SW Maths PD Conference : Using and Applying – teaching and assessing

1. SW Maths PD Conference: Using and Applying – teaching and assessing Lynn Churchman Lynn Churchman 28th September 2009

2. Intend ……to…. • tell you about my summer reading!! • take a ‘radical’ look at the teaching, learning, assessment of UAM • raise some key issues in relation to the learners’ perspective: What do they think maths is about? Why is engaging/stimulating them key? What does it take?

3. Summer ‘reading’ (-ish) • Prof John Hattie ‘Visible Learning’ (Routledge 2008) • Described by the TES as “perhaps education's equivalent to the search for the Holy Grail - or the answer to life, the universe and everything”.

4. Prof John Hattie • Director of Project asTTle (Assessment Tools for Teaching and Learning). • His areas of research include: • measurement models and their application to educational problems • meta-analysis • and models of teaching and learning.

5. The research involves…. ………..………many millions of students and represents the largest ever evidence based research into what actually works in schools to improve learning. Areas covered include the influence of the student, home, school, curricula, teacher, and teaching strategies. A model of teaching and learning is developed based on the notion of visible teaching and visible learning.

6. Publisher’s summary said.. “This unique and ground-breaking book is the result of 15 years research and synthesises over 800 meta-analyses on the influences on achievement in school-aged students. It builds a story about the power of teachers, feedback, and a model of learning and understanding”.

7. Meta-analysis • At the core of Professor Hattie’s work is a meta-analysis of the influences on student achievement • Effectively a graded scale showing how the effects of different factors compare. It is an objective continuum of positive and negative effects showing impact on achievement relative to each factor not being present.

8. Publisher’s summary said.. “Over the last 15-20 years Professor Hattie has studied what effect a very wide range of influences, interventions and initiatives has on student achievement. This has involved classroom observation and draws on academic research involving millions of students from across the world”

9. Some examples…. • Pre-school programmes 0.45 • Effective teacher feedback 0.73 • Class size less than 30 0.2 (9 months/sc life) • Being held back a year -0.18 • Moving to a different school -0.36 • Gender 0.12 • Web-based instruction 0.09 • Individualised instruction 0.2

10. Group Task - Guess! (all positive) • Web-based instruction • Homework • Ability grouping • Teacher training • Gender • Individualised instruction • Enrichment for gifted

11. Surprised? • Web-based instruction 0.09 • Homework 0.29 • Ability grouping 0.11 • Teacher training 0.11 • Gender 0.12 • Individualised instruction 0.2 • Enrichment for gifted 0.39

12. Hattie’s key findings 1 • Of the 100+ influences on student achievement about 90% are positive; ie: 90% of the things teachers do have an effect of greater than 0 and will therefore improve achievement. • Hence - a teacher can evaluate more or less any activity and conclude that it has boosted student achievement; effect of greater than 0 and is therefore positive – so it must have been worthwhile. Right? • Wrong. If 90% of the influences are positive, teachers have set themselves a ridiculously low pass-mark. Simply “improving achievement” is not good enough.

13. Hattie’s key findings 2 • To drive this point home, studies of students in developing world countries show that natural development while not going to school has an effect of 0.15. (ie: higher positive effect from not being in school than from ability grouping (0.09)!!) • The average effect score is 0.4. In other words, factors with an impact of 0.4 or greater will have a significant positive effect on student achievement. • Anything less than 0.4 will improve outcomes, but there are plenty of better things to do. Anything less than 0.15 is a waste of time – you might as well not be at school.

14. Hattie’s ‘effect size’ analysis • Challenging goals • Worked examples • Problem-solving teaching • Spaced vs mass practice • Teacher-student relations • Feedback • Teacher clarity • Acceleration up a year • Providing formative evaluation

15. Hattie’s ‘effect size’ analysis • Challenging goals 0.56 • Worked examples 0.57 • Problem-solving teaching 0.61 • Spaced vs mass practice 0.71 • Teacher-student relations 0.72 • Feedback 0.73 • Teacher clarity 0.75 • Acceleration up a year 0.88 • Providing formative evaluation 0.9

16. Summary • The important thing is that structural factors, which typically receive a great deal of attention, have a relatively small effect on achievement. Teaching has a far lower profile, but an incredible impact. • Professor Hattie is emphatic that his conclusion is not that ‘teachers make the difference’. Rather, ‘some teachers doing some things make the difference’. • Effects with the greatest impact come from good teaching and need to inform CPD inc Action research focii • Sharing ‘effective practice’ not just ‘good practice’

17. The major message is that ….. ……….what works best for students is similar to what works best for teachers - an attention to setting challenging learning intentions for all, being clear about what success means, and an attention to learning that develops skills and conceptual understanding and teachers knowing about what students know and understand.”

