Better mathematics conference

1. Better mathematics conference Keynote: understanding ways forward Jane Jones HMI,National lead for Mathematics Spring 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 figuresfor attainment and progress in mathematics Findings from our triennial report, Mathematics: made to measure, 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: at GCSE grades A*-C, due to a strong emphasis by schools at AS/A level with a huge increase in uptake. In primary schools, attainment has: risen in the EYFS with calculation weakest; 2013 new ELGs 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 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 application of 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. Early Years Foundation Stage The Early Learning Goals that were introduced in September 2012 represent substantially higher expectations than previously. Problem solving is an explicit part of each Early Learning Goal. (It used to be just one of eight points from which children had to meet any six to reach the age-related expectation.) Better mathematics conference keynote 2015

9. Progress (2013 figures; 2011 in brackets) 88% (82%) of pupils made the expected 2 levels of progress KS1KS2 but: 70% of L2c reach L4 compared with 91% of L2b; (58% cf 86% in 2011). 70% (62%) of pupils made the expected 3 levels of progress KS2KS4 but: 58% of L4c reached grade C; (48% in 2011) still only 29% of low attaining pupils made expected progress; (30% in 2011) over 31000 pupils who attained L5 at primary school got no better than grade C at GCSE; 2700+ got grade D or lower. Better mathematics conference keynote 2015

10. Gaps in attainment and progress (2013 in black; 2011 M2M figures in blue) Overall, 9% of pupils did not reach L2 at age 7, 15% did not reach L4 at age 11, and 30% 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! Better mathematics conference keynote 2015

11. 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

12. Achievement – key concerns The percentage of pupils meeting expected standards 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. FSM pupils do far worse than their peers at all key stages, most markedly at Key Stage 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. High attainers not challenged enough from EYFS onwards. 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

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

14. Teaching Better mathematics conference keynote 2015

15. Teaching – Ofsted’s findings The best teaching develops conceptual understanding alongside pupils’ fluent recall of knowledge and confidence in problem solving. 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

16. Teaching examples Problem solving The animal puzzle is an example of problem solving. Problems may, or may not, involve realistic contexts. 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

17. 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

18. 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

19. Fluency using conceptual understanding 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

20. 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

21. 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

22. Changes to the inspection of teaching From September 2014, inspectors will not grade the quality of teaching in individual lessons. In evaluating the overall quality of teaching in a school (or in the subject for a mathematics inspection), inspectors will consider strengths and weaknesses of teaching observed across a broad range of lessons and other activities, placed in the context of other evidence of pupils’ learning and progress over time. The judgement on leadership and management will include use of performance management and effectiveness of strategies to improve teaching, including account taken of the Teachers’ Standards. Better mathematics conference keynote 2015

23. 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 tacklespecific weaknesses in teaching (including temporary, part-time and non-specialist staff)? Better mathematics conference keynote 2015

24. Teaching – key concerns Wide in-school variation in teaching quality. Conceptual understanding and problem solving are underemphasised. Too often, teaching approaches focus on how, without understanding why, so that pupils have insecure foundations on which to build future learning. 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. 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

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

26. Curriculum Better mathematics conference keynote 2015

27. 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

28. Practical, mental and written methods The photo shows a pupil using practical equipment 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

29. Curriculum findings (Made to measure) The degree of emphasis on problem solving and conceptual understanding is a key discriminator between good and weaker provision. Planning in primary is usually based on National Strategy materials. It is detailed, but tends to lose the big picture of progression in strands of mathematics. In secondary, planning and schemes of work are commonly based on particular examination specifications. Pupils’ curricular experiences are inconsistent and depend too much on the teacher they have and the set/class they are in. Better mathematics conference keynote 2015

30. Variation in use of ICT All teachers should follow the school’s agreed approaches with ICT to help develop pupils’ conceptual understanding. Better mathematics conference keynote 2015

31. Curriculum – key concerns Problem solving is not emphasised enough in the curriculum. Teachers are not clear enough about progression, so teaching is fragmented and does not link concepts. Pupils’ curricular experiences are inconsistent because: teachers lack guidance and support on building conceptual understanding and progression over time teachers’ subject knowledge and pedagogic skills (subject expertise) vary. They are not enhanced enough through subject-specific professional development and guidance. Less experienced/non-specialist/temporary staff do not receive the specific guidance and support they need. Better mathematics conference keynote 2015

