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Raising real mathematical standards

This study examines the changes in mathematics classrooms in England from 1980 to 2010 and how they impacted the standards of mathematical education. It explores various reforms, curriculum changes, and their effects on teaching methods, assessment, and student performance.

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Raising real mathematical standards

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  1. Raising real mathematical standards Margaret Brown King’s College London

  2. 30 years of Changes in Mathematics Classrooms in England (5-16)(1980-1990) • Cockcroft (1982): • Investigations, discussion, practical work, problem-solving (as reaction to too much exposition and practice), • Contextual, utilitarian emphasis • Progression at different rates and differentiated work • Foundation stage: conceptual list of basic maths for application • GCSE (1988) • Coursework (practical problems & investigations) • 3-Tiered papers (some graded tests/assessments) • Contextual questions • National Curriculum (1989+) • Progression, levels and teacher assessment • Modular planning • Continues broad curriculum,

  3. 30 years of Changes in Mathematics Classrooms (5-16) (1990-2000+) • National Curriculum Changes (1992, 1995, 2000) • Ofsted (1992), national tests (1995)and league tables(1996), • Whole class teaching • Mental arithmetic • Procedural teaching to the test • National Numeracy Strategy (1999) & unit plans (2001)/ Secondary National Strategy (2002) • Whole class teaching & uniform curriculum • Number and calculation focus • Centrally directed planning (framework objectives and then, at primary level, unit plans)

  4. 30 years of Changes in Mathematics Classrooms (5-16) (2000-2010) • Smith Report/Tomlinson Report 2004 • 2-tier GCSE, Double GCSE • Functional Maths • Primary National Strategy (2006) • Planning changes to new units • More focus on standard written calculation • Making Good Progress (2007) (Tracking, APP, Single level tests?) • Renewed focus on teacher assessment (also AfL), and greater differentiation eventually? • 2-tier GCSE (2008) & removal of coursework (2009) • Less focus on algebra and challenge • New National Curriculum at KS3 & 4 (2008), KS1& 2 (2011??); Williams Report (2008)/Cambridge report/Rose Review (2009)/new GCSEs (teaching from 2010) • More focus on processes & rich tasks & more cross-curricular work • Relaxation of prescription of planning and teaching methods • More functional focus in GCSEs • Removal of KS3 tests (2009); maths required for 5+ GCSE index • More acceleration & early entry

  5. Dimensions of change • Uniformity of curriculum and teaching • centrally/locally controlled • differentiated by class/group/individual • Curriculum focus • individual creativity (process-focused) • traditional skills (procedure-focused) • utilitarian (concept /application-focused) • Pressure on teachers to raise results

  6. Primary Standards NFER tests and APU results showed little change in performance in primary mathematics between 1950s and 1990s Brooks, Foxman, & Gorman (1995) for NCE

  7. Primary Standards: National Tests

  8. Primary Standards: National Tests • Black (2006): international research shows high stakes tests ‘produce a short-term 3-year uplift in results before they plateau’. • Tymms (2004), backed by Statistics Commission established by a variety of methods (independent test results, trials in Northern Ireland of 1995 and 1999 tests) there was slippage in the standards of national tests between 1995 and 2000. Coe & Tymms (2009) estimate if definition of Level 4 had not shifted current results should be 69% at L4 not 79% • Single Level Tests – the National Tests were originally criterion-referenced i.e. to get a Level 4 you had to obtain 2/3 of the Level 4 marks. The attempt to set SLTs at KS3 was abandoned as they couldn’t be matched to test results – at KS2 they are still operating in a minority of pilot schools although ‘the tests would allow children to say they had achieved a particular national curriculum level without answering any questions that related to it’ (TES, 19/03/10)

  9. Primary Standards: Year 4 Leverhulme numeracy test results

  10. Primary Standards More Leverhulme findings: • 1/3 of our 35 schools had lower year 4 means in 2002 than in 1998; • standard deviations increased; • mean scores dropped for lowest attainers

