improving gcse maths results effective strategies and structural approaches [email protected]
TRANSCRIPT
© Chris OlleyVisit: www.themathszone.co.uk
Programme
We teach maths hereYou can and will succeed Lunch
Keeping on trackWinning at maths exams Close
© Chris OlleyVisit: www.themathszone.co.uk
The Score
1993 (Arrival) 13% A*- C at GCSE School: 5+ A*- C = 21% A level candidates = 32001 (Departure) 49% A*- C at GCSE School: 5+ A*- C = 34% A level candidates = 30+
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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?
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The Big Picture
An atomisation of the curriculum can lead to disconnected learning.For students, the problem is seeing the wood for the treesKing’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
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Big Ideas
Proof Pure mathematics Algebraic manipulation Explain/convince meModelling Solving real world problems! Critique The data handling cycle
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More Big Ideas
TransformationInfinity/LimitNumberFunction
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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?
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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, 1988Terezinha Nunes et al., Street mathematics and school mathematics, Cambridge, 1993
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Distance Time – A Real Life Problem
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Distance Time – A Real Life Problem
Volunteer
CBR
TI-83
Projector
Screen
About 6 metres
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Presentation Matters
Accurate mathsReadable mathsAnnotated mathsExemplified maths
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You Can Succeed
The language of success Achievement “Algebra from the off” HigherThe language of failure Ability “You can’t expect these kids to do
that” Foundation
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Achievement Groupings
Shirley Brice Heath (e.g. Ways with Words, Cambridge, 1983)Jo Boaler: Experiencing School Mathematics, Open University Press, 1997Paul 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
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Time to Respond ...
DISCUSSIONShare in pairs: What stops them succeeding?Group: What can we do about it?
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The National Maths Challenge
Gold, Silver and Bronze certificatesAverage 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/
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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%)
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A Structured Assessment Strategy
Notes and examplesDeep marking/shallow markingTutorial support(SMART) target setting
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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
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A Tracking Measure
0
12
34
5
67
8
0 5 10 15 20
Half term
NC
Lev
el
Under achievement
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A Tracking Measure
0
1
2
3
4
5
6
0 5 10 15 20
Half term
NC
leve
l
Good achievement
© Chris OlleyVisit: www.themathszone.co.uk
© Chris OlleyVisit: www.themathszone.co.uk
© Chris OlleyVisit: www.themathszone.co.uk
Monitoring and Tracking
Effort = achievement – expectationProgress = achievementx – achievementx-1
Prediction is the extrapolation of achievement over time
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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
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Exam Preperation
DISCUSSIONShare 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?
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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
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Structured development of investigative skills.
Exploration
Proof
Criticise
Write upRe-draftPresent
Extend
Using algebra
Justify and explain
Generalise and test
Pattern spotting
OrganisationTabulation
Breaking down
Diagrammatic representation
Design
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The Tower of Hanoi
‘Feel’ the structure to explain it.Pattern spot to algebra.Prove by induction.
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Data Handling
HypothesisMeasureIndicatorDataCharts and statisticsAnalysisCritique
Critique: sample size, validity, reliability, do a time series or a stratified random sample.
Is it a good indicator of the measure?
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Winning the Exam Game 2
Revision Notes and examples = proper revision
notes Mind mapsPreparation Organised practice Good exam techniqueOn the day