18. Pause for thought • Bring to mind a (KS1? KS2? KS3?) group you teach and know well; what do you think would be these students views (if asked): • What maths and the maths curriculum is about • The nature of maths lessons and maths learning? • Their confidence in their mathematical ability? Note 3-4 points to share then keep to return to later

19. Defining a challenging curriculum for all: Re-defining UAM

20. ……..In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures. A lack of mathematical competence keeps those doors closed…..there is no conflict between excellence and equity. A society in which only some have the mathematical knowledge needed to fill crucial economic, political and scientific roles is not………………

21. …….. consistent with the values of a just democratic system or its economic needs …………. The vision described is idealised and is not the reality in many classrooms, schools or districts. ……….The reasons for this deficiency are many and varied ……………………but improving the situation requires clear leadership at all levels. At national, local and school level, all must work together to create mathematics classrooms where all students have access to high quality, engaging mathematics instruction From ………….NCTM (US) Handbook

22. Creating challenging learning “………all learners are truly able to recognise pattern, to generalise, to imagine, to reason about shapes, to connect ideas to symbolic representations and to do the numerical and spatial reckoning which they need to function in the world. We need to give them all the chance to do so” Anne Watson/Mike Ollerton; Inclusive mathematics

23. Effective teaching and teachers Effective teachers share the same underlying principles and goals about the potential of their students: • that all can learn mathematics • that the teacher’s task is to develop students’ thinking and learning • that all students have a right as citizens to access all mathematics • that learning mathematics is intimately related to self-esteem and is a potential source of empowerment

24. Teaching and Learning “Simply because a teacher is teaching does not necessarily guarantee that the child is learning…..conversely, a child often learns when the teacher is not teaching. There is instead a complex, delicate, multi-faceted and human relationship between teaching and learning” Ainscow & Tweddle – ‘Preventing classroom failure: an objectives approach’ (1979) and ‘Encouraging classroom success’ (1988)

25. Model for effective learning 1 • classroom tasks that challenge learners to think and reason mathematically • a ‘classroom culture’ that encourages groupwork, discussion and collaborative learning • teachers who expect learners to develop a secure understanding of key mathematical concepts and constantly require learners to express their reasoning and understanding • the development of a “can do……..” culture where teachers believe that all learners can think mathematically and they convince learners they can succeed

26. Model for effective learning (2) • learners’ progress being checked and monitored with misconceptions being used constructively to help teaching • learners’ attitudes to mathematics are good and they take their share of responsibility for achieving to their full potential in mathematics • there is a confidence on the part of learners that they can continue to develop and extend their skills and knowledge in mathematics ……….and show a desire to do so

27. Task - What does this look like? Take learning to calculate a percentage of a quantity at age 10/11/12. Discuss in groups: What skills and aptitudes you want learners to have? What types of learning tasks are needed?

28. Tasking learners to think The best tasks are those which require pupils to: • think about the maths they are doing • avoid an instrumental approach to algorithms, instead developing reasoning and initiative. • search for understanding before they are satisfied • explain their reasoning • justify their methods and results • generalise – know when/where a method will and will not work

29. Task – moving to deeper understanding of percentages Discuss with 1 or 2 neighbours how you would do the following Percentage calculations • (3 mins) Slide no.

30. 18% of £25 • 19% of £75 • 23% of £15 • 25% of £18

31. Reasoning about Percentages For what values of x is x% a nice ‘friendly’ fraction?

32. Percentages • 25%

33. Percentages • 25% of £50

34. Percentages • 25% of £50 = £12.50

35. Percentages • 25% of £50 = £12.50 • 50%

36. Percentages • 25% of £50 = £12.50 • 50% of £25

37. Percentages • 25% of £50 = £12.50 • 50% of £25 = £12.50

38. Percentages • 25% of £50 = £12.50 • 50% of £25 = £12.50 For what sort of values is this true: x% of y = y% of x

39. Percentages revisited 18% of £25 19% of £75 23% of £15 25% of £18

40. Percentages revisited 18% of £25 = 25% of £18 19% of £75 23% of £15 25% of £18

41. Percentages revisited 18% of £25 = 25% of £18 19% of £75 23% of £15 25% of £18

42. Percentages revisited 18% of £25 = 25% of £18 19% of £75 = 75% of £19 23% of £15 25% of £18

43. Percentages revisited 18% of £25 = 25% of £18 19% of £75 = 75% of £19 23% of £15 = 15% of £23 25% of £18

44. The Maths Curriculum • Trying a model in ARK schools which is: • Based on NC • Ambitious • For all

45. ARK Academies - our mission: ‘We aim to ensure that every student achieves highly enough by age 18 to have real options: to go to university or college or to follow the career path of their choice’. 

46. Mathematics education in ARK schools: ….aims to develop, at all ages, confident and competent learners with the capacity to aim high: • learn and understand all the necessary mathematical knowledge and skills and conceptual understanding • think and reason mathematically • solve problems and present and justify solutions in the context of the problem • value mathematics and engage actively in learning it • believe in themselves as successful mathematicians (who can continue with their study of mathematics beyond age 16 if that is their choice)

47. The curriculum must: • Enable all children to develop the technical mathematical skills and conceptual understanding they need but •  also the necessary positive attitudes and dispositions to learning and working mathematically in order to solve problems and apply their mathematics in a range of contexts Helps to view it from three perspectives………..

48. Principles of curriculum design “For generations, high school students have studied mathematics that has very little to do with the way mathematics is created or applied outside of school ……..communicating established results and methods ……. giving students a bag of facts ………and properties …. then working some problems in which they apply learnt properties and then move on….. …….There is another way to think about it….

49. …….and it involves turning the priorities around. Much more important than specific mathematical results are the habits of mind used by the people who create those results ………. Although it is necessary to infuse courses/curricula with modern content …….it is even more important to give students the tools they will need to use and understand their mathematics.” Habits of mind: an organising principle for mathematics curricula Al Cuoco, E. Paul Goldenberg, June Mark Journal of mathematical behaviour 15 .....how do we convey this to learners ?

50. Students should develop habits as: pattern sniffers ……… experimenters …. tinkerers ……. inventors ………visualisers ………conjecturers and use: deduction ……multiple view points …….proportional reasoning ……. seeing what changes and what stays the same