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MEI Conference 2016 Preparing to teach forces Sue de Pomerai [email protected]

MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

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Page 1: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

MEI Conference 2016

Preparing to teach forces

Sue de Pomerai [email protected]

Page 2: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS level Further Mathematics

Page 3: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

A level Further Mathematics

Page 4: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Sample assessment materials

MEI AS level

Page 5: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

MEI A level

Page 6: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AQA AS level

Page 7: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AQA A level

Page 8: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Edexcel AS level

Page 9: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Edexcel A level

Page 10: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

OCR AS level

Page 11: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

OCR A level

Page 12: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level
Page 13: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Get set for September 2017

Further Mathematics

Page 14: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Session description

• In this session we will explore the main features of the new

Further Mathematics AS and A levels and discuss the

implications for teaching and learning

• This session is one of a series of 4 which are designed to

inform teachers of upcoming changes to A level. It is

therefore suitable to any teachers of A level and may be of

particular interest to heads of department or KS5

coordinators. The resources accompanying this conference

session will be suitable for using with departmental

colleagues in order to help teams prepare for the changes.

Page 15: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Structure of

FM

Page 16: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Further Mathematics

• 50% content specified, all pure

• Awarding bodies can decide on

the other 50% so they may (or

may not) be significant

differences

• There may be some element of

choice retained in FM

• All exam boards should be

producing at least one

specification that can run

alongside Mathematics

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

Page 17: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS FM

• This is designed to be a

separate, valuable

qualification

• It must be able to be co-

taught with the full A

level in Further

Mathematics

• AS Further Mathematics

must be at least 30%

Pure Mathematics

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

Specifically

prescribed

content

Optional

prescribed

content

A level FM

AS FM

Page 18: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS FM • The 30% Pure Mathematics

content of AS Further Maths

has to be constructed from

some compulsory content:

– Matrices

– Complex Numbers

• together with some

additional Pure Maths

content chosen from the

compulsory content for A

Level Further Maths

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

Specifically

prescribed

content

Optional

prescribed

content

A level FM

AS FM

Page 19: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Compulsory AS FM Complex

Numbers

Solve any quadratic, cubic or quartic equations with

real coefficients

Add, subtract, multiply and divide complex numbers

Complex conjugate; know that non-real roots of

polynomial equations with real coefficients occur in

conjugate pairs

Argand diagram

Evaluate the modulus and argument

Modulus-argument form (use of radians)

Multiply and divide complex numbers in modulus-

argument form

Simple loci

Page 20: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Compulsory AS FM Matrices Add, subtract, multiply, multiply by a scalar

Zero, identity

Linear transformations 2D, successive transformations

Simple linear transformations in 3D

Invariant points and lines

Determinant of a 2 2 matrix

Add, subtract, multiply, multiply by a scalar

Zero, identity

Linear transformations 2D, successive transformations

Simple linear transformations in 3D

Invariant points and lines

Determinant and inverse of a 2 2 matrix

Page 21: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Content and

structure of the

AS FP

examinations

Page 22: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS Further Mathematics AQA

Paper

Length

(mins)

Raw

Marks

AS Further Maths 1 90 80

AS Further Maths 2 90 80

TOTAL 180 160

• Paper 1: Pure

• Paper 2: Applied – enter for two of Discrete, Mechanics,

Statistics

Page 23: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Optional prescribed pure content for AS level

AQA

Vectors Vector and Cartesian forms of equation of a

line

Scalar product

Angle between two lines

Distance between two lines

Distance of point from a line

Vector product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Method of differences

Hyperbolic functions Hyperbolic and inverse hyperbolic functions

Logarithmic form

calculus Volumes of revolution

Mean value function

Page 24: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Optional prescribed content for AS level

AQA

Polar coordinates Polar and Cartesian coordinates

Curve sketching

Area enclosed by a polar curve

Algebra, Graphs and inequalities Inequalities involving polynomials

Modulus functions and their graphs

Conics Simple loci

Page 25: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS Further Mathematics

Edexcel

Paper

Length

(mins)

Raw

Marks

AS Further Maths 1 90 75

AS Further Maths option 90 75

TOTAL 180 150

• Paper 1: Pure compulsory

• Paper 2: Option – enter for one of Decision, Mechanics,

Statistics, Further Pure

Page 26: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Optional prescribed pure content for AS level

Edexcel

Complex Numbers Solving simultaneous linear equations

using matrices

Vectors Vector and Cartesian forms of equation

of a line and a plane

Scalar product

Angle between two lines

Distance between two lines

Distance of point from a line

Vector product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Proof by induction

calculus Volumes of revolution

Page 27: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS Further Mathematics MEI

Paper

Length

(mins)

Raw

Marks

AS Further Maths compulsory 75 60

AS Further Maths option 1 75 60

AS Further Maths option 2 75 60

TOTAL 225 180

• Paper 1: Pure compulsory

• Options – enter for two of Mechanics a, Statistics a,

Modelling with algorithms, Numerical methods,

Mechanics b, Statistics b

Page 28: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Optional prescribed pure content for AS level

MEI

Complex Numbers Solving simultaneous linear equations using

matrices

Vectors Vector and Cartesian forms of equation of a

line and a plane

Scalar product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Method of differences

