheets. Consider:  how well the teaching approach develops pupils’ conceptual understanding and reasoning  the depth, breadth and levels of challenge of the work set, including the problems. Better mathematics conference keynote 2015

18. Worksheet on short division (1) The teaching approach:  does not appear to link the written method for short division to any earlier work, for example use of mental methods or practical apparatus (eg Dienes blocks, place value counters)  pays no attention to place value in explaining the method (eg ‘25 ÷ 4’ rather than 25 tens ÷ 4)  does not use correct vocabulary (dividend÷divisor=quotient)  does not make use of the inverse operation, multiplication, or estimation to check the reasonableness of their solution. Note that the Y4 programme of study specifies short division that is exact. In the Y5 PoS, short division includes interpreting remainders appropriately for the context. Better mathematics conference keynote 2015

19. Worksheet on short division (2) The depth, breadth and challenge of the work set:  The questions are repetitive and not ‘intelligent practice’.  Q1-Q12 are all calculated in exactly the same way as the worked example; dividing larger numbers does not increase substantially the level of challenge  no calculation leads to a place-holder 0 in the quotient, which often causes difficulty, eg 612 ÷ 3 = 204.  The problems are basically the same as the previous questions. Pupils do not have to think for themselves if they need to divide or what steps to take to solve the problem. (Beware pseudo-realistic contexts.) Better mathematics conference keynote 2015

20. Worksheet on Pythagoras’ Theorem (1) The teaching approach:  fragments learning and understanding of the topic by presenting only part of the work on Pythagoras’ Theorem (finding length of hypotenuse). Subsequent lessons may well deal with other parts in a similarly fragmented way. The danger is that pupils never experience the full breadth and depth of the topic or make links between fragments.  does not appear to give any insight into why the theorem is true for all right-angled triangles. No evidence of reasoning being developed. (Was there any introductory practical activity or discussion about proof to lead into or explain the formula? Beware methods/rules introduced without any justification or building on prior learning.) Better mathematics conference keynote 2015

21. Worksheet on Pythagoras’ Theorem (2) The depth and breadth of work set, including problems:  The questions are repetitive and not ‘intelligent practice’.  Q1-Q10 can all be solved in exactly the same way as the worked example; giving the lengths as decimals does not increase the level of challenge  The triangles are all right-angled and oriented in the same way. (Pupils do not have to think where the right angle is or which side is the hypotenuse.)  The problems are basically the same as the previous questions, with diagrams showing similarly oriented triangles. Pupils do not have to think for themselves if Pythagoras’ Theorem applies or what steps to take to solve the problem. (Beware pseudo-realistic contexts.) Better mathematics conference keynote 2015

22. Teaching for mastery  ‘Intelligent practice’, also known as ‘variation’, is a characteristic of teaching for mastery. Such exercises usually concentrate on the same topic/method/concept but vary in how the questions are presented, often in ways that expose the underlying concept or mathematical structure, and make pupils think deeply for themselves.  A mastery curriculum often involves whole-class teaching, with all pupils being taught the same concepts at the same time. Challenge typically involves greater depth for the more able and support with grasping concepts and methods for less-able pupils.  The points on the next slide are taken from the NCETM’s paper on mastery. Better mathematics conference keynote 2015

23. Characteristics of a mastery curriculum  An expectation that all pupils can and will achieve.  The large majority of pupils progress through the curriculum content at the same pace. Differentiation emphasises deep knowledge and individual support/intervention.  Teaching is underpinned by methodical curriculum design, with units of work that focus in depth on key topics. Lessons and resources are crafted carefully to foster deep conceptual and procedural knowledge.  Practice and consolidation play a central role. Well-designed variation builds fluency and understanding of underlying mathematical concepts in tandem.  Teachers use precise questioning to check conceptual and procedural knowledge. They assess in lessons to identify who requires intervention so that all pupils keep up. Better mathematics conference keynote 2015

24. Teaching examples Problem solving The animal puzzle is an example of problem solving. Problems may, or may not, involve realistic contexts. Discussion about approaches taken help to develop pupils’ reasoning skills. Conceptual understanding The questions on the next slide illustrate the importance of understanding concepts within fractions in:  setting firm foundations for future work in fractions, algebra and proportional reasoning  avoiding developing misconceptions. Better mathematics conference keynote 2015

