effective classroom approaches to gcse maths · pdf fileth d ’t f l t d b t thithey...

Julia Smith

@tessmaths@tessmaths

Effective Classroom Approaches to GCSE Maths resitsGCSE Maths resits

[email protected]

Agenda

✦The context of GCSE resit in a post-16 setting✦The context of GCSE resit in a post 16 setting

✦An overview of the new GCSE

✦✦Key features of a revision year

✦Top tips, key resources and revision techniques

✦Using the practice papers, sample assessment material & milestones

✦Identifying next steps

Slide 2 Copyright © AQA and its licensors. All rights reserved.

That’s the way to do it...

• Shanghai Maths• Shanghai Maths...

• Masters...

• I ti• Innovation...

• Quirks...Ll C l• Llama Calmer

• Nov resits

• Walking Talking MocksWalking Talking Mocks

• Student Leaders

• Awards

• Working breakfast

The Context of a Post-16 yrs GCSE Resit

The Wolf Report

Considerations

✦ R lt✦ Results

✦ Attendance

✦ Recruitment

✦ Class size

✦ Behaviour✦ Behaviour

✦ CPD

✦ Ofsted

✦✦ The new GCSE & grade issues

✦ The legacy year (materials)

The Policy Exchange ‘Crossing The Line’

The Students

Th h ll th th b f b f✦ They have seen all the maths before, over a number of years - they have a D grade!

✦ They can do some maths

✦ They will have forgotten a lot since June

✦ Some will still have resat multiple times

Th d ’t f l t d b t thi✦ They don’t feel too good about this

FE

✦ FE is resilient and proactive

✦ FE faces the challenge head on with aggressively obstinate students who don’t want to be there... and often aren’toften aren’t

✦ FE Vocational Staff are teaching GCSEg

✦ FE is not a miracle worker...but we have got time to prepareprepare

The new GCSE specification


Philosophy from DFE / Ofqual


Specification content

The mathematical content is defined by the DfE’s GCSE subject content and assessment objectives document.

Subject area Foundation Tier weighting Higher Tier weighting

Number 25% (35%) 15% (17%)

Algebra 20% (17%) 30% (35%)

Ratio, proportion and rates of change

25% (subsumed in other areas)

20% (subsumed in other areas)

Geometry and measures 15% (28%) 20% (28%)

Probability and statistics 15% (20%) 15% (20%)


Figures in brackets show approximate weightings for the current qualification

Assessment objectives

• AO1 – Use and apply standard techniques

• AO2 – Reason, interpret and communicate mathematically

• AO3 – Solve problems within mathematics in other contexts


Formulae

• Restrictions on which formulae can be given (see specification appendix and formulae poster for details)

• AQA have decided that formulae that can be given will be given in the question and not in a separate formulae sheetand not in a separate formulae sheet.


Content changes


Content changes

• Five types

• Modified (eg up to 12 times table)

• Added to foundation tier (eg standard form)

• New to foundation and higher tiers (eg frequency trees)• New to foundation and higher tiers (eg frequency trees)

• New to higher tier only (eg area under a curve)

• Gone (eg stem and leaf)


Modified content

Some content

•is more explicitly stated but may have been implied previously•is more explicitly stated, but may have been implied previously

•results from more assumed knowledge from earlier key stages

For example:

•Key stage 2 requires knowledge up to 12 times table

•unique factorisation theorem•unique factorisation theorem

•limits of accuracy

•accelerationacceleration

•sequences of triangular, square and cube numbers

•ideas of randomness•ideas of randomness

•outliers

•expansion of more than two binomialsexpansion of more than two binomials


Content added to foundation tier - 1

Some content •was previously on higher tier only•is new content

For example•calculations and answers in terms of π

• solving quadratic equations by factorising

•standard form•inequality notation in error intervals•surds

• equations of parallel lines• simultaneous equations• density•surds

•reciprocal graphs•expanding and factorising quadratic

• density

• direct and inverse proportion (including graphical and algebraic

expressions representations)• similar shapes (including trig ratios)


Content added to foundation tier - 2

• trigonometry• congruence (SSS, SAS, ASA, RHS)• enlargement with fractional scale• enlargement with fractional scale

factors• surface area and volume of

spheres pyramids cones andspheres, pyramids, cones and composite solids

• arc length• area of a sector


Content new to foundation and higher tiers

Some content is completely new to both tiers.

For example:

•systematic listing strategies

•Fibonacci type sequences

•quadratic sequences

•simple geometrical progressions

•pressure

•functions

•frequency treesfrequency trees

•Venn diagrams


Content new to higher tier only

Some content is completely new but on higher tier only.Some content is completely new but on higher tier only.

