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Improving GCSE Maths Results

Improving GCSE Maths Results. Effective Strategies and Structural Approaches chris@themathszone.co.uk. Programme. We teach maths here You can and will succeed Lunch Keeping on track Winning at maths exams Close. The Score. 1993 (Arrival) 13% A*- C at GCSE School: 5+ A*- C = 21%

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Improving GCSE Maths Results

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

  2. Programme • We teach maths here • You can and will succeed • Lunch • Keeping on track • Winning at maths exams • Close

  3. 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+

  4. 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?

  5. The Big Picture • An atomisation of the curriculum can lead to disconnected learning. • For students, the problem is seeing the wood for the trees • King’s 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

  6. Big Ideas • Proof • Pure mathematics • Algebraic manipulation • Explain/convince me • Modelling • Solving real world problems! • Critique • The data handling cycle

  7. More Big Ideas • Transformation • Infinity/Limit • Number • Function

  8. 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?

  9. 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 TerezinhaNunes et al., Street mathematics and school mathematics, Cambridge, 1993

  10. Distance Time – A Real Life Problem

  11. Distance Time – A Real Life Problem

  12. Presentation Matters • Accurate maths • Readable maths • Annotated maths • Exemplified maths

  13. You Can Succeed • The language of success • Achievement • “Algebra from the off” • Higher • The language of failure • Ability • “You can’t expect these kids to do that” • Foundation

  14. 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

  15. Time to Respond ... DISCUSSION • Share in pairs: What stops them succeeding? • Group: What can we do about it?

  16. 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/

  17. 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%)

  18. A Structured Assessment Strategy • Notes and examples • Deep marking/shallow marking • Tutorial support • (SMART) target setting

  19. 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

  20. A Tracking Measure Under achievement

  21. A Tracking Measure Good achievement

  22. Monitoring and Tracking • Effort = achievement – expectation • Progress = achievementx – achievementx-1 • Prediction is the extrapolation of achievement over time

  23. 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

  24. 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?

  25. 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

  26. Exploration Design Diagrammatic representation Organisation Tabulation Breaking down Using algebra Pattern spotting Generalise and test Proof Justify and explain Extend Write up Re-draft Present Criticise Structured development of investigative skills.

  27. The Tower of Hanoi • ‘Feel’ the structure to explain it. • Pattern spot to algebra. • Prove by induction.

  28. Data Handling Is it a good indicator of the measure? • Hypothesis • Measure • Indicator • Data • Charts and statistics • Analysis • Critique Critique: sample size, validity, reliability, do a time series or a stratified random sample.

  29. Winning the Exam Game 2 • Revision • Notes and examples = proper revision notes • Mind maps • Preparation • Organised practice • Good exam technique • On the day

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