25. Understanding fractions A question for you: what is a fraction? Questions for pupils: 1.What fraction is shaded? 2a.What does ¼ mean? 2b.Tell me a fraction that is bigger than ¼ 3a.How do you work out one quarter of something? 3b.Can you work it out another way? Better mathematics conference keynote 2015

26. Models, images and practical apparatus All play an important part in supporting pupils’ conceptual understanding and reasoning skills. Can you name these? Flexibility with different representations is an important element of fluency. Better mathematics conference keynote 2015

27. Practical, mental and written methods  The photo shows a pupil using Dienes (base 10) blocks to help her understand the written method of column addition.  The extract shows how mental partitioning with jottings links to the process of column addition. Y3 pupils in this lesson were encouraged to see and discuss the connection. Better mathematics conference keynote 2015  All pupils benefit from using practical equipment, not just the low attainers.

28. Aims of the National Curriculum The three aims, summarised below, are consistent with Ofsted’s findings on effective teaching and learning.  Become fluent in the fundamentals of mathematics, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately  Reason mathematically  Solve problems The next slide gives an example of why conceptual understanding is intrinsic to fluency. Better mathematics conference keynote 2015

29. Fluency using conceptual understanding  Instant recall that 8 x 6 = 48, but also knowledge that 8 x 6 could be found quickly using 10 x 6 – 2 x 6  Understanding that multiplication is commutative, so 8 x 6 = 48 and 6 x 8 = 48 (also 48 = 6 x 8, 48 = 8 x 6)  Understanding that the inverse relationship between multiplication and division leads to equivalent statements, such as 8 = 48 ÷ 6 and 48 ÷ 8 = 6  Knowing division is not commutative, so 8 ≠ 6 ÷ 48  Deriving related facts, for example:  80 x 6 = 480, 6 = 480 ÷ 80 and 0.8 x 0.6 = 0.48  8 x 6 = 48 so 16 x 3 = 48 Better mathematics conference keynote 2015

30. Teaching – findings (Made to measure)  Wide variation between key stages and sets, especially in Key Stage 4 with high sets receiving twice as much good teaching as low sets, where 14% is inadequate.  Weakest teaching in Key Stage 3 (38% good or better and 12% inadequate).  Strongest teaching in the EYFS and Years 5 and 6 with around three quarters good or outstanding. Weaker in Key Stage 1 (particularly Year 1) than in Key Stage 2.  Wide in-school variation causes uneven progress and gaps in achievement, even in good and outstanding schools. Stronger staff are often deployed to key examination or test classes. Leaders appear to accept that other pupils may need to make up ground in the future. Better mathematics conference keynote 2015

31. In-school variation in 151 schools  half had at least one lesson with inadequate teaching  only two had consistently good or better teaching Better mathematics conference keynote 2015

32. Think for a moment … What choices do you make about staff deployment in your school? To think about back at school … How do you pinpoint and tackle specific weaknesses in teaching (including temporary, part-time and non-specialist staff)? Better mathematics conference keynote 2015

33. Changes to the inspection of t eaching  Inspectors have not graded the quality of teaching in individual lessons since Sept 2014.  From Sept 2015, inspectors judge the overall quality of teaching, learning and assessment for the whole school, thereby linking the impact of teaching and assessment with pupils’ learning. They do not grade teaching, learning or assessment in individual lessons or on learning walks.  Inspectors use first-hand evidence gained from observing pupils in lessons, talking to them about their work, scrutinising their work. They assess how well leaders are securing continual improvements in teaching. Direct observations in lessons are supplemented by a range of other evidence to enable inspectors to evaluate the impact teachers and support assistants have on pupils’ progress. Better mathematics conference keynote 2015

34. Teaching – key concerns 7.Wide in-school variation in teaching quality. 8.Conceptual understanding, problem solving and reasoning are underemphasised. a.Too often, teaching approaches focus on ‘how’, without understanding ‘why’ (or considering ‘why not’ and ‘what if’), so that pupils have insecure foundations on which to build future learning. b.Many pupils spend too long working on straightforward questions, with problems located at the ends of exercises or set as extension tasks, so that not all tackle them. 9.Circulating to check and probe each pupil’s understanding throughout the lesson and adapting teaching accordingly are not strong enough. Better mathematics conference keynote 2015

