Improving GCSE Maths Results Effective Strategies and Structural Approaches [email protected]

Improving GCSE Maths Results

Effective Strategies and Structural Approaches

[email protected]

© Chris OlleyVisit: www.themathszone.co.uk

Programme

We teach maths hereYou can and will succeed Lunch

Keeping on trackWinning at maths exams Close


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+


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?


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


Big Ideas

Proof Pure mathematics Algebraic manipulation Explain/convince meModelling Solving real world problems! Critique The data handling cycle


More Big Ideas

TransformationInfinity/LimitNumberFunction


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?


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


Distance Time – A Real Life Problem


Distance Time – A Real Life Problem

Volunteer

CBR

TI-83

Projector

Screen

About 6 metres


Presentation Matters

Accurate mathsReadable mathsAnnotated mathsExemplified maths


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


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


Time to Respond ...

DISCUSSIONShare in pairs: What stops them succeeding?Group: What can we do about it?


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/


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%)


A Structured Assessment Strategy

Notes and examplesDeep marking/shallow markingTutorial support(SMART) target setting


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


A Tracking Measure

0

12

34

5

67

8

0 5 10 15 20

Half term

NC

Lev

el

Under achievement


A Tracking Measure

0

1

2

3

4

5

6

0 5 10 15 20

Half term

NC

leve

l

Good achievement





Effort = achievement – expectationProgress = achievementx – achievementx-1

Prediction is the extrapolation of achievement over time



A reliable and consistent reporting mechanism To talk to students, parents, tutors To inform target setting and review To generate realistic (= useful)

predicted grades


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?


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


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


The Tower of Hanoi

‘Feel’ the structure to explain it.Pattern spot to algebra.Prove by induction.


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?


Winning the Exam Game 2

Revision Notes and examples = proper revision

notes Mind mapsPreparation Organised practice Good exam techniqueOn the day

Documents

Improving GCSE Maths Results Effective Strategies and Structural Approaches [email protected]