  11. Primary Standards: International Comparisons • 1995 TIMSS Year 5: Just below average with 48.4* • 2003 TIMSS Year 5: Largest international rise to 53.1 (but half accounted for by testing 3 months later) • 2007 TIMSS Year 5: Continuing rise to 54.1, top in Western Europe/Anglophone countries – but many did not take part

  12. Secondary Standards: GCSE A*-C pass rates In 1980s around 23% gained GCE grade C maths at first sitting, now around 55% get a grade C at maths GCSE. Through introduction of GCSE (1987-88) criteria slipped a grade (D to C) (GAIM data) Coe & Tymms (2009) between 1996 and 2007 performance in maths GCSE for equivalent student rose by 0.9 grade – more than for any other mainstream subject (e.g. double science rose 0.25 grade, mostly in 1996/7)

  13. Secondary Standards: International Comparisons: TIMSS • FIMS 1964 & SIMS 1982: Around OECD average • IAEP 1991 Slightly below OECD average • TIMSS 1995-2003: Year 9 fairly constant at 49.8, below OECD average • TIMSS 2007: increase to 51.3

  14. Secondary Standards: International Comparisons: PISA PISA tests 15 year-olds on mathematical literacy: • Decline in scores from 52.9 in 2000, to 50.8 in 2003 to 49.5 in 2006 (awaiting 2009 results)

  15. Secondary Standards: ICCAMS/CSMS(interim results)

  16. Secondary Standards: ICCAMS/CSMS

  17. Primary Attitudes • TIMSS 1995 and 2007 (Year 5) • Percentage with positive attitude dropped by 14 percentage points. Greatest fall in 1995-2003 period. • In 2007 low attainers had significantly worse attitude than average or above. In 1995 there had been very little difference. (See also Leverhulme results) • In 1995 more children than in any other country believed that ‘they usually did well in mathematics’; in 2007 we were 14th/36 in self-confidence, although this was slightly higher than in 2003.

  18. Secondary Attitudes • FIMS (1964): Anglophone countries negative about school learning and value of maths • TIMSS 1999-2007: drop of 25 percentage points in students with positive attitude to maths, 20% increase in those with negative attitudes (see also Nardi & Steward, 2003, Brown et al., 2008) • TIMSS 2003-7: small rise in confidence (+6%) to 53%, now among leading countries. Students value maths a little more in 2007 than in 2003 (+ 10%), to 74%

  19. Conclusion about Effects of Changes on Standards and Attitudes Over last 30+ years very little evidence of significant improvement in standards – at best about 3% gain in attainment at primary level, little positive movement in secondary or in attitudes.

  20. Reasons for lack of significant improvement 1) Learning is a complex process which takes a lot of time to make all the neurological connections

  21. Reasons for lack of significant improvement 2) We have wasted effort and money trying to change the wrong things.

  22. When other factors are removed, there is no effect on external results of: • being a specialist school (Mangan et al., 2007; Smithers & Robinson, 2009), an academy (Machin & Wilson, 2008) or an independent school (OECD 2004, 2007) • using computers (Cuban, 2002) • using interactive whiteboards (Moss et al., 2007) • having classroom assistants (Blatchford et al 2010) (Wiliam, 2010)

  23. The Leverhulme project found no effect on primary mathematics learning of: • the frequency of whole class teaching, • whether homework was set (also Farrow et al., 1999) • setting (also many other studies e.g. Ireson & Hallam, 2001 ) • calculator use (also SCAA, 1997)

  24. Reasons for lack of significant improvement 3) There is no evidence that the quality of teaching in mathematics is any better now than in the 1970s

  25. Ofsted (2008): ‘The fundamental issue for teachers is how better to develop pupils’ mathematical understanding. Too often, pupils are expected to remember methods, rules and facts without grasping the underpinning concepts, making connections with earlier learning and other topics, and making sense of the mathematics so that they can use it independently... pupils struggle to express and develop their thinking’ (Cf Cockcroft, 1982)