35. Teaching Highlight any of the national key concerns that are also a concern in your school. Better mathematics conference keynote 2015

36. Curriculum Better mathematics conference keynote 2015

37. Curriculum Key differences and inequalities extend beyond the teaching: they are rooted in the curriculum and the ways in which schools promote or hamper progression in the learning of mathematics.  Progression is different from progress.  Progress is the gain that pupils make in terms of knowledge, skills and understanding between one point in time and another.  Progression describes the journey in the development of concepts and skills along a strand within mathematics, drawing upon other strands and feeding into them as needed. Better mathematics conference keynote 2015

38. Transition  Ofsted’s report, Key Stage 3: the wasted years? identifies the particular concern of secondary pupils repeating primary mathematics work. Of Year 7 pupils surveyed, 39% said that in mathematics they were doing the same work as in primary school most or all of the time.  In the context of the new NC, readiness for the next stage is important at all transition points within a school as well as between schools. Two factors that influence the effectiveness of transition are:  the pupil’s mathematical readiness for the next (key) stage  the teacher knowing and building on the pupil’s prior learning in mathematics. Better mathematics conference keynote 2015

39. Think for a moment …  How well do you promote progression in strands of mathematics within your school, and beyond it?  For example, how does your partner primary/secondary develop and/or build on pupils’ knowledge and understanding of division?

40. NC appendix: formal written methods Better mathematics conference keynote 2015

41. Curriculum findings  Pupils’ curricular experiences are inconsistent and depend too much on the teacher they have and the set/class they are in.  Planning for individual lessons, and sequences of lessons, does not often capture the big picture of progression in strands of mathematics.  The degree of emphasis on problem solving, reasoning and conceptual understanding is a key discriminator between good and weaker provision.  Many teachers are not familiar with the aims of the NC. This leads to a focus on teaching the content rather than ensuring that the aims underpin pupils’ learning of all topics. Better mathematics conference keynote 2015

42. Curriculum findings: planning  Primary teachers’ planning is usually based on the yearly programmes of study:  either using objectives taken from lists of content in the PoS or provided by LAs/others  or by working from new text books/schemes that reflect the NC content.  Secondary schemes of work are:  increasingly being updated at KS3 to reflect changes to the content of the new NC  usually based on the new GCSE specifications at KS4, but not always adapted to take account of pupils’ prior learning. Better mathematics conference keynote 2015

43. Reasoning  Reasoning is integral to the development of conceptual understanding and problem-solving skills.  Of the three National Curriculum aims, it is the least well developed currently.  Not all classrooms have a positive ethos that encourages learning from mistakes.  Tasks are not used well enough to develop reasoning.  Talk often focuses on the ‘how’ rather than the ‘why’, ‘why not’, and ‘what if’ in:  teachers’ explanations and questions  pupils’ responses. Better mathematics conference keynote 2015

44. Think for a moment … … what does differentiation in mathematics look like in your school?

45. The National Curriculum: expectations The new NC states: The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on. These have implications for lesson planning and teaching. Better mathematics conference keynote 2015

46. Challenge through depth 1.Work outhttp://www.ukmt.org.ukhttp://www.ukmt.org.uk (999 – 99 + 9) ÷ 9 (adapted from junior challenge 2014) Can you do it another way? 2.P, Q, R, S and T represent single digits in this subtraction. Find their values. 3.What is the ratio of the areas of triangles A and B? A B 7Q2ST −P3R96 22222 Better mathematics conference keynote 2015

47. Problem solving – good practice  Problems are set as part of learning in all topics for all pupils.  Teachers/TAs resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.  Discuss alternative approaches with pupils to help them develop their reasoning and, if relevant, consider why one approach/solution might be more elegant than another.  Problems for high attainers/‘rapid graspers’ involve more demanding reasoning and problem-solving skills and not just harder numbers. Better mathematics conference keynote 2015

