2. Improving GCSE Maths Results Effective Strategies and Structural Approaches chris@themathszone.co.uk

3. © Chris Olley Visit: www.themathszone.co.uk Programme We teach maths here You can and will succeed Lunch Keeping on track Winning at maths exams Close

4. © Chris Olley Visit: www.themathszone.co.uk The Score 1993 (Arrival) 13% A*- C at GCSE School: 5+ A*- C = 21% A level candidates = 3 2001 (Departure) 49% A*- C at GCSE School: 5+ A*- C = 34% A level candidates = 30+

5. © Chris Olley Visit: www.themathszone.co.uk Maths v. School Maths What is mathematics? What do mathematicians do? What mathematics do professionals do? What is school mathematics? What do students learn in school mathematics lessons?

6. © Chris Olley Visit: www.themathszone.co.uk The Big Picture An atomisation of the curriculum can lead to disconnected learning. For students, the problem is seeing the wood for the trees Kings College, London: Effective Teachers of Numeracy connexionism Askew, M.; Brown, M.; Rhodes, V.; Wiliam, D. & Johnson, D. (1997). Effective Teachers of Numeracy: Report of a study carried out for the Teacher Training Agency. London: King's College, University of London

7. © Chris Olley Visit: www.themathszone.co.uk Big Ideas Proof Pure mathematics Algebraic manipulation Explain/convince me Modelling Solving real world problems! Critique The data handling cycle

8. © Chris Olley Visit: www.themathszone.co.uk More Big Ideas Transformation Infinity/Limit Number Function

9. © Chris Olley Visit: www.themathszone.co.uk Why Teach Maths? What do we say to students? What do we say to their parents? What do we say to each other? What do teachers of English Literature say to everyone?

10. © Chris Olley Visit: www.themathszone.co.uk Is it Useful? Lave and shopping maths No correlation between success I the supermarket and success at school. Problem solvers always succeed. Spradbery and pigeon maths No-one else validates your hobbies! Nunes and bubble gum maths School makes you worse at numeric problem solving. Jean Lave, Cognition in Practice, Cambridge, 1988 Terezinha Nunes et al., Street mathematics and school mathematics, Cambridge, 1993

11. © Chris Olley Visit: www.themathszone.co.uk Distance Time – A Real Life Problem

12. © Chris Olley Visit: www.themathszone.co.uk Distance Time – A Real Life Problem

13. © Chris Olley Visit: www.themathszone.co.uk Presentation Matters Accurate maths Readable maths Annotated maths Exemplified maths

14. © Chris Olley Visit: www.themathszone.co.uk You Can Succeed The language of success Achievement Algebra from the off Higher The language of failure Ability You cant expect these kids to do that Foundation

15. © Chris Olley Visit: www.themathszone.co.uk Achievement Groupings Shirley Brice Heath (e.g. Ways with Words, Cambridge, 1983) Jo Boaler: Experiencing School Mathematics, Open University Press, 1997 Paul Dowling: A touch of class: ability, social class and intertext in SMP 11-16 in Teaching and Learning School Mathematics eds. Pimm and Love, Hodder and Stoughton, 1991

16. © Chris Olley Visit: www.themathszone.co.uk Time to Respond... DISCUSSION Share in pairs: What stops them succeeding? Group: What can we do about it?

17. © Chris Olley Visit: www.themathszone.co.uk The National Maths Challenge Gold, Silver and Bronze certificates Average cohort = self selected 3-5 from each class, done as exam withdrawn from lessons. Outcome = around 10 bronze and 3 silver. http://www.mathcomp.leeds.ac.uk/

18. © Chris Olley Visit: www.themathszone.co.uk Early Entry Trial: Year 9. Nine students. All C+ including one A* - the first ever! Around 30% in year 9 All take intermediate Around 50% in year 10 D+ candidates take higher Year 11 D+ candidates take higher A* candidates take AS Almost nobody takes foundation (yet A*-G = 92%)

19. © Chris Olley Visit: www.themathszone.co.uk A Structured Assessment Strategy Notes and examples Deep marking/shallow marking Tutorial support (SMART) target setting

20. © Chris Olley Visit: www.themathszone.co.uk Monitoring and Tracking What do have to go on? Key stage 2, 3 results CATs, NFER, other external assessments Regular internal assessments Half termly tests EOY exams + past papers

21. © Chris Olley Visit: www.themathszone.co.uk A Tracking Measure Under achievement

22. © Chris Olley Visit: www.themathszone.co.uk A Tracking Measure Good achievement

23. © Chris Olley Visit: www.themathszone.co.uk

24. © Chris Olley Visit: www.themathszone.co.uk

25. © Chris Olley Visit: www.themathszone.co.uk Monitoring and Tracking Effort = achievement – expectation Progress = achievement x – achievement x-1 Prediction is the extrapolation of achievement over time

26. © Chris Olley Visit: www.themathszone.co.uk Monitoring and Tracking A reliable and consistent reporting mechanism To talk to students, parents, tutors To inform target setting and review To generate realistic (= useful) predicted grades

27. © Chris Olley Visit: www.themathszone.co.uk Exam Preperation DISCUSSION Share the strategies you use for the period after the course is finished up to the exams. How do you get the best coursework out of students?

28. © Chris Olley Visit: www.themathszone.co.uk Winning the Exam Game 1 Top Rated Coursework Structured practice over time Expectation of proof Hypothesis to Analysis Sharing the criteria With students In detail across the department

29. © Chris Olley Visit: www.themathszone.co.uk Structured development of investigative skills. Exploration Proof Criticise Write up Re-draft Present Extend Using algebra Justify and explain Generalise and test Pattern spotting Organisation Tabulation Breaking down Diagrammatic representation Design

30. © Chris Olley Visit: www.themathszone.co.uk The Tower of Hanoi Feel the structure to explain it. Pattern spot to algebra. Prove by induction.

31. © Chris Olley Visit: www.themathszone.co.uk Data Handling Hypothesis Measure Indicator Data Charts and statistics Analysis Critique Critique: sample size, validity, reliability, do a time series or a stratified random sample. Is it a good indicator of the measure?

32. © Chris Olley Visit: www.themathszone.co.uk Winning the Exam Game 2 Revision Notes and examples = proper revision notes Mind maps Preparation Organised practice Good exam technique On the day