  26. Reasons for lack of significant improvement 4) High stakes tests and fragmented-objectives-driven lessons lead to very instrumental teaching

  27. Reasons for lack of significant improvement 5) The quality of teaching materials being used is, with some exceptions, poorer than in the 1970s

  28. Decline in trialled materials written by groups of teachers (SMP, SMILE) • Growth in textbooks written by examiners and sometimes published by awarding bodies aimed at coaching for KS2 tests, GCSE • Evidence that recent textbooks compare badly with those used in EU (Haggarty & Pepin, 2002; Harries & Sutherland, 1999) • Use of internet and IWB packages of mixed quality

  29. Reasons for lack of significant improvement 5) Generally teachers have less preparation for teaching mathematics than in the 1970s

  30. Primary teachers have much less time to prepare for teaching mathematics in a PGCE rather than a BEd. • Little subject teaching focus in Teach First, GTP training • With exceptions (MaST, Mustained CPD not generally encouraged • Some classes covered by teaching assistants or teachers with weak mathematics backgrounds (GCSE max)

  31. Implications of Research for the Future • Teachers can make a difference

  32. Rate of learning with effective teachers is 2 x that with average; ineffective teachers ½ x average – Wiliam, 2010 (But some limit to this?)

  33. Implications of Research for the Future 2) International research reviews have suggested which innovations in teaching can make most difference

  34. Hattie (e.g. 2005) provides a meta-analysis of generic mean effect sizes of interventions worldwide classified according to the main factors involved. He points out that the mean effect size for innovations is 0.4 i.e. the mean improvement is 0.4 of a standard deviation, and for ‘normal teaching’ it is 0.24 (and maturation 0.10). Result is that additional mean effect is 0.16. So on average innovation is better than doing nothing! (Caveats: Unreported studies? Mostly small personal studies? 0.24 unreliable?)

  35. Hattie’s selection of typical factors above mean of 0.4: Factor No. of effects /Mean effect Feedback 13209 .81 Classroom behaviour 361 .71 Cooperative learning 1153 .59 Early intervention 30971 .49 (Hattie, 2005)

  36. Slavin & Lake (2008) reviewed effect sizes of primary and Slavin et al (2009) of secondary mathematics interventions: Primary Secondary Curriculum (textbks ) 0.10 (13) 0.03(40) CAI 0.19 (38) 0.10 (38) Instructional process 0.33 (36) 0.18 (22) Co-operative 0.29 (9) 0.46 (7) Metacognitive 0.31 (2) Individualised 0.36 (2)

  37. The innovations in England with highest effect size are those which require students and teachers to think more clearly: • formative assessment (Wiliam et al., 2004) • cognitive acceleration (Adey, 1992; Adey et al., 2002; Shayer & Adhami, 2006) • philosophy for children (Topping & Trickey, 2007) (Wiliam, 2010)

  38. In mathematics in England focus is now on mathematical understanding: • Swan (2006) successfully used collaborative learning, tasks to stimulate discussion and ideas of connectionist teachers (building on Askew et al, 1997) • ICCAMS now working with teachers on similar techniques including AfL in Algebra and Multiplicative Structures

  39. Implications of Research for the Future 3. Teachers find it difficult to change their practice, especially after teaching prescription and with high stakes tests – it needs time, talk, expertise and motivation (Millett, Brown & Askew, 2004)

  40. Implications of Research for the Future 4) Forget grand schemes of national change – local innovations have at least as high effect sizes on average

  41. Implications of Research for the Future 5) We must focus on releasing the creativity of teachers and others for a 10-year period of innovation. There should be a moratorium on central prescription and teacher unions should organise a 10-year boycott on centrally imposed assessment and inspections. Focus should be on what produces effect on standards (connected teaching for understanding). Is this impossible? It worked in the 1950s, and it works in other countries – why not here?

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