48. Curriculum – key concerns 10.Problem solving is not emphasised across all topics. 11.Reasoning is underdeveloped – many teachers need help with this. 12.Teachers are not clear enough about progression, so teaching is fragmented and does not link concepts. 13.Transition from one key stage to the next is, too often, not effective. 14.Pupils’ curricular experiences are inconsistent because: a.teachers lack guidance and support on building conceptual understanding and progression over time b.teachers’ subject knowledge and pedagogic skills vary. They are not enhanced enough through subject-specific professional development and guidance. Better mathematics conference keynote 2015

49. The importance of subject expertise Subject knowledge and pedagogic skills (subject expertise) underpin the development of:  conceptual understanding, knowledge and skills to build fluency and accuracy  problem solving and reasoning  progression and links. Subject knowledge and pedagogic skills are necessary for:  anticipating, spotting and overcoming misconceptions  observing, listening, questioning to assess learning and adapt teaching. Better mathematics conference keynote 2015

50. GCSE – findings  In 2011/12, nearly all schools entered some or all pupils early for GCSE, representing over half the cohort nationally. By 2015, early entry to GCSE has reduced hugely.  Some concern currently about multiple GCSE entry using different awarding bodies.  Pupils, even some of the highest attainers, are not equipped well enough for AS/A-level mathematics. This stems from:  insufficient time given to topics that underpin AS/A level, particularly algebra, geometry and graphs  teaching that focuses on exams and relies on pupils’ recall of disparate facts and methods.  Such teaching also impedes pupils’ study of other AS/A-level subjects and those resitting GCSE post-16. Better mathematics conference keynote 2015

51. GCSE – key concern Key concern 15.Emphases within GCSE teaching on examinations and limited time given to developing depth in important topics, combined with choices about qualification pathways, can limit pupils’ achievement and not prepare pupils well enough for further study of mathematics. Better mathematics conference keynote 2015

52. Curriculum Highlight any of the national key concerns that are also a concern in your school. Better mathematics conference keynote 2015

53. Leadership and management Better mathematics conference keynote 2015

54. Leadership and management findings Stronger management practices:  monitoring of teaching (e.g. learning walk, work scrutiny) particularly in secondary  use of data to track progress and for intervention  use of performance management to drive higher examination results. Key concern 16.Monitoring tends to focus on generic features rather than on pinpointing subject-specific weaknesses or inconsistencies. It is not used strategically to improve teaching, learning or the curriculum. Better mathematics conference keynote 2015

55. Think for a moment … Why does your school do work scrutiny? Better mathematics conference keynote 2015

56. The potential of work scrutiny To check and improve:  teaching approaches, including development of conceptual understanding and reasoning  depth and breadth of work set and tackled, including levels of challenge  problem solving  pupils’ understanding and misconceptions  assessment and its impact on understanding. To look back over time and across year groups at:  progression through concepts for pupils of different abilities  how well pupils have overcome any earlier misconceptions  balance and depth of coverage of the scheme of work, including reasoning and problem solving. Better mathematics conference keynote 2015

57. Jacob’s work With your partner, look at this extract of Jacob’s work, which includes his own marking and the teacher’s comments. It is unclear how the task was set and the objective is vague, but Jacob’s work shows he is finding pairs of factors. How systematically is he doing this? What does his work suggest about the way the teacher has taught this topic? How well does the teacher’s comment help him find factors and improve his reasoning? Better mathematics conference keynote 2015

58. Jacob’s work – teaching approach Jacob is not listing pairs of factors systematically. His lists:  are not in order  include some repeated pairs  omit 1xn or nx1 (a common error) and the pairs 2x22, 2x18 (all of which would fall outside a 12x12 tables square). This suggests the teacher:  did not teach a systematic approach  has not emphasised finding all of the factor pairs. Better mathematics conference keynote 2015

59. Jacob’s work - marking The teacher’s comment did not develop Jacob’s reasoning. It did not encourage him to:  check that all pairs were included  generate his lists more systematically. One systematic approach that includes all pairs starts at 1xn, then considers in turn whether 2, 3, 4 etc. are factors, and recognises when to stop, giving, for example Also, the teacher’s comment was imprecise about whether Jacob had to find factors or factor pairs. 1 x 24 2 x 12 3 x 8 4 x 6 Better mathematics conference keynote 2015