For example:

•inverse functions •other sequences•inverse functions

•composite functions

other sequences

•nth term of a quadratic sequence

t f h•graph of y = tan x

•velocity-time graphs

•rates of change

•iterative processes

•areas under graphs

•equation of a circle / tangent

•Invariance

•Equation of perpendicular line

•quadratic inequalities


Content not in the specification

Some content is no longer included in the specification.

For example:

t d l f di•stem and leaf diagrams•questionnaires and surveys•‘chance’ words•imperial to metric conversion factors•imperial to metric conversion factors•Trial and Improvement •reference to the Data Handling Cycle

•named sampling methods•Transformations y = af(x) and y = f(ax)•3D Coordinates


GCSE Assessment Objectives by element


Assessment Objective 1

Use and apply standard techniquesUse and apply standard techniques

Students should be able to:

•accurately recall facts, terminology and definitions

•use and interpret notation correctly•use and interpret notation correctly

•accurately carry out routine procedures or set tasks requiring multi-step solutionssolutions

Weighting: F 50% H 40%g g



Reason interpret and communicate mathematicallyReason, interpret and communicate mathematically

Students should be able to:•make deductions and inferences and draw conclusions from•make deductions and inferences and draw conclusions from mathematical information•construct chains of reasoning to achieve a given result•interpret and communicate information accurately•interpret and communicate information accurately•present arguments and proofs•assess the validity of an argument and critically evaluate a given way of processing informationprocessing information

Weighting: F 25% H 30%



Solve problems within mathematics in other contextsSolve problems within mathematics in other contexts

Students should be able to:t l t bl i th ti l th ti l t t i t•translate problems in mathematical or non-mathematical contexts into a

process or a series of mathematical processes•make and use connections between different parts of mathematics •interpret results in the context of the given problem•interpret results in the context of the given problem•evaluate methods used and results obtained•evaluate solutions to identify how they may have been affected by assumptions madeassumptions made

Weighting: F 25% H 30%


Key features of a revision year

Th S h f W k h t h k f t d ✦ The Scheme of Work has to have some key features and be presented in a different way. What didn’t work before will not work again! It has to look differentbefore will not work again! It has to look different.

✦ Recall

✦ Routine

✦ Revise

✦ Repeat

R d ✦ Ready

Recall and Routine

✦ Recall✦ a fast ‘n furious starter✦ name the 1st 20 prime numbers✦ draw the parts of a circle

k t h & ll th d il t l✦ sketch & name all the quadrilaterals✦ based on MA 48 Killer Facts for a C grade

R ti✦ Routine✦ practice, practice, practice

Corbett maths 5 a day✦ Corbett maths 5-a-day✦ Just Maths Bread & Butter✦ 30 second challenges✦ 30 second challenges✦ m4ths.com challenges

Revise and Repeat

✦Revise✦Revise✦key C/D borderline topics✦Hegarty Maths & Corbett Maths videos✦Hegarty Maths & Corbett Maths videos✦Just Maths Top 40✦m4ths com Help Sheet✦m4ths.com Help Sheet✦Resourceaholic

✦Repeat✦prethomework weebly com✦prethomework.weebly.com✦Corbett maths practice questions✦Topic questions✦Topic questions✦Studymaths.co.uk

Ready?

✦Passport

✦Help Sheet

S b ll✦Symballoo

✦Mathematical Association Postcards

✦Past Papers

✦Milestones

Top Tips, Key Resources & Revision

✦NCETM PD Module✦NCETM PD Module✦Do not presume students know how to revise✦Never assume they know the simple stuff✦Never assume they know the simple stuff

✦Teach them

✦How do you revise?

✦What do you revise?y

✦Where do you revise?

✦Wh d h d i ith?✦Why and who do you revise with?

✦When do you revise?

✦Answers on the tablecloth please

Top Tips

✦Fake results...

✦Double mark...once with grade gained, once giving back g g g gall the stupid errors...

✦Concentrate upon the language✦Concentrate upon the language

✦Problem Solving Framework

✦Homework

✦Mathematical Association Postcards✦Mathematical Association Postcards

✦QR reader for Starters

✦Twitter, Moodle & Edmodo

✦Whole Organisational Approach

Practice Papers Sample Assessment Material &Practice Papers, Sample Assessment Material & Milestones

✦ Used to past papers

✦ All about that C grade this year

✦ Diagnostic Questions

✦ Six Milestones

✦ Clever Marking✦ Clever Marking

Identifying next steps...

What observations do you have?y

What three things will you do as a result of theWhat three things will you do as a result of the

days training?days training?

effective classroom approaches to gcse maths · pdf fileth d ’t f l t d b t thithey...

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