32. The importance of subject expertise Subject knowledge and pedagogic skills 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

33. GCSE entry findings (Made to measure) In 2011/12, nearly 90% of schools entered some or all pupils early for GCSE. Nationally, over half of the cohort took GCSE early, with many pupils resitting it. Teaching commonly focuses on the next exam and includes much practice on exam-style questions. This approach relies on pupils’ recall of disparate facts and methods. Higher sets are not always given enough time on hard topics e.g. algebra, geometry, graphs – needed for AS/A level. Best practice for higher attainers is taking GCSE alongside additional qualifications at the end of Y11. A current concern (2014) is the use of multiple GCSE entry using different awarding bodies. Better mathematics conference keynote 2015

34. GCSE entry patterns – key concern Choices about GCSE entry and qualification pathways can limit pupils’ achievement and/or drive short-termism in teaching approaches: pupils entered early for GCSE generally attain less well after resits than do those entered only once at the end of Year 11, and few pupils who gain GCSE grade A early go on to resit with the aim of improving their grade teaching focuses on exams, relying on pupils’ short-term memory, rather than on progression and development of understanding pupils are less well prepared for their future studies in mathematics and other subjects, including resitting GCSE post-16. Better mathematics conference keynote 2015

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

36. Leadership and management Better mathematics conference keynote 2015

37. Leadership and management findings Stronger management practices, particularly in secondary: monitoring of teaching (e.g. learning walk, work scrutiny) use of data to track progress and for intervention use of performance management to drive higher examination results. Key concern 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

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

39. The potential of work scrutiny To check and improve: teaching approaches, including development of conceptual understanding depth and breadth of work set and tackled 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 using and applying mathematics. Better mathematics conference keynote 2015

40. Work scrutiny What does this extract suggest about how well: the pupil understands the topic (collecting like terms) the exercise provides breadth and depth of challenge the marking identifies misconceptions and develops the pupil’s understanding? The commentary on this extract shown in the next slides is also provided in the information pack for the workshops. Better mathematics conference keynote 2015

41. Work scrutiny – understanding The pupil adds like terms correctly but makes an error with subtraction. The exercise has too many straightforward questions on addition before subtractions start. This makes it too narrow and unchallenging to develop understanding of the whole topic. Such narrowness prevents the teacher from checking the extent of the pupil’s understanding. Better mathematics conference keynote 2015

42. Work scrutiny – teacher’s comments The teacher’s comment ‘only 1 wrong’ misses the pupil’s difficulty with subtraction shown by the wrong answer to Q8 and incomplete Q9. It is likely that the pupil left the signs unmoved when rearranging 3j – 4k + 2j + k to get 3j – 2j + 4k + k The comment does not help the pupil to overcome this misconception. Better mathematics conference keynote 2015

43. Work scrutiny and lesson observation The top priority to bear in mind when scrutinising work is ‘Are the pupils doing the right work and do they understand it?’ Thinking back to the extract, the pupil was not doing ‘the right work’. The questions lacked breadth, did not develop understanding fully, and included no problems. 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

44. Think for a moment … In your school, what is the relative emphasis on improving: • the quality of work pupils are given in order to promote their understanding • marking? Better mathematics conference keynote 2015

45. Work scrutiny – assessment policy In accordance with the school’s policy, the teacher has provided a ‘next step’. ‘Equations’ is not a‘next step’ to help the pupil improve in this topic. Understanding subtraction is needed first. Working with brackets, constant terms and powers would give fuller breadth of the topic. Better mathematics conference keynote 2015

46. Leadership and management 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 one substantial piece of work periodically refer to the lesson objective when marking identify ‘next steps’ to help pupils improve their work. 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 Some whole-school policies do not work well for mathematics. Better mathematics conference keynote 2015

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

48. Leadership and management Enabling teachers to work together (e.g. on a calculation policy or guidance on progression in algebra) supports consistency and improvement. However, teachers usually share ideas and good practice informally, rather than record them in guidance, schemes of work, or policies. Key concern 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

49. 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

50. Use of assessment data – key concerns 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. Intervention, particularly for lower attainers, is not early enough to overcome gaps and build a firm foundation for future learning. Gaps arising from misconceptions, absence, changing teaching group or school are not systematically identified or narrowed. Secondary schools rarely use intervention to overcome gaps in pupils’ understanding, particularly in Key Stage 3, choosing instead to focus on examination preparation. Better mathematics conference keynote 2015