60. Poppy’s work Look at the extract of Poppy’s work. The activity is to list all multiplication and division facts for each set of three numbers. (The first fact in each set was provided by the teacher.) With your partner decide what is good about:  the activity that the teacher has set  the teacher’s marking? Better mathematics conference keynote 2015

61. Poppy’s work – the activity The activity:  uses inverse operations to develop understanding and fluency. It is good practice to introduce multiplication and division together, as inverses  helps develop reasoning and finding all solutions systematically  increases difficulty through starting the second set with a division fact  introduces abstraction, an unknown. Better mathematics conference keynote 2015

62. Poppy’s work – the marking In the first set, Poppy has no errors but omitted two divisions. ‘Are you sure you have found them all?’ encourages Poppy to check her work and to be more systematic. T thinks Poppy should be able to correct her work unaided. In the second set, the teacher recognises Poppy’s deeper misconception that division is commutative. This time, T knows Poppy needs support. T’s skilful initial question prompts Poppy to reflect. Then T provides simpler numbers to help her see that division is not commutative. Better mathematics conference keynote 2015

63. Poppy’s work – after the marking In addition to marking the work, the teacher follows her usual practice. She:  expects Poppy to respond to her comments in the time she has set aside for this the next morning  does not rely only on written dialogue but has also planned small group support for pupils with the same misconception. Better mathematics conference keynote 2015

64. Think for a moment … In your school, how do teachers:  enable pupils to respond to their comments  provide support for overcoming misconceptions? Better mathematics conference keynote 2015

65. Marking and workload It is important that marking in mathematics is manageable for teachers while providing suitable support and challenge for pupils’ learning. By selecting work carefully, teachers can ensure that their marking has the greatest impact – a case sometimes of ‘less is more’! Enabling pupils to mark their own work well can prove a good investment in time. Better mathematics conference keynote 2015

66. Work scrutiny and lesson observation  The top priority to bear in mind when scrutinising work is ‘Are the pupils doing the right work? Do they understand it?’  Thinking back to the two worksheets, the pupils would not be doing ‘the right work’. The teaching approaches did not develop understanding fully, the questions lacked variation, and the problems were superficial. Improving these is more important than improving marking.  The skills you have just used in scrutinising the extract of work are equally applicable when observing lessons.  A key additional element when observing lessons is seeing how well teachers check and deepen each pupil’s understanding. Does the teacher move round the class observing and listening to pupils to check their progress? Better mathematics conference keynote 2015

67. Think for a moment … In your school, is the emphasis for improvement placed on:  the quality of work pupils are given, and their understanding of it  the quality of marking? Better mathematics conference keynote 2015

68. Whole-school policies  Whole-school policies may not work well for mathematics. For example, an assessment policy might expect teachers to:  assign an attainment grade to each piece of marked work  mark in depth one substantial piece of work periodically  refer to the lesson objective when marking  identify ‘next steps’ to help pupils improve their work. Another example is differentiation that does not, in practice, reflect high enough aspirations for each group of pupils.  Best practice ensures that policies can be customised for mathematics in ways that reflect its distinctive nature and thereby promote good teaching and learning. Key concern 17.Some whole-school policies don’t work well for mathematics. Better mathematics conference keynote 2015

69. Think for a moment … How mathematically friendly are your whole-school policies? Better mathematics conference keynote 2015

70. Leadership and management findings  Enabling teachers to work together (e.g. on a calculation policy, guidance on progression in algebra or on teaching approaches) supports consistency and improvement.  However, teachers usually share ideas and good practice informally, rather than record them in guidance, schemes of work or policies. Inexperienced/non-specialist/temporary staff do not receive the specific guidance and support they need. Key concern 18.Because sharing of good practice and provision of guidance are usually informal, only those who are involved can benefit. Not capturing these informal interactions in writing means that teachers who miss out or join the school later cannot benefit from them. Better mathematics conference keynote 2015