Proof by induction

Page 29: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

AS Further Mathematics OCR

Paper

Length

(mins)

Raw

Marks

AS Further Maths compulsory 70 60

AS Further Maths option 1 70 60

AS Further Maths option 2 70 60

TOTAL 210 180

• Paper 1: Pure compulsory

• Options – enter for two of Mechanics, Statistics,

Discrete, Additional Pure

Page 30: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Optional prescribed pure content for AS level

OCR

Matrices Determinant and inverse of a 3X3 matrix

Solving simultaneous linear equations using

matrices

Vectors Vector and Cartesian forms of equation of a

line

Scalar product

Angle between two lines

Vector product

Algebra, sequences and proof Roots of polynomials

Proof by induction

Page 31: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Structure of the

Further Maths

A levels

Page 32: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

A level Further Mathematics

AQA

Paper Length (mins) Raw Marks

Further Maths 1 120 100

Further Maths 2 120 100

Options 120 100

TOTAL 360 300

• Paper 1: Pure (compulsory)

• Paper 2: Pure (compulsory)

• Applied options– enter for two of Discrete, Mechanics,

Statistics

Page 33: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

A level Further Mathematics

Edexcel Paper Length (mins) Raw Marks

Further Maths 1 90 75

Further Maths 2 90 75

Option 1 90 75

Option 2 90 75

TOTAL 360 300

• Paper 1: Pure (compulsory)

• Paper 2: Pure (compulsory)

• Options – enter for two of Further Pure 3, Further Pure 4,

Mechanics 1, Mechanics 2, Statistics 1, Statistics 2,

Decision 1, Decision 2

Page 34: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

A level Further Mathematics MEI Paper Length (mins) Raw Marks

Compulsory Pure 160 144 (scales to 180)

Major 135 120

Minor 75* 60

TOTAL varies 360

* 105 minutes for Further Pure with Technology

• Choose EITHER major + minor OR three minors

• Major: Mechanics or Statistics

• Minor: Mechanics, Statistics, Modelling with algorithms,

Numerical methods, Extra pure, Further pure with

technology

Page 35: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

A level Further Mathematics

OCR Paper Length (mins) Raw Marks

Further Maths 1 90 75

Further Maths 2 90 75

Option 1 90 75

Option 2 90 75

TOTAL 360 300

• Paper 1: Pure (compulsory)

• Paper 2: Pure (compulsory)

• Options – enter for two of Statistics, Mechanics, Discrete

Mathematics, Additional Pure Mathematics

Page 36: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Deciding on a

specification

Page 37: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Looking at SAMs

• In your handout there are some AS and A level

questions on matrices from each awarding body

together with the mark schemes

• Look at the questions and discuss

– In what ways are they similar to current

papers?

– In what way are they different?

– Do the marks allocated reflect the degree of

difficulty in your view?

Page 38: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Points to consider

• There is no longer any advantage in choosing

the same awarding body for both Maths and

Further Maths

Consider choosing the awarding body which

looks:

• the best match for your department’s skills

• the most useful for your students’ likely career

path

• like it offers the best support

• the most fun to teach

… rather than the easiest or most familiar

Page 39: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Discussion Points

• What are the implications for planning and

staffing?

• Will you enter all students for AS at the end of

year 12? Is there a whole school policy?

• Will you offer AS Further Maths as a stand alone

qualification (possibly over 2 years)?

• What obsticles do you face?

Page 40: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Choosing a specification

On the FMSP

website there

is a Guide to

choosing a

new

specification

Page 41: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Further support

• Dedicated MEI website for the 2017 developments

mei.org.uk/2017

• MEI provides expert advice on the latest developments,

and supports you and your department as the changes

approach

• Support for all specifications is given

Page 42: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Further support - PD

‘Get Set for 2017’ courses:

mei.org.uk/2017-pd

A series of 4 one-day courses in an area near you coming

during the 2016-17

- Principles of the new mathematics A levels

- Statistics

- Mechanics

- Effective use of technology

Page 43: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Further support - PD Sustained PD courses for teachers looking to develop subject

knowledge & pedagogy for AS/A level Maths or Further Maths.

Teaching Advanced Maths (TAM) course mei.org.uk/tam

Teaching Further Mathematics (TFM) course mei.org.uk/tfm

TAM and TFM cover the pure mathematics content of A level

Maths and Further Maths respectively. For Mechanics and

Statistics PD we run the following:

Teaching Mechanics (TM) furthermaths.org.uk/teaching-mechanics

Teaching Statistics (TS) furthermaths.org.uk/teaching-statistics

Page 44: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

Further support - FMSP

• Dedicated FMSP website for the 2017 developments

furthermaths.org.uk/2017

• A wealth of advice, guidance and support form the FMSP

team on the latest developments as the changes approach

• Support for all specifications is given

Page 45: MEI Conference 2016 Preparing to teach forces Sue de Pomerai · MEI Conference 2016 Preparing to teach forces Sue de Pomerai Sue ... Edexcel A level . OCR AS level . OCR A level

About MEI

• Registered charity committed to improving

mathematics education

• Independent UK curriculum development body

• We offer continuing professional development

courses, provide specialist tuition for students

and work with industry to enhance mathematical

skills in the workplace

• We also pioneer the development of innovative

teaching and learning resources