71. Use of assessment data – findings  Primary schools have improved their use of assessment information to provide more focused and timely intervention. The best schools:  pick up quickly on misconceptions, difficulties and gaps  intervene speedily to overcome them so that pupils do not fall behind.  In secondary schools, interventions have tended to concentrate on practising topics for GCSE examinations. Schools use assessment data to identify key groups of pupils, particularly at the grade C/D borderline. Better mathematics conference keynote 2015

72. Use of assessment data – key concerns 19.Despite increasingly sophisticated tracking and analyses that identify pupils who are underachieving and topics/gaps where difficulties arise, schools rarely use such assessment information to improve teaching or the curriculum. 20.Intervention, particularly for lower attainers, is not early enough to overcome gaps and build foundations for future learning. Gaps arising from misconceptions, absence, new set/school are not systematically identified or narrowed. 21.Secondary schools rarely use intervention to overcome gaps in pupils’ understanding, particularly in Key Stage 3, often choosing instead to focus on examination preparation. Better mathematics conference keynote 2015

73. Assessment without NC levels  Schools are at different stages in developing their systems for assessment without NC levels.  Some approaches bear a resemblance to former systems of key objectives or expanded level descriptors. Others are linked to particular published schemes/textbook series  However, few systems include assessment of pupils’ skills in problem solving and reasoning. Key concern: 22.Schools are developing their systems for assessment without NC levels. These tend to focus on proficiency with knowledge and methods and do not consider problem solving and reasoning across the mathematics curriculum. Better mathematics conference keynote 2015

74. Leadership and management Highlight any of the national key concerns that are also a concern in your school. Better mathematics conference keynote 2015

75. Planning ways forward in your school Better mathematics conference keynote 2015

76. Integrated planning for improvement Better mathematics conference keynote 2015 Good quality teaching and learning Meaningful curriculum experiences and qualifications Insightful, rigorous leadership and management Good achievement with conceptual understanding

77. Think for a moment … Do the priorities in your mathematics improvement plan include all three of the areas:  teaching and learning  curriculum  leadership and management? Better mathematics conference keynote 2015

78. In summary  You have identified areas for improvement in mathematics in your school by highlighting some national key concerns.  Your school’s mathematics improvement plan also includes some areas for development.  The next activity involves using these sources to help you select one short-term priority and one long-term priority for which you can start to devise actions today. Planning actions for your priorities Better mathematics conference keynote 2015

79. Ideas for short-term priorities Short-term priorities:  raise attainment by the end of reception to ensure all children, especially those who are disadvantaged, are well prepared for Key Stage 1  improve pupils’ problem-solving skills across the mathematics curriculum  increase achievement in Year 7, ensuring a flying start through raised ambition and effective transition from Key Stage 2  raise attainment at GCSE grades A*/A by improving transition from KS3 to GCSE and increasing depth of teaching of important topics Better mathematics conference keynote 2015

80. An ideas for a long-term priority Long-term priority:  ensure teaching focuses on conceptual development Planning involves thinking about:  where to start (e.g. calculation/ Y7)  agreeing approaches, including professional development  monitoring through the subject leader checking that conceptual approaches are being planned and used well  evaluating through subject discussions with pupils to check their understanding. Better mathematics conference keynote 2015

81. Select one short-term priority and one long-term priority for which you can start to devise actions during this session. To inform your selection, refer to:  the key concerns you highlighted  your school’s mathematics improvement plan. For each priority, specify precisely:  the actions you will take, including coaching and targeted professional development, and how you will monitor their quality, providing support and challenge as needed  what you expect the impact of successful actions to look like and by when, and how you will evaluate this. Planning actions for your priorities Better mathematics conference keynote 2015

82. Further planning When you are back at school, you may find it helpful to:  look in detail at your school’s information/data to explore whether other areas of national concern might also be priorities for your school  continue to work together on your improvement plan for mathematics. Better mathematics conference keynote 2015

83. Further information At the back of your booklet, you will find:  the extract on inspecting mathematics from the school inspection handbook  the ‘think for a moment’ questions  links to various documents and websites. We hope you have found this morning useful. If you have any further questions or points you wish to raise, please speak with one of the HMI during the lunch break. Better mathematics conference keynote 2015

84. Better mathematics conference Keynote: understanding ways forward Jane Jones HMI, National lead for Mathematics Autumn 2015